CASSINI RADIO SCIENCE
A. J. KLIORE1,∗ , J. D. ANDERSON1 , J. W. ARMSTRONG1 , S. W. ASMAR1 ,
C. L. HAMILTON1 , N. J. RAPPAPORT1 , H. D. WAHLQUIST1 , R. AMBROSINI2 ,
F. M. FLASAR3 , R. G. FRENCH4 , L. IESS5 , E. A. MAROUF6 and A. F. NAGY7
1 Jet
Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA 91109, USA
2 Istituto di Radioastronomia CNR, Via Gobetti 101, I-40129, Bologna, Italy
3 NASA-Goddard Space Flight Center, Greenbelt, MD 20771, USA
4 Wellesley College, Wellesley, MA 02481, USA
5 Università di Roma ‘La Sapienza’, Via Eudossiana 18, I-00184 Roma, Italy
6 San Jose State University, One Washington Square, San Jose, CA 95192, USA
7 University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, USA
(∗ author for correspondence, e-mail: akliore@jpl.nasa.gov)
(Received 29 December 1999; Accepted in final form 4 April 2002)
Abstract. Cassini radio science investigations will be conducted both during the cruise (gravitational
wave and conjunction experiments) and the Saturnian tour of the mission (atmospheric and ionospheric
occultations, ring occultations, determinations of masses and gravity fields). New technologies in the
construction of the instrument, which consists of a portion on-board the spacecraft and another portion
on the ground, including the use of the Ka-band signal in addition to that of the S- and X-bands, open
opportunities for important discoveries in each of the above scientific areas, due to increased accuracy,
resolution, sensitivity, and dynamic range.
Keywords: atmospheres, Cassini, gravitational fields, gravitational waves, general relativity, ionospheres, occultations, planetary rings, radio science, Saturn, Titan
1. Introduction
This paper, produced by the Cassini Radio Science Team during the early cruise of
the Cassini spacecraft en route for the Saturnian system, records major reference
information concerning the investigations to be conducted, and the instrument that
will be operated to conduct these investigations. Section 2 describes the radio
science investigations. Section 3 is devoted to the radio science instrument. Section 4
contains a brief conclusion.
2. Radio Science Investigations
For each of the radio science investigations:
– Gravitational wave experiments,
– Conjunction experiments (a new test of general relativity, study of the solar
corona),
Space Science Reviews 115: 1–70, 2004.
C 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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A. J. KLIORE ET AL.
– Gravitational field measurements and celestial mechanics experiments (pertaining to Saturn, Titan, and the Icy Satellites),
– Ring occultation experiments,
– Atmospheric and ionospheric occultation experiments (pertaining to Saturn,
Titan, and the icy satellites),
we describe the scientific objectives with respect to the present state of knowledge,
the techniques, and the major requirements.
2.1. G RAVITATIONAL WAVE E XPERIMENTS
2.1.1. Scientific Objectives
This section of the paper outlines the method and experimental setup of the Cassini
Gravitational Wave Experiment (GWE).
The extensive and stringent tests of gravitation theories carried out in the solar
system, together with observations of binary pulsars, have dispelled most doubts
about Einstein’s theory of general relativity and the existence of the gravitational
waves it predicts. The direct detection of gravitational waves constitutes an outstanding challenge for experimental physics, however, and – when successful –
will open up a new window for observational astronomy (Thorne, 1987). Since
gravitational waves are virtually unaffected by intervening matter, their observation will probe the dynamics of cataclysmic events in the deep interiors of, for
example, supernovae and active galactic nuclei, regions which are inaccessible to
electromagnetic observations.
There are three main frequency bands of astronomical interest:
– The “high” frequency band, around 1 kHz, where the sources include supernovae
and stellar coalescences;
– The “low” frequency band, around 1 mHz, where the sources include compact
binary systems such as a binary pulsar, the formation of super-massive black
holes, and the coalescence of supermassive binary black holes;
– The “very low” frequency band, <1 µHz, where one might expect a stochastic background of waves from the superposition of stellar binaries, distant past
collapse events, and possibly the red-shifted remnant of a primordial cosmic
background created by density fluctuations in the Big Bang. (See Armstrong
et al., 2003 for results from Cassini’s GWE).
The variety of possible sources in the low-frequency band accessible to spacecraft Doppler tracking necessitates using a variety of signal detection techniques.
This is especially true because it is a search conducted largely “in the dark”; while
astronomical observations and theory almost guarantee the existence of gravitational waves, it is still beyond our capability to predict the shape, or even the likely
strength, of waves from these sources. So the best one can do is to do a systematic search for a variety of plausible waveforms (wide-band pulses, periodic and
quasi-periodic waveforms, stochastic backgrounds).
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For detection purposes, an ideal source would be the binary pulsar 1913 + 16.
Binary pulsars are objects for which clear evidence of gravitational radiation already exists and everything one needs to know about the system is available to
predict precisely the observed signal (Wahlquist, 1987). The wave frequency of
the strongest harmonic of the periodic signal from 1913 + 16 falls exactly where
the Doppler method is most sensitive. Unfortunately, the predicted amplitude of
the signal from 1913 + 16 is too weak to detect at Cassini’s sensitivity by many
orders of magnitude.
In addition to being of great intrinsic astrophysical interest, supermassive binary
black hole systems may be the most promising sources for detection with Cassini.
Clean binary systems, not too close to coalescence, are sufficiently simple that
detailed comparison of theory and observation is possible. Of course, since the
parameters of the system are not known in advance, it is necessary to employ a large
ensemble of signal templates to search for waves from one of these systems. Near
coalescence, the amplitude and frequency of the wave increase with time; special
methods to extract these “chirp” signals from both random and systematic noises
have been developed (Tinto and Armstrong, 1991; Anderson et al., 1993; Bertotti
et al., 1994; Bertotti, 1997; Iess and Armstrong, 1997; Bertotti et al., 1999). Very
close to coalescence, physical processes become more complicated and templates
may at best be a rough approximation to the emitted waveforms.
The existence of binary sources has become increasingly plausible with the recent observations of supermassive objects in galactic nuclei, together with evidence
for the frequent merging of galaxies in the early universe when their spatial density
was much higher than at present. Cassini should be able to detect signals of this
type, if they are present in the Doppler frequency band with the expected strength,
well beyond the Virgo cluster (≈17 Mpc), thus including thousands of candidate
galaxies.
The gravitational wave search on the Cassini mission has been the most sensitive Doppler experiment ever performed. The experiment has been repeated three
times during the cruise period from Jupiter to Saturn; i.e., when the spacecraft
was the antisolar direction from earth (November 2001–January 2002; December
2002–January 2003; December 2003–January 2004). At each opposition, Cassini
has been Doppler-tracked as continuously as possible for 40 days. Around-theclock tracking required using all three deep space network (DSN) complexes
(Goldstone, Madrid, Canberra), and may be supported additionally by non-DSN
radio antennas in Italy. The highest sensitivity was achieved with DSS-25, a
beam waveguide antenna located at the Goldstone complex, which has been
carefully designed for the utmost in frequency stability and which has Ka-band
uplink, precision frequency standards, and advanced tropospheric correction
equipment.
Cassini at opposition became one of the largest gravitational wave antenna’s
ever used (≈8 AU in length), attaining by far the highest sensitivity to date for
gravitational waves at the lower end of the low-frequency band.
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A. J. KLIORE ET AL.
2.1.2. Techniques
Detection methods for gravitational radiation depend on the time scale of the radiation. At high frequencies the main techniques are resonant bars and laser interferometers. These techniques achieve excellent sensitivity in the Fourier frequency
band where they operate. For frequencies lower than about 10 Hz, however, it becomes prohibitively difficult to isolate these detectors from seismic noise, other
acoustic noise in the environment, and from uctuating gravity gradients. For observations of sources radiating in the low frequency band (approximately 0.0001 Hz,
or lower, to 0.01 Hz), the detector must be spaceborne. Although at the moment the
low-frequency band is explored by means of Doppler tracking, the next generation
of space-based detectors will soon become a reality with the launch of the USA
mission, jointly funded by NASA and ESA (Bender et al., 1998). For very-low frequencies (below about 10−6 Hz) pulsar timing can be used to search for stochastic
gravitational waves.
In the spacecraft technique, the earth and a distant spacecraft act as separated test
masses. The Doppler tracking system measures the relative dimensionless velocity
of the earth with respect to the spacecraft
2
v
ν
=
=y
c
ν0
(1)
as a function of time; ν is the perturbation of the Doppler frequency from ν0 ,
the nominal radio frequency. A gravitational wave of amplitude h incident on the
system causes small perturbations in the tracking record. These perturbations are
of order h in y and are replicated three times in the Doppler data (Estabrook and
Wahlquist, 1975). That is, the gravitational wave signal in the observed Doppler
time series is the convolution of the waveform
s(t) = (1 − µ2 )−1 n · [h + (t)e+ + h × (t)e× ] · n
with the three-pulse response function
µ−1
L
1+µ
L
r (t) =
δ(t) − µδ t − (1 + µ)
+
δ t −2
2
c
2
c
(2)
(3)
Here µ is the cosine of the angle between the earth–spacecraft vector and
the gravity wavevector, L is the earth–spacecraft distance, n is the unit vector
from the earth to the spacecraft, h + (t) and h × (t) are the gravity waveforms for
each polarization and e+ and e× are transverse, traceless polarization tensors (Estabrook and Wahlquist, 1975; Wahlquist et al., 1977; Wahlquist, 1987). The sum of
the three pulses is zero; hence burst waves having a duration longer than about
L/c overlap in the tracking record and the net response cancels to first order.
The tracking system thus has a passband where it has maximum sensitivity: below about c/L, by pulse cancellation, the response is proportional to f; thermal
CASSINI RADIO SCIENCE
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noise in the radio system and the short-term stability of the frequency standard
to which the Doppler system is referenced limits the high-frequency response to
f ≈ 0.1 Hz.
2.1.3. Major Requirements
The anticipated signal amplitudes depend on the source generating the wave and the
earth–source distance, but are in any case expected to be small. Since the resulting
perturbations in the Doppler record are also expected to be small, careful attention
to noise and systematics is required.
Non-signal fluctuations in the Doppler time series are caused by charged particle scintillation, tropospheric scintillation, antenna mechanical noise, clock noise,
spacecraft unmodeled motion, ground electronic noise, thermal noise in the radio
link, spacecraft electronics noise, and systematic errors. The extent to which these
noises affect the ultimate sensitivity, depends on the gravity waveform because
the noises enter the observable with different transfer functions (e.g., Wahlquist
et al., 1977; Estabrook, 1978; Armstrong, 1989; Bertotti et al., 1999). However, it
is clearly important to minimize the absolute level of the noises. (A more complete
discussion of the error budget for precision Doppler tracking, with particular attention to the Cassini gravitational wave experiment, is given in Armstrong (1998),
Tinto and Armstrong (1998) and Asmar et al. (2004)).
Obviously any unmodeled motion of the spacecraft itself enters directly in the
Doppler record. Thus the Cassini gravitational wave experiment requires that activity on the spacecraft causing unmodeled motions be minimized during gravitational
wave observations.
Propagation noise (“scintillation”) arises from irregularities in the refractive index along the radio path. These fluctuations randomly advance and retard the phase
of the wave and thus cause frequency fluctuations. Charged particle scintillation,
which is dominated by solar wind scintillation, can be minimized by observing at
large sun-earth-spacecraft angles and by observing at high-radio frequency. The
Cassini gravitational wave experiment thus requires that observations be made in
the antisolar direction. The Cassini gravitational wave experiment has been the first
scientific user of Ka-band (≈32 GHz) up and downlinks. This has dramatically
reduced the contribution of charged particle scintillation relative to previous experiment. Scintillation in the neutral atmosphere is an important noise source. Cassini
gravitational wave experiments requires water-vapor radiometers colocated with
DSS-25 (the DSN Ka-band uplink station) to estimate and remove the tropospheric
scintillation to acceptable levels.
Clock noise is fluctuation in the frequency standard that drives the Doppler system. This noise is fundamental and must be minimized for a successful experiment.
Cassini-era frequency standards have been engineered for excellent stability in the
Fourier band of interest to the gravitational wave experiment and are expected to
enter the observable at a noise level less than or comparable to the other principal
noise sources.
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A. J. KLIORE ET AL.
Antenna mechanical noise is physical motion of the antenna and feed system as
the ground antenna moves to track the spacecraft, deforms under gravity, distorts
due to wind, etc. This noise source has been negligible in previous gravitational
wave experiments, but has been detected at the excellent sensitivity of the Cassini
Ka-band system.
2.2. CONJUNCTION E XPERIMENTS
Radio science experiments near solar conjunctions have been exploited for tests
of general relativity and probing of the solar corona. The unique radio system
of Cassini allows singling out plasma effects on carrier phase and is therefore
expecially suited for Doppler measurements near the sun. The 2002 Cassini solar
conjunction experiment has yielded the most accurate test of general relativity so
far.
2.2.1. A New Test of General Relativity
2.2.1.1. Scientific Objectives. The gravitational deflection of light rays, a crucial test of the theory of general relativity, has been performed so far with two
methods:
– by measuring the differential deflection of the apparent position of stars or radio
sources near the Sun;
– by measuring the change in the light transit time from a spacecraft near solar
conjunction.
Within the parametrized post-Newtonian (PPN) (Will, 1993) approximation in
its minimal form, in which the metric depends on two dimensionless parameters
γ and β, these effects are controlled by γ . Before the Cassini experiment this
parameter was constrained to be within 10−3 of unity, the general relativistic value.
Several experiments have been done in the past, all more or less with similar
results, and it was apparent that new ideas and instrumentation were needed to
obtain a major increase in accuracy. It is remarkable that the test performed more
than 20 years ago by measuring the two-way travel time of radio signals from
the earth to the Viking landers (Reasenberg et al., 1979; Borderies et al., 1980)
has been marginally improved only very recently (Eubanks et al., 1997), using
more accurate VLBI (very-long-baseline interferometry) techniques for precision
deflection measurements.
In the past, these experiments have played an essential role in the rejection of
several alternative theories of gravity and in strengthening our confidence in the
theory of general relativity. The main candidate for an alternative theory within this
constraint is a scalar field coupled to the metric, which is the most obvious way to
produce an inflationary cosmology; as the Universe starts its decelerated expansion
phase, this field becomes progressively weaker, but its remnant, still present today,
determines a small correction to the parameters γ and β. In the absence of a
CASSINI RADIO SCIENCE
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reliable theory of inflation, it is difficult to assess the order of magnitude of these
corrections; however, values from 10−7 to 10−5 have been considered (Damour and
Nordtvedt, 1993). It is therefore most important to devise new methods to improve
the measurement of γ .
The new technological developments required by the Cassini mission, in particular, the use of Ka-band radio links have allowed us to test general relativity
to a substantially greater accuracy. The outstanding radio system of the spacecraft
and ground station allows a nearly complete calibration of the plasma noise and
an unprecedented stability of the interplanetary link. A crude estimation of the expected accuracies (Iess et al., 1999) indicated that γ could be measured to levels of
about 10−5 , almost two orders of magnitude better than the previous experimental
accuracy. The analysis of the data aquired between June 6 and July 5, 2002 fully
confirmed the expectations: the experimental value for γ was found to be 1 + (2.1
± 2.3) 10(–5) (Bertotti et al., 2003).
2.2.1.2. Techniques. The measurement of γ with Cassini is based upon a third,
new observable: the frequency shift induced on a radio wave when the spacecraft
is near solar conjunction (Bertotti and Giampieri, 1992; Iess et al., 1999). Solar
gravity has an effect on the frequencies of photons, since the relative frequency
shift y = ν/ν due to the solar metric is just a time derivative of the delay of radio
signals measured in space experiments:
d
y = τ,
(4)
dt
where
r1 + r2 + r12
,
(5)
τ = (1 + γ )M ln
r1 + r2 − r12
expressed in terms of the geometrical units in which G = c = 1 and M = 5 µs, has
the well-known dependence on the sun–earth, sun–spacecraft and earth–spacecraft
distances r1 , r2 and r12 . For a two-way link, as in the case of Cassini, y is actually
the sum of two contributions, respectively from the uplink and the downlink. Near
conjunctions, Equation (5) can be approximated using the impact parameter b of
the beam:
4r1r2
τ ≈ 2(1 + γ )M ln 2 .
(6)
b
The corresponding value of y is therefore
M
y ≈ 4(1 + γ )
ḃ.
(7)
b
In the case of Cassini, with a nearly grazing conjunction, y ≈ 10−9 , five orders
of magnitude larger than the expected stability of the radio link at time scales of 104
s (σ y = 3 × 10−15 ). This rough comparison indicated that the Cassini experiment
could lead to a test of general relativity with unprecendented accuracy.
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Another instructive way of looking at this experiment is to consider the effect on
the frequencies as a consequence of the solar gravitational deflection. For a beam
with impact parameter b, the deflection angle
δ = 2(1 + γ )
M
b
(8)
changes in time, therefore producing a variation in the direction of arrival n of
photons. Since the observable quantity is essentially the radial velocity v · n of
the spacecraft with respect to the earth, a deflection by an angle δ changes n and
therefore produces an additional velocity along the line of sight of order vδ. Again,
for a grazing incidence, this amounts to approximately 10−9 .
The relativistic Doppler signal evolves over time scales of order b/(orbital velocity) ≈105 s. Thus, a Doppler experiment requires short observation periods to
minimize the effects of non-gravitational accelerations. On the other hand, large
Doppler signals are obtained only at small impact parameters, when the radio beam,
well inside the solar corona, undergoes strong frequency fluctuations. Until the recent implementation of multi–frequency radio links at X- and Ka-bands, which
allows a full plasma calibration, Doppler experiments could not compete with the
more familiar tests based on range measurements.
The main hindrance to precise measurements near conjunctions is indeed the
solar corona, whose large and changing electron density induces severe propagation
effects. In the past, spacecraft tracking near solar conjunction using S- and X-band
radio links has provided important information about the coronal plasma. Since the
coronal contribution to the fractional frequency change y is inversely proportional
to the square of the carrier frequency ν, the noise due to the corona is particularly
large at the lower frequencies, such as S-band. With Cassini, besides the standard
communication link in X-band (7.1–8.4 GHz), an additional link in Ka-band (32–
34 GHz) was available, with two neighbouring downlink carriers driven by the
Ka-band uplink and the X-band uplink, respectively. This configuration, with multi–
frequency transmission from the ground and the spacecraft, will allow for the first
time a complete plasma calibration both in the uplink and the downlink (Bertotti
et al., 1993). Moreover, the use of higher frequency carriers makes the link nearly
immune to frequency jitter and cycle slips. The experimental results showed an
excellent phase stability (about 2 × 10−14 or smaller), a value generally obtained
close to solar opposition (Tortora et al., 2003; Tortora et al., 2004).
2.2.1.3. Major Requirements. The experiment was planned during two useful
conjunctions in the cruise phase, in June 2002 and June 2003, at times when there
was very little activity on the spacecraft. Unfortunately, due to a malfunction of
the key onboard instrument (the Ka/Ka frequency translator, see sect. 3.2), only the
data collected in 2002 have been used. The very small inclination of the Cassini
orbit makes the geometry of the experiment particularly favorable, with a minimum
impact parameters of 1.6 R . The main tracking station was DSS-25, the only DSN
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station capable of supporting a full multi–frequency link (with uplink both at Xand Ka-band).
Measuring γ to levels of 10−5 requires a very stable radio link, with an accurate
calibration for the effects of the media (solar corona and troposphere). The instrumental specifications set by the gravitational wave experiments are adequate, but
now the complete multifrequency link becomes essential.
While the two experiments share a good degree of commonality (after all, they
are based upon the same observable), the different time scales of the signal introduce
new and subtle problems in the analysis of conjunction data. As the relativistic effect
evolves overtime scales of, say, 105 s (i.e., longer than the period of gravitational
waves considered so far) the orbital contribution to the Doppler shift needs to be
determined with great accuracy. Polar motion, earth solid tides and errors in the
station locations give important effects to be accounted for. Other contributions
come from non-gravitational accelerations, which are a potentially large source of
errors in an experiment based on a free flying spacecraft. Fortunately, the large
distance from the sun and the nearly constant solar aspect angle make these errors
quite small or easily accounted for in the data analysis.
2.2.2. Study of the Solar Corona
Tracking interplanetary spacecraft near solar conjunction has provided a wealth of
information on the structure of the solar corona and the origin of the solar wind. This
powerful tool, in combination with SOHO’s ultraviolet coronograph spectrometer,
has been used recently to locate the sources of the slow wind, which stems from
the stalks, narrow structures of the sun’s streamer belt (Woo and Habbal, 1997).
The same measurements seem to indicate also that the conventional understanding
of the nature of the fast wind needs to be modified. It is likely that in the next years
new measurements and observations will be required to confirm the new, emerging
views on the solar wind.
The outstanding radio system of Cassini provides a unique opportunity for solar
physics as well, without any additional allocation of resources from the spacecraft
and the DSN. The effects of the solar plasma on Doppler signals are known with
great precision separately for the uplink and the down-link paths, thanks to the
multifrequency radio link (Bertotti and Giampieri, 1998). Moreover, the use of
higher frequency carriers will strongly reduce the difficulties and the instrumental
problems encountered when tracking near the sun.
2.3. G RAVITATIONAL FIELD MEASUREMENTS
AND
CELESTIAL
MECHANICS EXPERIMENTS
2.3.1. Scientific Objectives
2.3.1.1. Introduction. Over the past 35 years, radio Doppler data generated
with interplanetary spacecraft have yielded masses and densities for all the planets, except Pluto, as well as masses for all the larger satellites, and higher-order
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A. J. KLIORE ET AL.
gravitational moments are available for the planets and for Jupiter’s Galilean satellites (Anderson et al., 1996a,b, 1997a,b). With the addition of Doppler data from
the Cassini mission we expect to improve the description of Saturn’s gravitational
field, as well as to map Titan’s second-order field in detail.
If a planet or satellite were perfectly spherical, its total mass would be sufficient
to describe its external gravitational field. However all natural bodies deviate from
spheres at some level, so what is needed is a general potential function that satisfies
Laplace’s equation for an arbitrary distribution of mass. With the origin at the
center of mass and coordinates r for radius, φ for latitude, and λ for longitude,
the standard form for the gravitational potential is written as follows in terms of
spherical harmonics and the Legendre functions Pnm
V (r, φ, λ)
n n
∞
GM
R
=
(Cnm cos mλ + Snm sin mλ)Pnm (sin φ) ,
1+
r
r
n=2 m=0
(9)
where M is the planet or satellite’s mass, the external field is referred to a reference
radius R (usually the planet’s mean equatorial radius, but sometimes the semimajor axis of a reference ellipsoid); G is the gravitational constant. The gravity
coefficients Cnm and Snm are determined from the Doppler data by iterative linear
weighted least squares. A particular coefficient with indices nm is referred to as a
gravity harmonic of order m and degree n. Coefficients with m = 0 are called zonal
harmonics, coefficients with n = m are called sectorial harmonics, and the rest are
called tesseral harmonics. Zonal harmonics divide the surface of the sphere into
m + 1 zones of latitude, sectorial harmonics into sectors of longitude or “orange
slices,” and tesseral harmonics into a checker-board pattern.
The outer planets and their larger satellites are effectively in hydrostatic equilibrium. As a result, measured gravity harmonics provide important boundary conditions on their interior structure. If the giant Jovian planets and their satellites were in
hydrostatic equilibrium and did not rotate, and if they were not subjected to external
forces, their gravitational fields would provide no information on internal structure.
However, because the giant planets rotate rapidly, their shapes and gravity fields
yield information on the distribution of density with depth. The Galilean satellites
and Titan are inuenced by comparable tidal forces from their parent planet, and
so both rotation and tides must be accounted for. For the giant planets, the two
parameters for shape and rotation are the flattening f and the rotation parameter q
defined by,
a−b
,
a
ω2 a 3
,
q=
GM
f =
(10)
(11)
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where a is the planet’s equatorial radius, b its polar radius, ω its rotational angular
velocity, and G is the gravitational constant. Even without gravity measurements, the
ratio f /q would yield some limited information on interior structure because it has a
minimum value of 1/2 for a body with an extreme mass concentration at its center,
and a maximum value of 5/4 for a homogeneous body. For a spinning planet in
hydrostatic equilibrium, we assume that only the even zonal gravity harmonics Jn =
−Cn0 (n = 2, 4, 6, . . .) are non-zero. The importance of the gravity coefficients Jn
is that they are related to the internal density distribution by the following volume
integral over the planet’s interior
1
Jn = −
MR n
v
ρ(r, φ, λ)r n Pn (sin φ)dv
(n = 2, 4, 6 . . .).
(12)
The Jn coefficients represent boundary conditions that must be satisfied for any
viable interior model. The deep interior stimulates the second zonal harmonic J2 ,
while the outer layer is sounded by higher harmonics to a depth of about 3100 km
for Jupiter and 3600 km for Saturn. For example, in a simple polytrope of index one,
a reasonably good first-order approximation for Jupiter and Saturn’s outer layers,
the pressure p and density ρ are related by,
p = Kρ 2 ,
(13)
and the constant K is determined from the measured gravity coefficients J2 and J4
by the expression,
2π Gb2
q 2
K =−
J2 +
.
35J4
3
(14)
For nonpolytropic models, a general density distribution with depth can be derived
from measured gravity coefficients J2 and J4 . The coefficient J6 may also be useful,
although differential rotation and deep atmospheric winds may complicate its interpretation. With a given density distribution, the pressure can be computed under
the assumption of hydrostatic equilibrium, and the temperature follows from the
equation of state for the assumed material in the outer layer.
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A. J. KLIORE ET AL.
2.3.1.2. Objectives for Saturn. The scientific objectives at Saturn are to:
– determine the mass of Saturn and its zonal gravitational harmonics, at least
through degree six;
– constrain models of Saturn’s interior.
The product of the gravitational constant by Saturn’s mass, GM S , has been
determined to considerable accuracy from Pioneer and Voyager flybys (Campbell
and Anderson, 1989). After dividing by G = 6.67259×10−20 km3 s−2 kg−1 (Cohen
and Taylor, 1987), we obtain a total mass MS = (5.68464 ± 0.0003) × 1026 kg. A
fundamental constraint on interior models is that this total mass must be contained
within an equipotential surface defined by Saturn’s mean equatorial radius, RS =
60,268 km (Lindal et al., 1985). The shape of the equipotential surface is defined
by the zonal harmonics, which also serve as additional boundary conditions on
interior models. The current unnormalized values, in units of 10−6 , from Pioneer
and Voyager Doppler data are (Campbell and Anderson, 1989)
J2 = 16332 ± 10,
(15)
J4 = −919 ± 40,
(16)
J6 = 104 ± 50.
(17)
Current interior models based on these values are nonunique (Guillot et al.,
1994), although some fail to satisfy the more rigid observational constraint given
by Campbell and Anderson (1989),
|0.23δ J2 + 2.20δ J4 − 3.13δ J6 | ≤ 1,
(18)
where the δ corrections are with respect to the values of Equations (15)–(17). Because interior models are fundamentally constrained by the gravitational moments,
improvements in accuracy by means of Cassini radio Doppler data may yield a better understanding of Saturn’s interior. The Cassini mission can provide improved
determinations for all three zonal harmonics. Our best estimate of the expected
one-sigma accuracy, again in units of 10−6 , is ±0.1 for J2 , ±0.4 for J4 , and ±1.5
for J6 . In addition, the Cassini mission should improve other important parameters,
most notably the rotational period of Saturn’s magnetic field (10.6549 h) (Davies
et al., 1983), its intrinsic power output (8.63 × 1016 J s−1 ) and internal energy
flux (2.01 J m−2 s−1 ) (Hanel et al., 1983), the temperature of the atmosphere at
the one bar level (134 K) (Lindal et al., 1985), and the mean equatorial radius.
These various boundary conditions must be satisfied by solving the nonlinear differential equations for the interior structure (see for example Guillot et al., 1994).
Post-Cassini models may lead to a better understanding of the energy transport in
Saturn’s interior and consequently to a better understanding of its cooling history
and evolution.
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2.3.1.3. Objectives for Titan. The Radio Science gravitational scientific objectives at Titan are to:
– determine the mass of Titan and its low degree and order gravitational harmonics
(J2 , C22 );
– measure the tidal variation of Titan’s gravitational quadrupole moments;
– constrain models of Titan’s interior.
a) Determine Titan’s mass and low degree and order gravity field: The most
accurate determination of Titan’s mass MT has been obtained by a combination
of radio Doppler data from Pioneer 11, Voyager 1 and Voyager 2 (Campbell and
Anderson, 1989). Voyager 1 encountered Titan at a closest approach distance of
6500 km. Pioneer 11 and Voyager 2 encountered Titan at much farther distances of
363,000 and 666,000 km, respectively. The best current value of GMT is 8978.2 ±
1 km3 s−2 .
None of the Titan encounters has yielded any information on gravitational harmonics beyond the zero-degree mass term. The values of J2 and C22 can be derived
theoretically by assuming that Titan’s low degree and order gravitational field reects
the satellite adjustment to the perturbing potentials excited by Titan’s rotation and
by Saturn’s tides. The static part of the perturbing potential produces a permanent
deformation of the body with coefficients (Rappaport et al., 1997)
5kf MS RT 3
kf
J2 =
=
(19)
0.49 × 10−4 ,
6 M T aT
1.5
k f MS R T 3
kf
C22 =
0.15 × 10−4 ,
=
(20)
4 M T aT
1.5
in Titan’s principal axes of inertia frame. In Equations (19) and (20), RT is Titan’s
equatorial radius, aT is Titan’s orbital semi-major axis, and kf is the fluid Love
number. For a homogeneous uid, kf = 3/2, but it could be as much as two times
smaller if there were substantial central condensation in the interior of Titan. Note
that for all possible internal mass distributions in hydrostatic equilibrium, J2 is
exactly 10/3 of C22 .
An order of magnitude calculation (Rappaport et al., 1997) indicates that measurements of the Doppler frequency shift in the two-way radio signal between the
Cassini spacecraft and a ground station will allow an excellent determination of J2
and C22 with absolute accuracy of order
2
cbv
b
σ2 =
σ y 4 × 10−8 ,
(21)
GMT RT
where we assume the distance at closest approach b is twice Titan’s radius RT , c
is the speed of light, the spacecraft’s speed v 5 km s−1 , and the Allan deviation
of the Cassini radio signal over a typical Doppler integration time is σ y 10−14 .
14
A. J. KLIORE ET AL.
Equation (21) is consistent with results for Ganymede obtained with the Galileo
spacecraft (Anderson et al., 1996b).
An analytical covariance analysis (Rappaport et al., 1997) suggests that J2 and
C22 can be measured with the Cassini mission to an absolute accuracy between
10−8 and 10−9 , which is consistent with the rough estimate of Equation (21). That
covariance analysis allows us to estimate the accuracy afforded by various flyby
geometries. Favorable conditions include a small impact parameter, a small flyby
velocity, a velocity at closest approach not too far from the line of sight, and an
asymmetric flyby with respect to Titan’s principal axes of inertia.
b) Determine tidal variation of Titan’s quadrupole moments: In addition to a
permanent deformation, Titan must undergo a periodic deformation in response
to the changing tidal force caused by the significant eccentricity of Titan’s orbit.
The periodic tidal perturbation has a frequency equal to Titan’s orbital angular
frequency, and Titan’s response is fundamentally different from its static response.
While Titan responds more or less as a fluid body to the static potential, it responds
as an elastic body to the periodic potential.
The tidal variation of Titan’s quadrupole moment is described in terms of (Rappaport et al., 1997)
3k2 MS RT 3
k2
J2 =
e cos f =
(22)
× 2.58 × 10−8 cos f,
2 M T aT
0.015
3k2 MS RT 3
k2
C22 =
× 1.29 × 10−8 cos f,
e cos f =
(23)
4 M T aT
0.015
where e = 0.029 is Titan’s orbital eccentricity, f is its true anomaly, and k2 is the
Love number of degree 2 (Love, 1906). For an incompressible body with uniform
density ρ (for Titan, ρ = 1.88 g cm−3 ) and elastic shear modulus (or rigidity) µ,
k2 =
3/2
.
1 + 19µRT /2GMT ρ
(24)
While deviations from incompressibility and homogeneous density require only
small corrections to Equation (24) (Kaula 1964), a varying rigidity has important
consequences (Cassen et al., 1982).
The rigidity of Titan is highly uncertain. For a range of rigidity’s values from
µ = 4 × 1010 dyne cm−2 (appropriate for an icy body) to µ = 7 × 1011 dyne cm−2
(appropriate for a rocky body) we obtain a range of values of k2 from 0.22 to 0.015.
It follows that the amplitudes of variations of J2 and C22 (estimated in Equations
(22) and (23) to be 2.6 × 10−8 and 1.3 × 10−8 , respectively) could be as much as
15 times larger. From covariance analysis results we conclude that a determination
of k2 to within 0.05 absolute accuracy is possible.
c) Constrain models of Titan’s interior: The assumption of hydrostatic equilibrium will be tested by determining J2 and C22 (Hubbard and Anderson, 1978).
CASSINI RADIO SCIENCE
15
Indeed, important departures from hydrostatic equilibrium would invalidate the
relationship between J2 and C22 .
If the assumption of hydrostatic equilibrium is verified, then the value of kf will
provide the value of the greatest moment of inertia C from the Radau equation (see
Hubbard, 1984)
1/2
C
2
5
2
1−
−1
.
(25)
=
3
5 kf + 1
MT RT2
The value of C/(MT RT2 ) depends on the degree of differentiation of the body. It
will be compared to values predicted by various models of internal structure (e.g.,
Sohl et al., 1995).
Finally, the value of k2 will be used to distinguish between volatile-rich and
volatile-poor models of Titan (Stevenson, 1992). The above-mentioned range of
k2 values (from 0.22 to 0.015) represent the extreme range from volatile rich to
volatile poor models. Volatile-rich models are so-called because they have a deep,
internal, water–ammonia ocean (Lunine and Stevenson, 1987; Cynn et al., 1989;
Grasset and Sotin, 1996). These models are supported by our ideas of the formation
of satellites, but imply large amounts of methane which could be present in part as
surface hydrocarbon oceans. These seem inconsistent with a primordial origin of
Titan’s orbital eccentricity (Sohl et al., 1995). Indeed, oceanic tidal friction would
have circularized Titan’s orbit by now.
On the other hand, the volatile-poor models, in which Titan’s mantle is completely solid, are consistent with a primordial orbital eccentricity, but have cosmogonic problems described by Stevenson (1992).
These problems lead us to briey re-examine underlying assumptions concerning
Titan’s orbital eccentricity and Titan’s formation; such ideas can be tested by the
gravity measurements.
Early work by Sagan and Dermott (1982) implicitly assumed that Titan’s orbital
eccentricity is primordial. These authors identified two scenarios consistent with the
persistence of eccentricity in the presence of tidal dissipation: either Titan is covered
by a nearly global methane ocean deeper than 400 m, or there is no methane ocean
on the surface. The first picture was favored because such an ocean would resupply
the atmosphere in methane and hence balance atmospheric methane destruction by
photolysis, which will remove the present atmospheric inventory in 107–108 years
(Yung et al., 1984).
However, the speculated global ocean was dispelled by radar (Grossman and
Muhleman, 1992; Muhleman et al., 1990, 1992) and infrared (Griffith, 1993;
Lemmon et al., 1993; Coustenis et al., 1994; Han and Owen, 1994; Smith et al.,
1994) observations of Titan, although these allow for seas or lakes.
Sears (1995), using a more sophisticated tidal dissipation model than Sagan
and Dermott (1982), concluded that even ignoring land masses, the present orbital
eccentricity of Titan requires that the depth of any global ocean be at least 500 m.
16
A. J. KLIORE ET AL.
Dermott and Sagan (1995) found that confining the fluid on Titan to a number of
disconnected seas or crater lakes greatly extends the damping timescale of Titan’s
orbital eccentricity. One problem with this idea is that restricted seas and crater
lakes may not contain sufficient amount of methane to resupply the atmosphere
over the age of the solar system (Lunine, 1996). Stevenson (1992) suggested that
the hydrocarbon ocean is stored in porous spaces and caverns within the upper crust
of Titan. This model may reconcile the need for a reservoir of hydrocarbons with
the tidal argument against a global ocean, though it demands a rather porous crust.
Lorenz et al. (1997) proposed the idea that Titan’s atmosphere may be unstable
and exists only episodically in its present extensive state. This model may be able
to solve the eccentricity problem if Titan’s surface remains frozen for long periods
of time corresponding to epochs in which the atmosphere is collapsed.
Finally, the possibility remains that Titan’s orbital eccentricity was produced
recently (less than several hundred million years ago) by a large impact, though
few bodies larger enough to do so are expected to exist on highly eccentric orbits.
If Titan formed around Saturn, an ammonia–water layer may have formed inside
Titan and persisted (Grasset and Sotin, 1996).
However, Prentice (1980, 1984) suggested that Titan could be a captured moon
of Saturn. Lewis and Prinn (1980) showed that only small amounts of methane and
ammonia were present in the solar nebula, so that Titan could have formed as a
volatile-poor body. If produced from solar nebula material in the vicinity of Saturn’s
orbit, then Zahnle et al. (1992) and Griffith and Zahnle (1995) showed that volatiles
could have been delivered to Titan by comets. Impact-driven chemistry (Jones and
Lewis, 1987) would have led to production of organic compounds in a manner which
may or may not be compatible with Titan’s atmosphere and surface composition, but
some comets themselves contain significant complements of organic compounds
which may survive impact on Titan.
2.3.1.4. Objectives for the Icy Satellites. The radio science gravitational scientific objectives at the icy satellite are to:
– determine the gravity fields of Enceladus and Rhea (J2 , C22 );
– determine the masses of Mimas, Tethys, Dione, Hyperion and Phoebe.
a) Enceladus’ gravity field: Enceladus is a special focus of interdisciplinary
science in the Cassini mission. Indeed, two major objectives of the Cassini Satellite Surface Working Group are to acquire optical remote sensing observations of
Enceladus and to measure its gravity field.
This interest is explained by the intriguing characteristics of Enceladus, among
which figures the remarkably high and uniform albedo and the presence of old and
recent terrains. The mean geometric albedo is close to unity, and the total range
of albedo over the surface is 20%. This is even more intriguing considering that
Enceladus topography contains both old cratered terrains dating from the period of
heavy bombardment and smooth terrains recently resurfaced, indicating endogenic
CASSINI RADIO SCIENCE
17
activity. Buratti (1988) investigated the photometric properties of Enceladus and
concluded that the satellite is completely covered by a young, bright surface layer.
Buratti argues that the E-ring, whose thickness peaks at the orbit of Enceladus,
is the most likely source for this layer, and that the E-ring itself is probably the
result of active surface processes on Enceladus. Alternatively, the bright surface of
Enceladus may result from dissipation associated with tidal interactions, perhaps
with Dione.
Enceladus’s mean radius is 250 km. How can such a small satellite have undergone substantial evolution? This may be due to the fact that ammonia ice, which
plays an important role in lowering the melting point, may have been incorporated
into Enceladus. Evidently, the surface properties alone are insufficient to provide
information on the interior composition. To understand the nature and history of
Enceladus and the other Saturn’s satellites, modeling of the interiors and of the
thermal evolutions is in order.
As far as Enceladus is concerned, even the most basic parameter, i.e., the mass
density, is very poorly known. Indeed, the mass of Enceladus is know with about
50% accuracy. Assuming GM E = 4.9 km3 s−2 (Campbell and Anderson, 1989),
hydrostatic equilibrium, and a value of the fluid Love number equal to half its value
for a homogeneous body, we obtain J2 = 0.0056 and C22 = 0.0017.
A determination of the mass of Enceladus and of its harmonic coefficients of
degree 2 from data acquired during a targeted flyby will allow us to determine the
greatest moment of inertia from Equation (25), and hence to constrain models of
internal structure.
b) Rhea’s gravity field: With a radius of 765 km, Rhea is the largest satellite
of Saturn after Titan. This is the reason why Rhea was selected for gravity field
determination. Recently, Anderson et al. (1996a, 1996b) came to the surprising but
inescapable conclusion that both Io and Ganymede contain large metallic cores. It
will be very interesting to find out whether the smaller Rhea is differentiated and
to compare its internal structure to that of Titan and Enceladus. In this regard, note
that distinct terrain ages and endogenic resurfacing were suggested by Plescia and
Boyce’s (1982) discovery that two polar regions have retained large craters while
they are absent in another region near the equator.
c) Icy satellites’ masses: The objective is to determine the masses of the icy
satellites (especially Mimas, Tethys, Dione, Hyperion and Phoebe) in order to
determine their mean density to high accuracy, and hence constrain their bulk
composition. This is essential for an improved understanding of their dynamical
behavior and evolution. Tyler et al. (1981) determined the masses of Titan and Rhea
from Voyager 1 radio science measurements at Saturn, and Voyager 2 permitted
Tyler et al. (1982) to determine the masses of Tethys and Iapetus. Using the mass of
Tethys in combination with the theory of the Tethys-Mimas resonance, they derived
the mass of Mimas. Campbell and Anderson (1989) used the combined data set
of Pioneer and Voyager data to redetermine the masses of Tethys, Rhea, Titan and
18
A. J. KLIORE ET AL.
TABLE I
Masses of the large icy satellites of Saturn.
Satellite
Mimas
Mass
(×1023 g)
0.46 ± 0.05
0.375 ± 0.009
Enceladus
Tethys
Dione
Rhea
Iapetus
Reference
Tyler et al., 1982
(derived)
Kozai, 1976
Mean Radius
(×105 cm)
196 ± 3
198.6 ± 0.6
0.74 ± 0.36
Kozai, 1976
250 ± 10
0.74 ± 0.36
Kozai, 1976
249.4 ± 0.3
7.55 ± 0.90
Tyler et al., 1982
6.22 ± 0.13
Kozai, 1976
529.8 ± 1.5
10.52 ± 0.33
Kozai, 1976
560 ± 5
10.52 ± 0.33
Kozai, 1976
560 ± 5
24.9 ± 1.5
Tyler et al., 1981
760 ± 5
23.1 ± 0.6
Campbell and
Anderson, 1989
Tyler et al., 1982
764 ± 4
Campbell and
Anderson, 1989
718 ± 8
18.8 ± 1.2
15.9 ± 1.5
530 ± 10
730 ± 10
Reference
Smith et al.,
1982
Davies et al.,
1996
Smith et al.,
1982
Davies et al.,
1996
Smith et al.,
1982
Davies et al.,
1996
Smith et al.,
1982
Davies et al.,
1996
Smith et al.,
1982
Davies et al.,
1996
Smith et al.,
1982
Davies et al.,
1996
Density
(g cm−3 )
1.46 ± 0.23
1.14 ± 0.04
1.13 ± 0.69
1.14 ± 0.56
1.21 ± 0.21
1.00 ± 0.03
1.43 ± 0.08
1.43 ± 0.08
1.33 ± 0.11
1.24 ± 0.05
1.15 ± 0.12
1.02 ± 0.13
Iapetus, but recommended the earlier ground-based determination (Kozai, 1957)
for Tethys. No mission has yet yielded the masses of Mimas, Enceladus, Dione,
Hyperion and Phoebe.
Mass, size and density for the intermediate-size satellites are listed in Table I.
For each satellite, the density on the first line is computed from the mass determined
or recommended by Tyler et al. (1982) and the mean radius determined by Smith et
al. (1982) from Voyager images. The density on the second line is computed from
the mass determined or recommended by Campbell and Anderson (1989) and the
mean radius from Davies et al. (1996).
Phoebe, on an inclined, retrograde orbit, may be a captured object. Determining
the density of Phoebe is important to find out whether or not Phoebe is asteroidal
in nature.
CASSINI RADIO SCIENCE
19
2.3.2. Techniques
2.3.2.1. Saturn. Cassini will orbit Saturn at a fairly wide range of periapsis radii
between 1.3 and 7.3 RS , at inclinations between 0◦ and 85◦ , and with a wide range
of orbital periods from 3 months to 8 days. By fitting a second degree and order
gravitational field, in addition to J4 and J6 , to the radio Doppler data, the mapping
of Saturn’s gravitational field will be complete.
Flybys of Saturn on previous NASA missions occurred at periapsis radii of 1.34
RS for Pioneer 11, 3.05 RS for Voyager 1, and 2.67 RS for Voyager 2. However, the
Pioneer 11 Doppler noise is a factor of 260 times that expected from the Cassini
X-band data, while the Voyager noise is a factor of 12 larger than the expected
Cassini noise. Given the improved Doppler accuracy for Cassini, and the expected
smaller non-gravitational accelerations, plus the advantage of multiple orbits of
Saturn, it is realistic to expect a factor of 100 improvement over Pioneer 11 and
Voyager in our knowledge of Saturn’s gravitational moments.
The radio Doppler data may be complemented by the reduction and analysis of imaging data for the study of the orbital mechanics of smaller inner
satellites and eccentric ringlets. It was demonstrated during the Voyager mission
that such orbital data can place independent constraints on Saturn’s gravitational
field (Nicholson and Porco, 1988), which when combined with the radio Doppler
data, provide significantly better determinations of the higher-order gravitational
moments.
2.3.2.2. Satellites. The gravity fields of Titan, Enceladus and Rhea will be determined by the same type of global technique as used for Saturn.
The tidal variation of the low degree and order gravity field will be measured
from independent determinations of J2 and C22 obtained from flybys occurring near
Titan’s periapsis and apoapsis.
2.3.3. Major Requirements
2.3.3.1. Saturn Requirements. The major requirement for the determination of
the gravitational moments is to obtain coherent X-band Doppler data over an interval
of 5 h, centered on the closest approach in each Saturn orbit. Outside of closest
approach, the data do not need to be continuous, but we require as nearly continuous
data as possible for an interval of ±4 h. Although our covariance analysis, based
on an assumed Allan deviation of 2 × 10−14 at a 1000 s integration time, is valid for
X-band tracking only, the determination of Saturn’s gravitational field will most
likely be improved further with a dual–band radio capability at X- and Ka-bands.
The most significant enhancement will be the relative insensitivity of the data noise
to solar longation angle, thereby enabling a high quality moment determination on
every orbital revolution.
The best orbits of opportunity are those with periapsis radii of less than 4.5 RS .
About 40 such opportunities are anticipated. The first and closest orbit at 1.3 RS
will receive the highest priority. A wide range of inclination angles is practically
20
A. J. KLIORE ET AL.
assured because of the mission requirement to raise the inclination to a near polar
orbit during orbits 34–59.
In principle, we require that there be no spacecraft maneuvers or momentum
dumps of the reaction wheels during the two days of data acquisition for Saturn
radio science. In practice, this may not be achieved. But when it is, we anticipate that
the RSS total unmodeled acceleration by spacecraft subsystems, particularly the
attitude and articulation control subsystem and the propulsion module subsystem,
when inactive, will be less than 5 × 10−14 km s−2 , about 100 times smaller than
comparable acceleration noise on the Voyager spacecraft.
2.3.3.2. Titan Requirements.
a) Tour requirements and flybys selection: The tour must contain at least four
Titan flybys in the following conditions:
– The spacecraft must not be occulted by Titan during ±2 h around closest approach. This is to allow us to track the spacecraft.
– The distance at closest approach b must be such that 1.5 ≤ b/RT ≤ 2. As a matter
of fact, a flyby such that b < 1.5RT would require firing the thrusters, which
would introduce noise in the data. On the other hand, given that the accuracy of
the determination is proportional to (b/RT )3 (see Equation (21)), there is a rapid
loss of sensitivity as the flyby’s altitude is raised.
– Two flybys must occur near Titan’s periapsis, and include one flyby at low inclination with respect to Titan and another one at high inclination. Two other
flybys must occur near Titan’s apoapsis, with the same inclination requirement.
The inclination requirement will allow a good separation of J2 from C22 . The
Titan’s periapsis and apoapsis requirement will allow us to determine the tidal
variations of Titan’s quadrupole moments.
– The flybys should occur far from solar conjunction to minimize the effects of
plasma noise. For example, plasma noise increases by two orders of magnitude
between sun–earth-spacecraft angles of 120◦ and 7◦ .
– Goldstone viewing by the deep space station DSS-25 is desirable because the
use of Ka-band afforded by this station reduces the plasma noise by one order of
magnitude.
b) Tracking requirements: Tracking data must be acquired continuously for ±2
h around the time of closest approach.
2.3.3.3. Icy Satellite Requirements.
– The determination of Enceladus and Rhea’s gravity fields requires that one targeted flyby of each satellite be dedicated to gravity field measurements.
– Mass determination can be performed with non-targeted flybys which have a
distance at closest approach smaller than 50,000 km and preferably smaller than
25,000 km. Tracking data of Phoebe will be acquired during the Phoebe flyby,
19 days before Saturn orbit insertion.
CASSINI RADIO SCIENCE
21
2.4. R ING O CCULTATION EXPERIMENTS
2.4.1. Objectives
Voyager observation of Saturn’s rings in 1980 provided the only radio occultation
observation available to date of the remarkable Saturnian ring system (Tyler et al.,
1980). All features of the main ring system were probed using coherent 3.6 and
13-cm wavelengths sinusoidal signals. Cassini ring observations will significantly
expand on the Voyager observations, primarily taking advantage of new three simultaneous wavelengths capability (0.94, 3.6, and 13 cm, or Ka-, X-, and S-bands,
respectively) as well as multiple occultation opportunities at large, intermediate,
and small ring opening angle B.
2.4.1.1. Ring Structure and Physical Properties. Analysis of the Voyager radio
occultation observations has contributed a wealth of information regarding radial
ring structure (Tyler et al., 1983; Marouf et al., 1986; see also maps in Rosen,
1989), the particle size distribution of several broad ring features (Marouf et al.,
1983; Zebker et al., 1985), physical ring thickness (Marouf et al., 1982; Zebker
and Tyler, 1984; Zebker et al., 1985), and ring dynamics (Marouf and Tyler, 1986;
Marouf et al., 1987; Gresh et al., 1986; Rosen and Lissauer, 1988; Rosen et al.,
1991a,b).
A small ring opening angle B = 5.9◦ (angle between a unit vector in the Earth
direction and the ring plane) at the time of the Voyager observations increased the
effective path length of the radio signal through the rings by a factor of about 10
relative to its normal value. The increased length enhanced sensitivity to regions
of small to moderate optical depth (Rings C, Cassini Division, and Ring A), but
accentuated signal attenuation over most of Ring B as well as other optically thick
ring features (Tyler et al., 1983).
Accurate, high spatial resolution, multiple wavelengths characterization of ring
structure and of its variability with ring longitude, ring opening angle, and time
are major objectives of the Cassini radio science ring observations. The characterization is at the heart of understanding of ongoing physical and dynamical processes and is of prime importance for eventual understanding of ring origin and
evolution.
Radio occultation opportunities implemented early in the Cassini tour when
the rings are nearly fully open (B ≈ 20–24◦ ) will overcome a major Voyager limitation, allowing for the first time probing at radio wavelengths of the optically
thick Ring B, which dominates the overall mass of the ring system. The optimized
near-diametric geometry of these occultations will yield an order of magnitude
resolution improvement in mapping the radial structure of ring features compared
with Voyager. Other occultations later in the mission at intermediate and small ring
opening angle B will provide complementary information regarding vertical ring
structure, optical depth profiles of tenuous ring features, and the variability of ring
structure with longitude and time.
22
A. J. KLIORE ET AL.
The Cassini observations will also determine the particle size distribution of
major ring features, including Ring B, over the millimeters to tens of meters size
range. Knowledge of the size distribution constrains the surface mass density of a
ring feature if the ring material is assumed to be solid water ice. Alternatively, the
size information may be used to constrain the material density of ring particles if
independent estimates of the surface mass density are available from analysis of
local dynamical features.
The multi-wavelength observations will also yield high spatial resolution information regarding the abundance of millimeter to decimeter size particles within
local ring features, a unique capability of the radio occultation observations. Of
particular interest is mapping the possible variability in the abundance of this particle population within dynamically active ring features (density and bending waves,
wakes of embedded satellites, resonant edges, etc.). Interesting sorting of particle
sizes across narrow ring features has been noted in the Voyager observations (Tyler
et al., 1983; Marouf et al., 1986) and has motivated the proposal of innovative
ring models to explain the observations (Eshleman, 1983; Eshleman et al., 1983;
Michel, 1982).
Specific objectives include:
– High-resolution profiling of radial ring structure and characterization of its variability with wavelength, longitude, ring opening angle, and time. Profiling of the
relative abundance of millimeter to decimeter radius particles and characterizing
of their variability across resolved ring features.
– Determination of the full particle size distribution over the approximate size range
1 mm to 20 m of broad ring features that can be resolved in the spectra of the
near-forward scattered signal. Determination of the vertical ring structure, of the
physical ring thickness, and of the particle packing fraction within such features.
– Determination of ring surface mass density, ring viscosity, and bulk density of
particle material. Characterization of the variability of these parameters among
global ring features (A, B, C, . . .) and within local broad features.
– Characterization of the dust abundance within the main rings, especially in dynamically active regions, through collective analysis of radio, stellar, and solar
ring occultation observations.
2.4.1.2. Ring Kinematics and Dynamics.
a) Geometry of the ring system: The Voyager 1 and 2 encounters provided a
detailed view of Saturn’s complex ring system, with its density and bending waves
and its non-circular features, and gave some indications about the composition and
particle size distributions of the rings, but additional observations are required to
refine the determination of ring orbits, the planetary gravitational field, and the
orientation of the ring plane. This is in part because a long time baseline between
observations is required for accurate measurement of the precession rates of nearly
circular ring features, and also because a suite of different viewing geometries is
CASSINI RADIO SCIENCE
23
needed to constrain the direction of the planet’s spin axis. An important goal of the
radio science ring occultation observations is to determine the absolute radius scale
of the ring system and the instantaneous direction of Saturn’s pole to high accuracy.
Surprisingly, the radius scale of Saturn’s rings has a much larger uncertainty
– about 1 km – than the Uranian rings, whose orbital radii are accurate to a few
hundred meters or less. This is because the Uranian rings have been observed using dozens of stellar occultations over a twenty-year period, providing a dense
set of measurements of ring occultation event times. In contrast, stellar occultations by Saturn are much more difficult to observe because of the brightness of the
rings in reflected sunlight. Ground-based observations of the 1989 occultation of
a very bright star, 28 Sgr (French et al., 1993; Hubbard et al., 1993), and subsequent occultations observed from the Hubble Space Telescope (HST) (Elliot et al.,
1992; Bosh and Olkin, 1996), have provided the only post-Voyager occultations
with sufficient Signal-to-Noise Ratio (SNR) to be used for refinement of the ring
orbits.
An accurate radius scale for Saturn’s rings is essential for detailed dynamical
investigations of the rings, as well as accurate inter-comparisons of individual
occultation profiles. Since the radial dependence of eccentric ringlet free precession
rates is governed by the gravitational harmonics J2 , J4 , J6 , . . . , (Longaretti and
Borderies, 1991; Borderies-Rappaport and Longaretti, 1994) a long time series of
precise measurements of non-circular features can be used to determine the loworder gravitational harmonics of Saturn. As pointed out above, these give important
information about the internal mass distribution of the planet.
The determination of the radius scale is strongly coupled to the assumed pole
direction of the mean ring plane, and thus we must solve for both from the occultation observations. From their analysis of the 28 Sgr and Voyager observations,
French et al. (1993) concluded that the pole direction had shifted measurably between the 1980/1981 Voyager epochs and the stellar occultation in 1989, and they
interpreted this as evidence for precession of Saturn’s pole. Although the solar
torque exerted on Saturn itself is quite small, the Sun also exerts a torque on the
satellites, principally Titan, which effectively increases the J2 of the system by
a factor of 4 and reduces the precession period by a comparable factor. They
found that the rate of motion of Saturn’s pole on the sky was 0.86 ± 0.31 times
the predicted rate of 0.339 per year. The principal uncertainty in the theoretical
value is Saturn’s moment of inertia. By incorporating the full set of Cassini occultation observations of the rings, both from radio science measurements and from
stellar occultations observed by other Cassini instruments, we have the prospect
of greatly improving the accuracy of the precession rate of the pole, with the ultimate goal of determining the principal moment of inertia of Saturn to within a few
percent.
For earth-based stellar occultations, the a priori uncertainty in the stellar position relative to the planet is relatively large, and least-squares fits for the occultation geometry must include the offset between the star and planet as a pair of free
24
A. J. KLIORE ET AL.
parameters. For spacecraft occultations, the analogous uncertainty is in the spacecraft location with respect to the planet’s center. Errors in the assumed spacecraft
trajectory map directly into errors in the derived ring plane radius scale. For this
reason, we place a very high value on accurate reconstruction of Cassini’s trajectory.
b) Ring morphology: A major goal of ring dynamics studies is to explain the
presence of nonaxisymmetric features such as eccentric ringlets and density waves,
and nonequatorial features such as inclined ringlets and bending waves. Since the
Keplerian shear, the differential precession of periapses and nodes, and viscous
diffusion tend to erase these features on short time scales, the existing ones must
be dynamically maintained.
Satellites are responsible for shaping a number of morphological features. They
give rise to density waves (Goldreich and Tremaine, 1978a,b, 1979a; Shu, 1984;
Borderies et al., 1986; Longaretti and Borderies, 1986) and bending waves (Shu
et al., 1983), open gaps (Goldreich and Tremaine, 1978a; Borderies et al., 1982,
1988), shepherd rings (Goldreich and Tremaine, 1979c; Hanninen and Salo, 1994,
1995; Goldreich et al., 1995), excite eccentricities and inclinations in narrow rings
(Goldreich and Tremaine, 1981; Borderies et al., 1983b, 1984a), create ring arcs
(Goldreich et al. 1986), and sometimes perturb rings by penetrating them (Borderies
et al., 1983c).
The above effects of satellites on rings require that particles behave in a collective
manner, which is insured by the ring self-gravity and viscous stresses. Self-gravity is
invoked to explain the rigid precession of eccentric and inclined ringlets (Goldreich
and Tremaine, 1979b; Borderies et al., 1983a, b). Viscous stresses can lead to
instabilities (Lin and Bodenheimer, 1981; Lukkari, 1981; Ward, 1981; Borderies
et al., 1985) or over-stabilities (Longaretti and Rappaport, 1995).
The objectives are:
– To test theoretical models for density waves, bending waves, shepherding, excitation of eccentricities and inclinations, ring arcs, precession of elliptical and
inclined ringlets, viscous instabilities, etc.
– To identify profiles of gravitational wakes of embedded satellites (Showalter et al.,
1986; Marouf et al., 1986; Marouf and Tyler, 1986). Characterize the evolution
of profile morphology with longitude and its dependence on background optical
depth. Determine the masses and orbits of identified satellites.
– To explain the presence in the C ring and the Cassini Division of several ringlets
which are not associated with any known satellite. Study their interaction with
the surrounding rings (Rappaport, 1998).
– To explain the presence in the B ring of non-axisymmetric features which are not
associated with any known satellite (Lane et al., 1982; Borderies et al., 1984b).
c) Ring evolution: Angular momentum and energy are transferred between the
rings and the satellites with which they interact (Goldreich and Tremaine, 1980).
The small satellites outside the main rings of Saturn are repelled outwards over
a time scale of a few tens of millions years. This short-time scale suggests that
CASSINI RADIO SCIENCE
25
the interaction between rings and satellites includes accretion and disruption of
satellites and that Saturn’s rings as we observe them now may be recent. Alternatively, ring/satellite systems may be maintained by effects that we do not understand
yet.
A key parameter in modeling this evolution is the ring’s viscosity. This parameter
has been measured indirectly from the damping of density and bending waves (Cuzzi
et al., 1981; Lane et al., 1982; Lissauer et al., 1982; Shu et al., 1983). Cassini will
allow us a more direct determination (Borderies, 1992).
The objectives are:
– To characterize and model viscous stresses.
– To characterize the transport of angular momentum and energy within the rings
and their transfer between rings and satellites.
2.4.2. Techniques
Observables during a ring occultation experiment can be derived from the effects
of ring material on a sinusoidal signal linking the spacecraft and an earth receiving
stations of the DSN (Marouf et al., 1982). Temporal coherence of the radio link is
ensured through the use of an ultrastable oscillator (USO) onboard the spacecraft
and an atomic frequency standard at the ground receiving station. During an occultation, Cassini generates and transmits through the rings three coherent sinusoidal
signals (wavelength of 0.94, 3.6, and 13 cm, or Ka-, X-, and S-bands, respectively)
using the USO as a common reference for all three signals. The coherency of the
signals allows measurement on the ground of the complex amplitude (magnitude
and phase) of the perturbed signals.
Modeled as a discrete random medium, the collective effects of ring particles
on an incident sinusoidal signal are well characterized (Marouf et al., 1982; Tyler
et al., 1983; Marouf et al., 1983; Simpson et al., 1984; Zebker et al., 1985; Marouf
et al., 1986; Tyler, 1987; Gresh et al., 1989). Two main signal components may
be identified and separated in the spectrum of the observed perturbed signal. The
first is the direct or coherent signal, a sinusoidal component whose amplitude and
phase can be measured relative to the corresponding values of the incident sinusoid.
The direct signal characterizes the average effect of ring particles on the incident
signal. The time history of its amplitude and phase provides information regarding
detailed radial ring structure. The differential amplitude and phase of two signals of
wavelength λ1 and λ2 provide information about the relative abundance of particles
of radius a determined by λ1 , λ2 , and the refractive index of particle material
(Marouf et al., 1982, 1983).
Initial measurements of the coherent signal amplitude and phase are diffractionlimited (Marouf and Tyler, 1982). Measurement of the direct signal phase allows
reconstruction of the observations to remove diffraction effects, yielding highresolution profiles of the complex ring transmittance, hence of optical depth and
phase-shift profiles (Marouf et al., 1986). Achievable resolution is a small fraction of
26
A. J. KLIORE ET AL.
the corresponding Fresnel scale of diffraction and is determined by several factors,
including geometry of the occultation orbit, stability of the reference phase, SNR
of the observations, and processing complexity (Marouf et al., 1986). A better
Cassini USO and an optimized set of Cassini occultation orbits promise significant
improvements in achievable resolution over the Voyager observations.
The second component of the perturbed signal is the scattered or incoherent signal, a spectral-broadened component that represents the fraction of average power
scattered by ring particles and intercepted by the ground receiving station (Marouf
et al., 1982). The spectral broadening is caused by the Doppler shift introduced by
the relative motion of the spacecraft and ring particles. Its time history (spectrogram) provides information regarding the relative abundance of meter size particles
within broad ring features that can be resolved in the measured spectrograms.
The measured near-forward scattered signal of a resolved ring feature provides
significant information about the distribution of particle sizes that populate the
feature, its physical thickness, and the degree of particle crowding, among other
physical parameters. Procedures have been developed to invert the measurements to
recover physical model parameters for the classical many-particle-thick ring model
(Marouf et al., 1982, 1983) and for the thin-layers ring model (Zebker et al., 1983,
1985). The more general problem of crowded and clustered ring models of arbitrary
thickness is a subject of continued investigation (Marouf, 1994, 1996, 1997).
Contribution to the scattered signal measured during occultation is dominated
by the diffraction lobes of large ring particles. Particles of radius a larger that the
spacecraft antenna radius (2 m) have diffraction lobes of width narrower than the
spacecraft antenna beamwidth, and information regarding their size distribution
is captured in scattered signal measurements. The limit on the upper particle size
captured is set by the sampling interval of the measured collective diffractionpattern, hence by the SNR of the measurement, and is typically few to several tens
of meters. Thus, scattered signal measurement during occultation yields the particle
size distribution over the range 2 m < a < several tens of meters. Other techniques
are used to extend the distribution to the range a <2 m.
Over the millimeter to decimeter size range, measurement of the differential
extinction and phase shift of the X-, S-, and Ka-bands coherent may be used to
constrain the size distribution. In the case of Voyager, measured differential optical
depth and phase shift of the coherent X- and S-band signals (3.6 and 13 cm-λ)
provided clear evidence for the presence of ring particles of sizes in the centimeter
to decimeter radius range, both in local and global ring features (Tyler et al., 1983;
Marouf and Tyler, 1985; Marouf et al., 1986). The additional availability of the
Ka-band (0.94 cm-λ) signal on Cassini will allow similar inference of the abundance
of the population of millimeters to centimeters size ring particles.
Particles of size in the decimeter to meter size range do not differentially affect the coherent signals significantly and have diffraction lobes that are essentially
isotropic over the spacecraft antenna beam width. Determination of their size distribution is based on a yet different technique, referred to here as the bistatic-scattering
CASSINI RADIO SCIENCE
27
technique. It relies on observation of the scattered signal with the direction of the
boresight of the spacecraft antenna shifted away from the earth direction so as to
sample the broader diffraction lobes of particles in this range. Because the width
of a diffraction lobe of a particle of diameter D = 2a observed at wavelength λ
is roughly λ/D, the maximum angular shift of the spacecraft antenna boresight is
determined by the minimum particle size whose diffraction lobe is to be sampled
and is wavelength dependent.
Sampling the diffraction lobes of particles of radius a ≥ 20 cm, for example,
requires bistatic-scattering observations over a maximum angular range equal to
approximately five times the antenna beamwidth at the wavelength of interest.
Thus, for both X- and Ka-bands, maneuvers to shift the antenna boresight away
from the earth direction are limited to no more than a few degrees change in
the antenna boresight direction. The exact limit is set by available SNR. Optimal
maneuver strategies to observe bistatic-scattering given available SNR are still
under development.
The capability of determination of the particle size distribution of resolved ring
features over the millimeters to tens of meters range (millimeter to decimeter using
differential extinction, decimeters to meters using bistatic scattering, and meters to
tens of meters using forward-scattering) is a unique capability of the radio science
ring observations. For ring features for which bistatic scattering may be noise
limited or not available, a selfconsistent model fitting approach that bridges the
lower and upper ends of the distribution provides a viable alternative (Marouf et
al., 1983; Zebker et al., 1985).
2.4.3. Major Requirements
The quality of ring occultation observations is determined by the phase and amplitude stability of the radio link, available SNR, and the geometry of occultation
orbits, among other factors. These impose stringent requirements on the performance of the radio subsystems on board the spacecraft and at the ground receiving
stations, as well as on the design of the Cassini tour.
Consider first the requirements on the phase stability of the radio link, a critical
parameter for successful reconstruction of the diffraction-limited direct signal measurements. In the absence of phase noise, the limit on achievable radial resolution
R is set by the Fresnel scale of diffraction F and the width W of the radial interval
over which diffraction limited measurements are processed, where R = 2F 2 /W
(Marouf et al., 1986). In reality, finite phase instability over W limits actual achievable resolution to a larger value Rφ > R, where Rφ is determined by the nature
of the random reference phase fluctuations, usually dominated by the behavior of
the USO onboard the spacecraft (Marouf et al., 1986).
In the Voyager case, phase stability of the USO (Allan deviation σ y 5 × 10−12
at 1 s time interval) limited Rφ to the range Rφ ≥ 250 m (Marouf et al., 1986).
The Cassini USO is over ten times better than Voyager (σ y 2 × 10−13 at 1 s).
Calculations based on the assumptions of a random walk phase noise model (white
28
A. J. KLIORE ET AL.
frequency noise) and likely Cassini occultation orbits indicate that Rφ ≥ 10 m,
more than an order of magnitude improvement over Voyager. A requirement that
the Allan deviations of the atomic frequency standard used at the earth receiving
stations be at least three times better than that of the USO ensures that the latter
is the limiting factor. Actual Cassini resolution will depend, of course, on in-flight
performance of the USO and ability to model and remove long term phase drift,
and other factors including the degree of variability of F over W and available SNR
(Marouf et al., 1986).
Like Voyager, Cassini conducts all occultations in a downlink mode (that is,
transmission from the spacecraft and reception on the earth), hence the available
free-space signal-to-noise ratio SNR0 is limited by the relatively small transmitted
power. Indeed, both spacecraft have comparable SNR0 (for Cassini, SNR0 52,
40, 41 dB/Hz for the X-, S-, and Ka-band signals, respectively). Unlike Voyager,
Cassini enjoys the advantage of arriving at Saturn when the ring system is almost
fully open as seen from the earth (ring opening angle B −24◦ ), and remains
in orbit as B gradually increases to a Voyager-like value of about −6◦ over the
four-year mission lifetime. Given a ring feature of normal optical depth τ , the
actual measurement SNR is reduced from its free-space value SNR0 by the factor
exp[−τ/sin(B)] (due to attenuation by ring particles). For a τ = 1 ring feature, for
example, the measurement SNR is a factor of 1200 higher at B = 24◦ than at a
Voyager-like B = 6◦ ; the SNR is 1.5 million times higher for τ = 2!
Given the extreme sensitivity of the measured SNR on the ring opening angle,
a major requirement on the Cassini tour design was to implement a set of radio
occultation orbits as early as possible after Saturn orbit insertion (SOI). The early
occultations take full advantage of a unique opportunity provided by nature to
probe all ring features, including the B Ring, with the limited available SNR0 . An
additional requirement of an occultation distance D 4 − 6RS ensures moderate
Fresnel scale F, hence moderate complexity in reconstruction of the diffraction
limited observations. A remarkable set of early near-diametric occultation orbits
was designed and implemented by the Mission Design Team and is an integral part of
the selected orbital tour. The orbits span the range 24◦ < B < 20◦ . Exceptional Xband radial resolution of 100 m or better is expected everywhere, including regions
of Ring B of normal optical depth τ ≤ 2.5, an order of magnitude improvement over
Voyager. Requirements for two additional occultation opportunities at intermediate
(B 15◦ ) and small (B < 10◦ ) ring opening angle complement the first set and
allow more complete characterization of the variability of the observables with B,
longitude, and time.
Additional requirements on occultation orbit geometry are necessary to improve
the spatial resolution of scattered signal measurements. As indicated before, the
intrinsic resolution is determined by the size of the spacecraft antenna “footprint”
on the ring plane. The footprint can be very large (with a characteristic scale of
thousands to hundreds of thousands of km, depending on wavelength, the spacecraft
distance D behind the ring, and the ring opening angle B). The resolution may be
CASSINI RADIO SCIENCE
29
improved if contours of constant Doppler shift over the footprint align closely
with boundaries of ring features so that the contribution of a given feature may be
identified in the measured spectrograms (Marouf et al., 1982). The Voyager flyby
trajectory was optimized in part to enhance this alignment (Marouf et al., 1982),
allowing spatial resolution in the range 1000–6000 km to be achieved (Marouf et
al., 1983; Zebker et al., 1985). Similarly, Cassini early occultation orbits have been
optimized to provide good Doppler contour alignment with ring boundaries. Spatial
resolution as good as 500–1000 km is expected for some occultations.
2.5. A TMOSPHERIC
AND I ONOSPHERIC
OCCULTATION E XPERIMENTS
The refraction of monochromatic radiation emitted from the spacecraft toward earth
as it passes through a spherical or oblate atmosphere produces Doppler shifts in the
received frequency that allow the retrieval of refractivity as a function of altitude.
This in turn leads to vertical profiles of electron density in the ionosphere and of
density, pressure, and temperature in the neutral atmosphere. Much of the value
of occultation profiles lies in their high vertical resolution, typically better than 1
km. This is to be contrasted with that achievable from passive remote sounders, for
which the vertical resolution is more comparable to a scale height.
2.5.1. Scientific Objectives
2.5.1.1. Atmospheres.
a) Saturn: The Pioneer 11 spacecraft provided the first radio occultation of
Saturn’s ionosphere and atmosphere (Kliore et al., 1980a; Kliore and Patel, 1980),
with ingress and egress soundings both at equatorial latitudes. Later, Voyager 1 and
2 gave two additional occultations, which sounded latitudes near the equator, at
36◦ N, 31◦ S, and 73◦ S (Lindal et al., 1985; Tyler et al., 1981, 1982).
All the retrieved temperature profiles (Figure 1) in the neutral atmosphere
have a well-defined troposphere (where temperature decreases with altitude), a
tropopause, or temperature minimum, located at the ≈60–80 mbar level, and a
stratosphere (where temperature increases with latitude). The Voyager occultations,
which had higher signal-to-noise ratio than those from Pioneer 11, gave atmospheric
profiles that extended from a few tenths of 1 mbar to 1.3 bar. The lower pressure
limit was dictated by the USO stability on the spacecraft, signal-to-noise ratio,
and the resulting ability to separate the effects of the neutral atmosphere from the
ionosphere on the refractivity. The limit at 1.3 bar resulted from absorption by NH3 ,
which extinguished the signal transmitted from the spacecraft to earth.
Both the Pioneer and Voyager temperature profiles at low latitudes exhibit a
marked undulatory structure in the upper troposphere and stratosphere that is suggestive of vertically propagating waves. Vertical wavelengths are ∼2 scale heights,
although smaller-scale behavior is also present. The undulations are more subdued
at mid and high latitudes. This structure has not been interpreted or analyzed in
30
A. J. KLIORE ET AL.
Figure 1. Temperature profiles in Saturn’s atmosphere retrieved from Voyager and Pioneer 11. The
dashed curve in the right panel is from the Pioneer egress (Kliore et al., 1980b). After Lindal et al.
(1985).
any depth. In their analysis of the zonal (i.e., east-west) variations of temperatures
retrieved from the Voyager infrared spectroscopy experiment (IRIS), Achterberg
and Flasar (1996) found evidence of a coherent wave structure in the tropopause
region that extended from 40◦ N to low latitudes. They deduced that it was most
probably a Rossby wave, forced by a critical-layer instability at the more northern latitude. The wave amplitude they derived, ±1 K, seems consistent with the
reduced amplitude seen in the mid-latitude radio-occultation profiles. Coverage
of the equatorial region, particularly at southern latitudes, by IRIS, which was
primarily a nadir-viewing instrument, was minimal, because of interference from
Saturn’s rings and, for Voyager 2, a malfunction of the remote-sensing scan platform. Temperatures retrieved from radio occultations show structure in Jupiter’s
atmosphere that is similar to Saturn’s (Lindal et al., 1981). Allison (1990) has suggested that the structure in the equatorial profiles of Jupiter is produced by Rossby
waves.
Waves are meteorologically significant, because they can be sensitive indicators
of the conditions of the background mean atmosphere through which they propagate. In their study, Achterberg and Flasar (1996) were able to relate the observed
meridional structure of the thermal wave they identified to the thermal structure
of Saturn’s atmosphere and spatial variation of its zonal winds. Waves can also be
dynamically important, as they typically transport angular momentum over large
distances. This could be an important factor in maintaining the large-scale zonal
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CASSINI RADIO SCIENCE
wind system on Saturn, which is notwell understood. Cassini is expected to provide
occultations yielding temperature profiles at nearly 50 locations on Saturn, with a
reasonably good distribution in latitude. This is far denser coverage than has been
realized to date. With the zonal structure provided by the mapping capabilities of
the composite infrared spectrometer (CIRS), wave structure in Saturn’s troposphere
and stratosphere should be well characterized.
Knowledge of temperature and pressure as functions of altitude and latitude
leads to the zonal wind u through the gradient wind equation,
u
1 ∂P
u sin
2 +
=−
,
(26)
r cos pc
ρr ∂
φ
and the thermal wind equation,
u
∂
u sin
2 +
∂ln P
r cos
pc
R
=
mr
∂T
∂
.
(27)
P
Here r is radius to the planet’s center of mass, and is the internal uniform
planetary rotation rate of Saturn, presumably equal to that implied by the kilometric radiation modulation (=1.66 × 10−4 s−1 ); P is pressure, ρ is atmospheric
mass density, T is temperature, R is the universal gas constant, and m is the mean
molecular weight of the atmosphere; is the planetographic latitude, determined
by the intersection of the local normal to the equipotential surface, and pc is planetocentric latitude, determined by the intersection of the line to the planet center of
mass with the equatorial plane; φ denotes the geopotential,
z
g dz ,
(28)
φ=
0
where g is the local effective gravitational acceleration, representing both gravitational attraction and the centrifugal repulsion associated with the uniform planetary
rotation. The geopotential function φ, therefore incorporates both gravity and uniform rotation; the altitude coordinate z is normal to the geopotential surface. Note
that in Equation (26) the gradient in pressure is at constant altitude relative to
the geopotential associated with uniform rotation. In Equation (27) the gradient
in temperature is along isobars. Because of Saturn’s rapid planetary rotation, the
geostrophic term, the one containing 2 on the left-hand sides of Equations (26)
and (27), generally dominates.
The Pioneer 11 and Voyager soundings were too sparse for inferring winds,
but the much denser coverage afforded by the Cassini radio occultations make this
much more feasible. Although the occultations will not densely sample longitude,
they will sample latitude very well. Temperatures retrieved from the Voyager IRIS
spectra indicate that, atleast in the upper troposphere and lower stratosphere, the
zonal variations of temperature are smaller than the variation with latitude. Thus the
latitude variations in the pressure and temperature fields are fairly good indicators
of the zonal winds on Saturn. Comparison with the temperatures retrieved from the
32
A. J. KLIORE ET AL.
CIRS instrument, which can obtain global maps, will facilitate this derivation. A
very important advantage for radio science lies in the capability to retrieve pressure
as a function of altitude, and hence obtain the zonal winds directly through the
application of Equation (26) (c.f., Newman et al., 1984). When using temperatures
to infer winds from Equation (27), as, for example CIRS must do, the winds need to
be specified along a (usually lower) boundary. Winds will also be derived with high
spatial resolution from cloud tracking using both the visible (ISS) and perhaps the
near infrared (VIMS) images. In this analysis there always remains some ambiguity
in the altitudes probed at a particular observing wavelength. Comparison of the
winds derived from cloud tracking with those obtained from Equation (26) using
radio science data should greatly facilitate the altitude assignment in the cloudtracking studies.
The sensitivity of the radio signal passing through Saturn’s atmosphere to absorption by gaseous ammonia permits the retrieval of vertical profiles of NH3 below
the 1-bar level. Lindal et al. (1985) have presented such profiles from the Voyager
Saturn occultations, as well as from those for Jupiter (Lindal et al., 1981). The large
number of Cassini occultations will permit a mapping of the three-dimensional distribution. Both passive ground-based microwave observations and observations at
infrared and visible wavelengths have indicated that gaseous and condensed NH3
vary latitudinally over Saturn and Jupiter. These variations are probably indicative
of the vertical motion field near the 1-bar level. Particularly intriguing in the observed radiances at radio and far-infrared wavelengths is a “warm” broad band on
Saturn that is centered about 30◦ N (Conrath and Pirraglia, 1983; Grossman et al.,
1990). The corresponding latitude range in the southern hemisphere is much colder.
This has been interpreted as caused by a diminution in cloud opacity and ammonia
gas in the northern latitude range. Curiously, the Voyager radio occultation data
at 36◦ N and 31◦ S give no hint of such asymmetry in the derived NH3 abundance
(Lindal et al., 1985). Whether an “atypical” region at the northern latitude was
sounded by the radio occultations is open to question. The more complete coverage
of Cassini should help address questions like this.
The helium abundance of the giant planets is an important indicator of their
formation and evolution. One of the more sensitive methods to determine the helium
abundances of the atmospheres of the outer planets from remote sensing has entailed
the combination of radio-occultation soundings with far infrared spectra. The radio
occultations provide profiles of the refractivity versus altitude, from which T(z)
is derived. For uniform composition, the quantity T (z)/m is invariant. To first
order, varying the assumed composition shifts the profile T(z) towards higher or
lower values without changing its shape. If the source of infrared opacity of the
atmosphere is known, a synthetic infrared spectrum can be computed and compared
to an observed spectrum.
Comparison of Voyager radio occultation retrievals with IRIS spectra led to
values of helium that were slightly depleted relative to solar abundance on Jupiter
(Gautier et al., 1981) and quite depleted on Saturn (Conrath et al., 1984). This
CASSINI RADIO SCIENCE
33
appeared to be consistent with the notion that differentiation of the heavier helium
from hydrogen was occurring in the planets’ interiors.
Recently, however, direct determinations of the helium abundance from the
Galileo probe (Niemann et al., 1996; von Zahn and Hunten, 1996) have yielded
values that are higher than that determined from Voyager and more nearly solar.
Recent planetary evolution models (Hubbard et al., 1999) have also called into
question the low value of helium derived for Saturn, and they suggest that the current
value of Saturn’s intrinsic luminosity, which derives from cooling of its interior, is
more consistent with a larger helium abundance for Saturn’s atmosphere than was
derived from Voyager data. Conrath and Gautier (2000) have also re-examined the
helium retrieval from Voyager IRIS observations of Saturn. In this analysis, they
used the redundant information in the IRIS spectrum between 200 and 600 cm−1 to
simultaneously retrieve profiles of temperature, the parafraction of hydrogen, and
the helium abundance. In this spectral region the principal opacity is from absorption
by the pressure-induced dipole of molecular hydrogen, caused by collisions with
other hydrogen molecules and with helium. The absorption is sensitive to all three
of the aforementioned atmospheric variables. Although this “internal” method of
determining the helium abundance is not as sensitive as combining radio-occultation
profiles with infrared spectra, Conrath and Gautier (2000) nonetheless were able to
conclude the helium abundance must be higher than the value derived earlier.
Evidently there is some as yet unidentified source of systematic error in the
earlier determination. Having CIRS spectra at the numerous locations of Cassini
radio occultations, where the haze structure varies, may help elucidate the source
of the problem and produce a more reliable determination of the helium abundance.
There are no planned in situ measurements of helium on Saturn in the foreseeable
future, so a reliable determination via remote sensing remains a high priority.
b) Titan: Prior to the arrival of the Voyager 1 spacecraft at Saturn, the surface
pressure and temperature of Titan’s atmosphere were not well determined. Indeed,
predictions of the surface pressure differed by a factor of 100 (Danielson et al., 1973;
Caldwell, 1977; Hunten, 1978). In traversing the Saturn system, Voyager 1 flew
behind Titan and provided a diametric occultation near the equator as viewed by
Earth. Because of the gross uncertainty in the atmosphere base pressure, one could
not perform a normal limbtracking maneuver (see Section 2.5.2.2), in which the
spacecraft attitude is continually adjusted to ensure that the refracted radio waves
reach Earth. This would have required a reasonably accurate model of the mean
vertical structure of Titan’s atmosphere for predicting the attitude control. Instead,
the Voyager team hedged its bets, using constant offsets of the spacecraft antenna
boresight from the line of sight to Earth, 0.1◦ during the ingress, and 2.4◦ during the
egress (Lindal et al., 1983; Hinson et al., 1983). It turns out that the bending angle in
the neutral atmosphere increases more or less monotonically with depth, reaching
2◦ for the ray that grazes the surface. The Voyager spacecraft antenna transmitted
at both S- and X-bands. The S-band data, for which the half-power full width of
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A. J. KLIORE ET AL.
the antenna was 2.5◦ , covered the full range of atmospheric pressures during both
ingress and egress, whereas the X-band data, with an antenna width of 0.6◦ , only
proved useful in limited altitude ranges, above 28 km during ingress and within a
few km of the surface during egress.
The Voyager 1 soundings provided vertical profiles of temperature and pressure
at altitudes below 200 km. As discussed in Section 2.5.2, the refractivity profile is
the fundamental quantity retrieved from the soundings, and obtaining temperature
and pressure profiles requires that the atmospheric bulk composition be specified.
The combination of data from the thermal infrared spectrometer (IRIS) with the
radio occultation data led to the conclusion that the mean molecular weight of Titan’s atmosphere is ∼28 AMU, highly suggestive of N2 as the dominant constituent
(Tyler et al., 1981; Hanel et al., 1981; Vervack et al., 1999). This was supported by
the identification of several nitriles in the IRIS spectra, as well as the detection of
atomic and molecular nitrogen in the thermosphere by the ultraviolet spectrometer
on Voyager (Broadfoot et al., 1981). Lindal et al. (1983) retrieved vertical profiles
of temperature and pressure from the Voyager soundings, assuming an atmosphere
of pure N2 . The ingress and egress soundings were nearly identical in the troposphere, and they obtained a surface temperature and pressure of 94 K and 1.5 bar,
respectively. Below 4 km the lapse rate in temperature was nearly dry adiabatic,
suggesting efficient mixing by small-scale convection.
The effect of composition on the retrieved temperature profiles is an important
consideration for Titan. When the composition is spatially uniform, the retrieved
temperature, as a function of altitude, scales linearly with the molecular mass (see
Equation (54)). However, when there is a spatially varying condensible, such as
CH4 , contributing to the refractivity, the behavior of temperature with altitude can
be markedly different. Flasar (1983) retrieved temperatures for atmospheres with
different N2 –CH4 mixtures. He demonstrated that a vertical profile of saturated
CH4 implied increasing lapse rates of temperature near the surface. By imposing
the stability constraint that the lapse rate not exceed the dry adiabat, he deduced
that the lowest 4 km of Titan’s atmosphere had to be unsaturated and the maximum
CH4 mole fraction just above the surface was ∼0.09 or less. Later, Lellouch et al.
(1989) did a systematic study of N2 –CH4 -36,38 Ar atmospheres. Retrieving temperature profiles from the radio occultation refractivity profiles, they found a range of
possible surface temperatures, from 92.5 to 101 K, and tropopause temperatures in
the range 70.5–74.5 K. All the profiles were qualitatively similar in shape to that
for the N2 atmosphere. Although Ar was initially thought to be a bulk constituent of
Titan’s atmosphere (see e.g., Samuelson et al., 1981), no evidence of it has turned
up, and indeed, recent work (Strobel et al., 1993; Courtin et al., 1995; Samuelson
et al., 1997) suggests that the Ar mole fraction may be quite low, < 0.01. For atmospheres composed of N2 and CH4 , Lellouch et al. (1989) found the range of
allowable temperatures to be smaller: maximum temperatures are 71.8 K at the
tropopause and 95.2 K just above the surface; the minimum possible temperatures
are unchanged from before. Although the implied range of uncertainty amounts
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to only ∼3 K, the IRIS spectra indicate that this is comparable to the meridional
contrast seen at the surface and in the troposphere (Flasar et al., 1981). Because
of the likely spatial variation of tropospheric CH4, it is important to reduce the
current uncertainty in the radio occultation results, which are mostly attributable to
uncertainty in the composition.
Despite this limitation, the Voyager radio-occultation profiles have formed the
basis of much of the analysis of Titan’s atmospheric structure, for example, in constructing global radiative-equilibrium and radiative-convective models (Samuelson,
1983; McKay et al., 1989). The occultation profiles have also been directly used in
the interpretation of IRIS spectra. Radiances in the thermal infrared depend both
on atmospheric temperature and the infrared opacity. In the absence of independent information, the separation of these two effects requires redundancy in the
infrared spectrum. This was generally not the case for the IRIS spectra, because
much of the thermal infrared spectrum accessible to IRIS was dominated by aerosol
opacity, whose heterogeneous distribution is not known (see Flasar (1998b) for a
discussion). Hence, it was not possible to retrieve atmospheric temperatures from
the spectra over most altitudes. Temperatures could only be retrieved in the upper
stratosphere, using the ν4 -band of CH4 as a “thermometer”, under the assumption
of a uniform abundance of CH4 in the stratosphere (Flasar, 1998a). Some information on physical temperatures was also available at the tropopause and at the
surface (Flasar et al., 1981). The latter was possible because of a “window” that
occurs in the thermal infrared spectrum near 530 cm−1 . Although surface emission
is an important component of the radiances here, the stratospheric emission is not
negligible.
Several studies of the spatial distribution of stratospheric compounds, based on
emission lines in the mid-infrared portion of the IRIS spectra, have relied on the
radio occultation refractivity profiles. For instance, Coustenis and Bézard (1995), in
retrieving the meridional distribution of several hydrocarbons and nitriles, started
with a mean temperature profile based on the equatorial radio-occultation profiles.
They assumed that temperatures in the troposphere did not vary meridionally, but
rescaled temperatures in the stratosphere to vary linearly with altitude from the
radio-occultation profiles at the 40-mbar level, just above the tropopause, to the
temperatures retrieved from the IRIS spectra in the upper stratosphere. Similarly,
Courtin et al. (1995) and Samuelson et al. (1997) compared synthetic spectra, computed from temperature profiles derived from the radio occultation refractivities,
with IRIS spectra in the far-infrared (200–600 cm−1 ) to constrain the distribution
of tropospheric CH4 . They both reached the amazing result that, in a global sense,
CH4 in the middle and upper troposphere must be supersaturated to provide the
opacity needed to yield a good match between the synthetic and observed spectra.
Samuelson et al. (1997) went on to derive the meridional distribution of tropospheric
CH4 , including that near the surface. To do this, they had to account somehow for
temperature variations in the troposphere. In effect, they used the IRIS spectra to
constrain the temperatures at the tropopause and at the surface, and assumed that
36
A. J. KLIORE ET AL.
occultation profiles retained their general shape with latitude. Although this is not
unreasonable, it still remains an educated guess.
The Voyager 1 radio occultation data provided one of the few indications of
waves in Titan’s atmosphere. Hinson et al. (1983) analyzed the intensity scintillations found in the occultation profiles. They found a region of weak scintillation
extending from 25 to 90 km altitude that they attributed to a vertically propagating
internal gravity wave with little or no attenuation. At 44 km, near the tropopause,
the implied vertical and horizontal wavelengths were 1 km and 4 km, respectively,
and the wave amplitude was ∼1 K. They also detected strong scintillations over the
altitude range 5–10 km. Later simulations by Friedson (1994) suggested that these
might be attributed to an internal gravity wave that saturates and breaks near 15
km (see Flasar (1998b) for a more detailed review). Hinson and Magalhães (1991)
have discussed how an atmospheric wave modulates a radio wave as it traverses
an occulting atmosphere and is refracted. The amplitude response of the signal is
dominated by diffraction effects, and it is most sensitive to atmospheric
√ structure
on scales that are smaller than the diameter of the first Fresnel zone, 2 λD, where
λ is the wavelength of the radio wave, and D the distance of the spacecraft to the occulting limb. The contribution
from larger-scale fluctuations is filtered out. For the
√
Voyager occultation, 2 λD ≈ 1–3 km at the S- and X-band wavelengths, and it is
not surprising that Hinson et al. (1983) detected waves with a vertical scale that was
comparable to this. The phase response of the received signal, on the other hand, is
dominated by atmospheric structure with vertical scales that are large compared to
the Fresnel scale, for which diffraction effects are small. The temperature profiles
of Titan’s atmosphere retrieved from the Voyager occultations do suggest some
larger-scale wave-like structure (Lindal et al., 1983), but the characterization of
this is incomplete. While systematic analyses of the phase scintillations have been
performed on radio occultation soundings of some of the outer planets (Hinson and
Magalhães, 1991, 1993), such a study has yet to be undertaken for the Titan data.
The Cassini radio science experiment is more capable than Voyager’s, and it has
several attractive features relevant to the issues discussed. One of the most important
is that the orbiter will provide a distribution of Titan occultations with latitude,
so that temperature profiles can be retrieved from measurements instead of from
inspired guesswork. The Cassini thermal infrared spectrometer, CIRS, is also much
improved from its predecessor, IRIS. It extends to longer wavelengths through the
submillimeter portion of the spectrum, which will permit the pressure-induced S(0)
line of N2 to be used as another “thermometer,” probing the upper troposphere and
middle and lower stratosphere (Flaser et al., 2004). However, except for the surface,
CIRS cannot retrieve temperatures below 30 km altitude. The radio occultation
soundings provide the only means of doing so from the orbiter. By virtue of its limb
sounding capability, CIRS can use the 530 cm−1 radiances observed on the limb, for
which deep space is the background, to subtract the stratospheric contribution to the
radiances observed in nadir viewing, so that the surface emission and temperature
can be better determined. The combination of this with radio occultation refractivity
CASSINI RADIO SCIENCE
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profiles will permit a more accurate determination of the distribution of CH4 in the
lower troposphere.
The latitude coverage will also provide important information on the zonal wind
field, through application of Equations (26) and (27) to the retrieved pressures and
temperatures, as discussed earlier for Saturn. With only two equatorial occultations,
this was not possible with the Voyager data. The ability to assign a reference altitude
scale to the zonal wind velocities may be even more important for Titan than for
Saturn, as the identification and tracking of discrete features by the ISS and VIMS
experiments to determine horizontal wind velocities will probably be more difficult
for the former body.
Figure 2 depicts the characteristic vertical resolution of the occultations over
the altitude range in which temperature and pressure profiles will be retrieved.
Because the USO on Cassini is a factor of 20 more accurate than the one used
by Voyager, atmospheric refraction should be detectable at higher altitudes, and
temperature and pressure profiles up to 300
√ km altitude should be achievable. In
the stratosphere, the vertical resolution is 2 λD. The vertical resolution is higher in
the troposphere, because differential refraction and defocusing become important,
and the Fresnel zone flattens vertically (Haugstad, 1978; Karayel and Hinson, 1997).
Figure 2 indicates that vertical resolution lies between ∼1 km and 100 m, depending
on the altitude and wavelength used, with Ka-band soundings providing the higher
resolution. As discussed earlier, in Section 2.4, higher resolution is possible through
inverse Fresnel reconstruction techniques. Although planetary atmospheres present
Figure 2. Vertical resolution (solid curves) of temperature profiles on Titan retrieved from radio
occultations at S-, X-, and Ka-bands, for a nominal spacecraft-to-occulting limb distance of 5000 km.
Dashed curve: temperature retrieved from Voyager radio occultation soundings below 200 km, after
Lellouch et al. (1989); above 200 km, temperatures are from Yelle’s (1991) model.
38
A. J. KLIORE ET AL.
a more complex situation than rings, which behave as sharp edges in a vacuum,
recent work on sub-Fresnel-scale inversion for atmospheres has been encouraging
(Karayel and Hinson, 1997).
The high vertical resolution afforded by radio science is important for elucidating several atmospheric phenomena. In addition to resolving a large spectrum of
vertically propagating waves, already discussed, the occultation soundings should
be able to detect any thin cloud or aerosol layers in the stratosphere or troposphere, provided they have sufficient opacity to modify the temperature profile.
The structure of the convectively mixed planetary boundary layer is of interest
in understanding the exchange of heat and volatiles between the atmosphere and
surface. The Voyager occultations indicate that the mixed layer extends to ∼4 km
altitude at the equator, but its altitude probably varies with latitude. On Earth, the
structure of the planetary boundary layer is complex, reflecting both dry and moist
convective processes. Often the upper boundary is marked by a sharp stable inversion as, for example, at the top of the trade cumulus layer at subtropical latitudes
(see e.g., Augstein, 1978). The latitude variation of the the top of the planetary
boundary layer can be indicative of meridional circulations in the troposphere,
with subsiding regions characterized by lower heights of the boundary layer. Aside
from the Huygens atmosphere structure investigation on the probe, which will take
data at only one location, radio occultations will provide the highest resolution of
tropospheric vertical structure.
The addition of a new wavelength [Ka band, 0.94 cm] should prove very important for atmospheric studies. In addition to providing the highest vertical resolution,
it may prove to be an important probe of atmospheric absorption. Voyager occultations gave no indication of atmospheric absorption at S- and X-bands (Lindal et
al., 1983), but the absorption properties of Titan’satmosphere in the Ka-band are
not known.
2.5.1.2. Ionospheres.
a) Introduction: Any object in our solar system that has a neutral gas envelope
surrounding it, due either to gravitational attraction (e.g., planets) or some other
processes such as sublimation (e.g., comets), has an ionosphere. Radio occultation
observations during the flybys of the Pioneer 11 (Saturn) and Voyager 1 and 2 spacecraft have clearly established the existence of a robust ionosphere around Saturn.
The retrieved electron density profiles exhibit primary maxima at altitudes 2000–
3000 km above the 1-bar level. Those from Pioneer, in particular, exhibit a complex
structure that suggest multiple layers of ionization. Multiple-layer structure in the
Voyager ionospheric profiles is much more subdued, but this may be in part due to
the fact that they were inverted only for higher altitudes. Originally, these profiles
were retrieved only for 1500 km or higher (one profile from Voyager 2 did extend
down to 700 km) (Eshleman et al., 1979a,b). Recently, Hinson et al. (1998a) have
extended the electron density retrievals from the Voyager 2 occultations by Jupiter
down to 300 km, and at the lower altitudes layered structure is quite in evidence.
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The Pioneer measurements were carried out using a single frequency S-band
signal, the Voyager measurements employed dual frequencies at S and X-bands.
The signal-to-noise ratios achieved in the Voyager observations were significantly
better than the Pioneer ones. Furthermore the dual frequency technique is particularly advantageous in the signal analysis/inversion process in the presence of sharp
ionospheric layers, which may lead to multipath propagation.
The three-frequency Cassini radio science subsystem will provide opportunities
to obtain a significant number of new and high quality electron density profiles with
a good coverage of latitudes and local time. These density profiles, combined with
information on the time variation of the peak electron density values, to be deduced
from the observations of Saturn electrostatic discharges (SED’s) by the plasma
radio wave experiment, will help to advance our understanding of the physical
and chemical processes controlling the behavior Saturn’s ionosphere. Furthermore,
ionospheric information, combined with upper atmospheric data from the UV occultation experiment will also help to elucidate the aeronomy of Saturn’s upper
atmosphere.
The radio occultation data from the flyby of Titan by the Voyager 1 spacecraft
provided an estimate of the peak electron density at a solar zenith angle near the
terminator. Cassini will provide, during its baseline mission, further occultation
opportunities, with improved signal-to-noise ratios. The information from these
occultations, combined with in situ measurements of the ionospheric plasma, will
lead to major advances in describing Titan’s aeronomy.
b) Saturn: As indicated above our presently available direct information regarding the ionosphere of Saturn is based on a handful of electron density profiles obtained by radio occultation measurements and peak electron density values deduced
from SED’s. This information, combined with neutral atmospheric data obtained
mainly from UV occultation measurements, has been used develop our present
understanding of Saturn’s ionosphere. The major neutral constituent in Saturn’s
upper atmosphere is molecular hydrogen, therefore the major primary ion, which
is formed by either photoionization or particle impact, is H+
2 . In the equatorial and
low-latitude regions electron–ion pair production is believed to be mainly due to
solar EUV radiation, while at higher latitudes impact ionization by precipitating
particles becomes very important. Although over 90% of all initial ions produced
are H+
2 , their actual concentration is very small, because they undergo rapid charge
transfer reactions. The rest of the discussion in this section will be based, for the
sake of brevity, on photoionization (photodissociation) only, because particle ionization leads to similar products and processes. Solar radiation with wavelength
short of 2768, 804, and 686 Å,respectively, leads to
H2 + hν → H + H,
H2 + hν →
H+
2
+
+ e,
H2 + hν → H + H + e.
(29)
(30)
(31)
40
A. J. KLIORE ET AL.
The resulting neutral atomic hydrogen can also be ionized
H + hν → H+ + e.
(32)
At high altitudes where hydrogen atoms are the dominant neutral gas species,
H+ can only recombine directly via radiative recombination, which is a very slow
process, given the recombination rate of order ∼10−12 cm−3 s−1 . It was suggested
some time ago that H+ could charge-exchange with H2 excited to a vibrational
state ν > 4. The vibrational distribution of H2 is not known, but recent calculations
(Cravens, 1987) appear to indicate that, while there are some vibrationally excited
molecules present at Saturn, the corresponding charge exchange rate is not significant. H2 is very rapidly transformed to H+
3 , especially at the lower altitudes where
H2 is dominant; H+
then
in
turn
undergoes
dissociative recombination
3
+
H+
2 + H2 → H3 + H,
(33)
H+
3 + e → H2 + H.
(34)
Significant uncertainties have been associated with the dissociative recombination rate of H+
3 . However, recent measurements have shown that the rate is rapid,
even if the ion is in its lowest vibrational state (Sundstrom et al., 1994). Models
based upon the above discussed processes predict an ionosphere which is predominantly H+ , because of its long lifetime (∼106 s). In these models H+ is removed by
downward diffusion to the vicinity of the homopause (∼1,100 km), where it undergoes charge exchange with heavier gases, mostly hydrocarbons such as methane,
which in turn are lost rapidly via dissociative recombination. The main difficulties
with these models are:
1. the calculated ionospheric density at the apparent main peak is about an order
of magnitude larger than the observed one;
2. the altitude of the calculated ionospheric main peak is much lower than the
observed one; and,
3. the predicted long lifetime of H+ is inconsistent with the observed large diurnal
variations in the electron density peak.
A number of suggestions have been put forward during the last decade in order
to overcome these difficulties. The most recent and successful models are based
on the suggestion/assumption that water from the rings is being transported into
Saturn’s upper atmosphere, which then modifies the chemistry of the ionosphere.
The presence of H2 O results in the following catalytic process
H+ + H2 O → H2 O+ + H,
(35)
H2 O+ + H2 O → H3 O+ + OH,
(36)
+
H3 O + e → H2 O + H.
(37)
A block diagram of the chemistry scheme involving water is shown in Figure 3.
The models which take into account this water chemistry and the recent values of
CASSINI RADIO SCIENCE
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Figure 3. Block diagram of the chemistry scheme, including water (from Schunk and Nagy, 2000).
Figure 4. Calculated and measured (solid lines) ion densities for the ionosphere of Saturn. The
calculations take into account the inux of water and a soft electron precipitation source (from Waite
and Cravens, 1987).
+
+
the recombination rate for H+
3 , lead to ionospheres consisting mainly of H , H3
+
and H3 O . It was shown that a downward flux of water from the rings into the
atmosphere of the order of 1–10 × 107 cm−2 s−1 leads to electron density values
consistent with the observations (see Figure 4); however, no current model has
been able to reproduce the implied large diurnal variations (Majeed and McConnell,
1996).
c) Titan: Titan is surrounded by a substantial atmosphere and therefore one
expects a correspondingly significant ionosphere. The only opportunity for a radio
42
A. J. KLIORE ET AL.
occultation measurement of such an ionosphere occurred when Voyager 1 was
occulted by Titan. A careful analysis of those data by Bird et al. (1997) found that
the peak electron density is about 2.4 × 103 cm−3 .
Indirect evidence of the existence of an ionosphere was also obtained by the
low-energy plasma analyzer measurements in the plasma wake. The various ionization sources which may be responsible for the formation of Titan’s ionosphere
are solar Extreme Ultra-Violet (EUV) radiation, photoelectrons produced by this
radiation, and magnetospheric electrons. Cosmic rays can cause some low altitude ionization (e.g., Capone et al., 1976) and proton and other ion precipitation
may also make some contributions. To complicate matters even further, it is possible that under certain circumstances, e.g., high solar wind pressure, Titan will
be beyond the magnetopause and in the magnetosheath of Saturn. Under these circumstances, the nature and intensity of the particle impact ionization source will
be quite different. Calculations to date have concentrated on EUV and magnetospheric electron impact ionization, the two sources believed to be the dominant
ones.
The next question which needs to be addressed is how do magnetospheric electrons reach the upper atmosphere. Gan et al. (1992) considered draped magnetic
field lines and assumed that electrons enter these field lines far down the wake
region at the “end” of these field tubes, for ram conditions, but can enter in a radial
fashion on the wakeside. Keller et al. (1992) found that, contrary to earlier suggestions, photoionization is the main source for the dayside ionosphere, followed
by photoelectron impact, and finally magnetospheric electron sources. Of course,
magnetospheric electrons must dominate in the nightside ionosphere. The comprehensive photochemical calculations of Keller et al. (1992), found that the electron
density peak is about 5 × 103 cm−3 at an altitude around 1,100 km, for χ = 60◦ ,
and that the peak density is 3 × 103 cm−3 , at an altitude of about 1,195 km, for
χ = 90◦ , close to the Voyager results. Similar results were obtained by Ip (1990),
using his model published a few years earlier. Both Ip (1990) and Keller et al.
(1992) predicted that HCNH+ is the major ion near the density peak. The block
diagram shown in Figure 5 indicates the production and loss pathways leading to
HCNH+ . Fox and Yelle (1997) and Keller et al. (1998) have published results from
their new Titan ionospheric models. The Fox and Yelle (1997) results indicate that
the pseudo-ion Cx H+
y (this is the sum of all ions with three or more carbon atoms)
is the major one. Their result is shown in Figure 6. The Keller et al. (1998) model
gives very similar electron densities and peak altitude. However, they still predict
that HCNH+ is the major ion in a narrow region near the peak; the sum of the heavy
hydrocarbon ions is also very significant in their model.
A variety of different studies examined the issue of the transition from chemical to diffusive control in the ionosphere. Simple time constant considerations,
as well as more detailed model solutions, have indicated that the transition from
chemical to diffusive control takes place in the altitude region around 1,500 km.
The magnetospheric plasma velocity (∼120 km s−1 ) is subsonic (∼210 km s−1 ) and
CASSINI RADIO SCIENCE
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Figure 5. Block diagram of a proposed ion chemistry scheme for Titan (from Schunk and Nagy,
2000).
Figure 6. Calculated electron density profiles for Titan, assuming particle impact ionization by 30
and 50 eV electrons (from Fox and Yelle, 1997).
superalfvenic (∼64 km s−1 ), therefore, no bow shock is formed and the magnetic
field is gradually slowed as it enters Titan’s exosphere by mass loading. The magnetic field strength increases, piles up and eventually drapes around Titan. This piled
up magnetic field, similar to the so-called magnetic barrier at Venus, is expected
to be the dominant source of pressure against the ionosphere. Using reasonable
magnetospheric parameters Keller et al. (1994) found that the total incident magnetospheric pressure is about 1.6 × 10−9 dynes cm−2 . Using a peak electron density
of 5 × 103 cm−3 , this means that if the corresponding plasma temperature is greater
than 700 K, the ionosphere is capable of holding off the external plasma. This
pressure corresponds to about 20 nT, much of which is convected into the upper
ram ionosphere, resulting in near-horizontal magnetic fields. Figure 7 is a pictorial
44
A. J. KLIORE ET AL.
Figure 7. Pictorial representation of the interaction of Titan’s ionosphere with magnetospheric plasma
on the ram side (from Keller et al., 1994).
representation of the situation for the ramside ionosphere. As indicated earlier,
there are a large number of cases that can be considered, such as full solar and
magnetospheric ionization sources, near-terminator conditions, and only magnetospheric sources.
d) Icy satellites: The environments of the icy satellites of Jupiter, Europa,
Ganymede, and Callisto, have been observed through radio occultations of the
Galileo spacecraft. Europa, and probably Callisto, were found to have a very tenuous ionosphere (Kliore et al., 1997) most likely produced by the sputtering effects
of Jupiter’s magnetospheric particles upon their icy surfaces (Johnson et al., 1998).
There are no deliberate occultations of Cassini by any of Saturn’s icy satellites
designed into the current satellite tour.
2.5.2. Techniques
2.5.2.1. The Radio Occultation Technique. Radio occultation, in which a spacecraft emitting one or more coherent monochromatic radio signals, appears to move
behind a planet or satellite as seen from the earth, affords an opportunity for the
spacecraft-to-earth radio links to traverse the ionosphere and atmosphere of the
occulting body. The interpretation of the observed effects of refraction by the planetary atmosphere and ionosphere allows one to determine the vertical electron
density structure in the ionosphere and the temperature–pressure profiles and absorption characteristics of the neutral atmosphere (c.f., Fjeldbo, 1964; Kliore et al.,
1964).
This technique has been applied successfully to measure the characteristics of
the ionospheres and atmospheres of Mars (Fjeldbo et al., 1968; Kliore et al., 1965;
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Kliore et al., 1969; Kliore et al., 1972a; Kolosov et al., 1975; Lindal et al., 1979),
Venus (Fjeldbo et al., 1971; Howard et al., 1974b; Kliore et al., 1967; Kolosov et
al., 1976; Kliore et al., 1979; Kliore and Patel, 1980a, 1982; Savich et al., 1986;
Jenkins et al., 1993; Kliore and Mullen, 1989; Kliore and Luhmann, 1991; Yakovlev
et al., 1991), Mercury (Fjeldbo et al., 1976a; Howard et al., 1974a), Jupiter (Kliore
et al., 1974; Fjeldbo et al., 1975; Fjeldbo et al., 1976b; Kliore et al., 1976, 1977;
Eshleman et al., 1979a,b; Hinson et al., 1997; Lindal et al., 1980, 1981; Flasar
et al., 1998), Saturn (Kliore et al., 1980b; Lindal et al., 1985; Tyler et al., 1981),
Uranus (Lindal et al., 1987; Tyler et al., 1986), Neptune and Triton (Tyler et al.,
1989; Lindal, 1992), Titan (Lindal et al., 1983), Saturn’s rings (Marouf and Tyler,
1985), and Jupiter’s satellites Io, Europa, Ganymede, and Callisto (Kliore et al.,
1975; Hinson et al., 1998a, in press; Kliore et al., 1997; Kliore et al., 1998a, b). The
radio occultation technique depends on being able to invert the observed changes in
the frequency and amplitude of the radio signals during the time of the occultation
to produce vertical profiles of the index of refraction and absorption coefficient. For
the case of spherical symmetry, in which the atmospheric structure depends only on
the radial distance from the center of the planet, the inversion techniques have been
firmly established (c.f., Fjeldbo and Eshleman, 1968; Kliore, 1972b). This technique
also provides a good approximation in the case of oblate planets, in which case the
center of refraction is determined by the local radius of curvature at the occultation
location (c.f., Kliore et al., 1976, 1977). The method by means of which which
the refraction angle, or bending angle, ε, and the ray asymptote distance, p, are
determined for each time t0 can be deduced with reference to Figure 8.
Figure 8. Geometry of a radio occultation observation.
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A. J. KLIORE ET AL.
Figure 8 displays the geometry in a plane defined by the position of the center
of refraction at time t0 (the time at which the photon in question came closest to
the center of refraction), the position of the spacecraft at time t0 − TSL (the time
when the photon was emitted from the spacecraft antenna), and the position of the
receiving antenna on earth at time t0 + TLE (the time when the photon reached the
receiving station, i.e., the time of the observation). These times and positions are
iteratively computed from the ephemerides of the spacecraft, the planet center, and
the earth center relative to the Sun, as well as the exact location of the receiving
station. This defines the plane of refraction at t0 . Referring to Figure 8, the Doppler
frequency observed with no refraction is
ν0
νE = v E ,
(38)
c
where vE is v · ê, the component of the planetocentric inertial spacecraft velocity v
in the plane of refraction, in the direction of the virtual earth (receiving station at
time of observation). If δν is defined as the frequency residual, relative to the “free
space” Doppler frequency, that is caused by a refractive bending angle ε, then it
may be shown that (c.f., Phinney and Anderson, 1968)
νE + δν
cos(ψE − β) =
,
(39)
νS
where
ν0
νS = v,
(40)
c
and,
vE
ψE = arccos
.
(41)
v
Equation (39) can then be used to determine the angle β, which under the usual
condition of REL RSL is equal to the bending angle, ε. The corresponding ray
asymptote distance (ray parameter), p, can then be computed as
p = RS sin(α + β),
(42)
where
cos α = ê · ŝ,
(43)
and ŝ is the unit vector from the spacecraft position to the center of refraction. The
actual bending angle is then
RSL
ε = β + arcsin
sin β
(44)
REL
Thus, for each time of observation t0i one can determine the corresponding
bending angle and ray parameter, (εi , pi ). In order to invert these data to obtain a
vertical profile of the index of refraction, it is necessary to make use of the Abel
CASSINI RADIO SCIENCE
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integral transform (c.f., Fjeldbo and Eshleman, 1968; Fjeldbo et al., 1971; Kliore,
1972b). In a spherically stratified medium, the refractive bending angle can be
expressed as
∞
dχ
dn
ε( p) = −2 p
.
(45)
dχ n χ 2 − p 2
p
where n is the index of refraction. The inverse transform is then
1 ∞ ε(ξ )dξ
ln n( p) =
,
π p
ξ 2 − p2
and the radius of closest approach of the ray, r0 , corresponding to n(r0 ) is
p
.
r0 =
n( p)
(46)
(47)
The index of refraction in an atmosphere is very nearly 1.0, therefore it is more
convenient to work with the refractivity, which is defined as
N = (n − 1) × 106 .
(48)
In order to calculate profiles of pressure and temperature from the refractivity,
it is necessary to define the chemical composition of the atmosphere. For the outer
planets, the neutral atmosphere can be assumed to consist of hydrogen and helium.
Under those conditions, the mass density, ρ, in g cm−3 is related to the refractivity
by
ρ=
m̄ N
,
Rq
(49)
where m̄ is the mean molecular weight
m̄ = f H2 m H2 + (1 − f H2 )m He ;
(50)
and q is the specific refractivity
q = 0.26943(135.77 f H2 + 34.51(1 − f H2 )).
(51)
In the above equations, f H2 is the number fraction of hydrogen in the atmosphere,
the numerical refractivities of hydrogen and helium in Equation (51) are from
Newell and Baird (1965), and R is the universal gas constant. Assuming that the
atmosphere is in hydrostatic equilibrium
d P = g(z)ρ(z)dz,
and hence
P(r ) = P0 +
r0
P(z)g(z)dz,
r
(52)
(53)
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A. J. KLIORE ET AL.
and the temperature is computed from the perfect gas law, as follows:
r0
m̄
N (r0 )
T (r ) = T0
+
N (z)g(z)dz.
(54)
N (r )
R N (r ) r
Thus, once one has a profile of the index of refraction in an atmosphere, and
its chemical composition, any other geophysical property of the atmosphere can be
readily computed. In case of the ionosphere, since the index of refraction is dependent only on the number of free electrons, it is independent of the ion composition
of the ionosphere, and so the refractivity is directly related to the electron density,
as follows:
n e (r ) = 2.479 × 10−14 N (r )ν02 ,
(55)
where ν0 is the transmitted frequency in Hz, N (r ) is the refractivity in n-units, and
n e (r ) is the electron density in cm−3 .
The effects of absorption and scattering in a planetary atmosphere can be described by the absorptivity (or, absorption coefficient), (σ )(r ), having units of
dB km−1 , as follows:
∞
τ (r ) = 2
σ ds.
(56)
r
In Equation (56), τ represents the total absorptive attenuation, or extinction
along the path of the ray, in dB as follows:
I
= −τ
(57)
10 log
I0
where I is the intensity of the signal. For a refracted ray tangentially propagating
through a spherically stratified atmosphere with index of refraction n(r ), Equation
(56) becomes
∞
τ ( p) = 2
p
σ (χ)
dr (χ )
dp
χ dχ
χ 2 − p2
,
(58)
and this can be inverted by using the Abel integral transform pair, c.f., (Jenkins
et al., 1993) to yield the absorptivity
∞
1
τ (ξ )ξ dξ
dp(r ) d
σ ( p) = −
.
(59)
πP
dr
dp p
ξ 2 − p2
It is customary to express the attenuation of a radio frequency signal in decibels
relative to an unattenuated signal power level, W0
W0
A(z) = 10 log
(60)
W (z)
The attenuation due to absorption is obtained by subtracting refractive defocusing attenuation and correcting for antenna mispointing
τ (z) = A(z) − Adef (z) + Acorr (z),
(61)
CASSINI RADIO SCIENCE
where
dε(z)
,
Adef (z) = 10 log 1 − D(z)
dz
49
(62)
and
ε(z)
.
(63)
2
The value of the optical depth, τ (z) is then
ln 10
(64)
0.23026Aa .
τ (z) = Aa (z)
10
When a profile of the absorptivity, σ (z) is obtained through the procedure outlined above, it can be used to infer the abundances of specific absorbers in the atmosphere, such as NH3 and PH3 in the atmosphere of Saturn, and the three frequencies
available on Cassini will make it possible to determine their relative abundances.
Radio occultation data from oblate or otherwise not spherically symmetrical bodies
can also be inverted by applying raytracing techniques (Lindal, 1992; Melbourne
et al., 1994)
D(z) = RS (z) cos(α + β) + p(z)tan
2.5.2.2. Limb Tracking Maneuvers. During an occultation experiment,
monochromatic waves at X, S, and/or Ka bands are downlinked to earth by the
spacecraft high-gain antenna, using the onboard ultrastable oscillator to maintain
coherence. When a planetary body with an atmosphere begins to occult the spacecraft, the radio wave transmitted from the spacecraft to earth traverses the atmosphere and is refracted. In a neutral atmosphere, the molecular constituents raise the
index of refraction above one, and the wave is refracted toward higher atmospheric
densities, more or less inward along the potential gradient. In an ionosphere, the
electrons dominate refraction, and decrease the index of refraction to less than one.
In this case the wave is refracted away from high electron densities. In general,
the ionospheric electron density does not increase monotonically with depth, and
there can be isolated peaks in electron density. The refraction of radio waves away
from these peaks can cause complicated diffraction patterns, leading to so-called
multipath effects with different frequencies being detected simultaneously at earth
(see e.g., Fjeldbo et al., 1971; Hinson et al., 1997).
The effects of the atmosphere on the index of refraction are small. In the neutral
portion of the atmosphere, these are largest at the highest barometric pressures
traversed by the radio waves. At the surface of Titan (≈1.5 bar) or at the 1–2 bar
level on Saturn, where NH3 will likely extinguish the received signal, the index
of refraction deviates from 1 by only 10−3 . In ionospheres, the differences are
even smaller, typically 10−6 at S-band for an electron densities of 1 × 105 cm−3 ,
less at X and Ka wavelengths. (The change to the index of refraction induced by
electrons is proportional to the square of the wavelength in the radio spectrum; in
a neutral atmosphere, the change is independent of wavelength.) However, these
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A. J. KLIORE ET AL.
Figure 9. Idealized geometry for that portion of the entry phase of an occultation when the radio
waves traverse the neutral portion of an atmosphere.
small differences, particularly in the neutral atmosphere, can induce large enough
changes in the direction of the propagation of the radio wave and in its frequency in
the earth-fixed frame of reference, relative to what would occur in the absence of the
atmosphere, that an active strategy is required to avoid loss of the received signal.
Figure 9 illustrates an idealized geometry for that portion of the entry phase of
an occultation when the radio waves traverse the neutral portion of an atmosphere.
Here, the spacecraft moves on a trajectory perpendicular to the earth–spacecraft
line of sight, but this does not materially affect the following discussion. During
entry the radio waves, depicted as rays in the figure, progressively traverse deeper
layers of the atmosphere, and the bending angle, ε, increases. At the surface of
Titan, the bending angle amounts to 2◦ ≈ 34 mrad, and this is also comparable to
that at the 2-bar level in Saturn’s atmosphere. This angle is close to the full-width at
half power of the S-band diffraction limited spacecraft high-gain antenna pattern,
but much larger than those at X-band (9 mrad) and Ka-band (2 mrad, designed to
be slightly defocussed from the diffraction limit).
Hence the spacecraft high-gain antenna must continuously track the virtual image of earth on the occulting limb in order to avoid loss of the signal. This is
necessary not only to maintain lock in the Doppler tracking, but also to measure
the signal intensity accurately. The observed attenuation is the sum of that from refractive defocusing and that from absorption by the atmosphere. The former results
from the rays being refracted through larger angles as they successively lie deeper
in the atmosphere (Figure 9). This can be computed once the Doppler shifts in frequencies from refraction in the atmosphere are determined. The absorption is the
difference between the observed attenuation and that computed from defocusing.
It is important to distinguish between variations in signal intensity from atmospheric effects and those associated with errors in maintaining the virtual image
of earth in the boresight of the antenna beam. Inevitably errors in both spacecraft
CASSINI RADIO SCIENCE
51
pointing control (currently 2 mrad) and reconstruction (much smaller) arise during
an occultation, and these need to be minimized.
The effects of refraction must also be taken into account when selecting the
frequencies from the local oscillator to mix with the received signal at the DSN
tracking station and the bandwidth to be used for the digitized recordings. The
mixing must be done in order to convert the GHz frequencies of the received signal
to the kHz, or audio-range, so that digitization of the signal is possible. From
Figure 9, the Doppler shift in frequency from refraction is given approximately as:
v
δν = ν0 ε
(65)
c
for small ε to first order in v/c, where v denotes the planetocentric spacecraft
velocity component normal to the earth direction in the plane of refraction. For
typical Titan occultations, this velocity is at most 5.6 km s−1 . With ε ≈ 34 mrad,
ν/ν ∼ 6 × 10−7 , or ν ∼ 1.5 kHz at S-band.
Generating the local oscillator frequency record for the receiving station thus
requires a model atmosphere for the occulting body to simulate the effects of
refraction on the frequency shift, so as to maintain the mixed signal near the center
of the audio-range recording bandwidth. The bandwidth itself is selected to account
for navigation errors and actual variations in atmospheric properties from the model.
Typically, this is chosen as conservatively as possible to minimize the possibility
of signal loss without making the digitized recordings intractable. For example,
Galileo radio occultations by Jupiter and its satellites were recorded with a 2.5-kHz
bandwidth at S–band (see e.g., Hinson et al., 1997; Kliore et al., 1997). Voyager
occultations of the outer planets and Titan were recorded at larger bandwidths, as
these atmospheres were less well characterized at the time: 5–25 kHz was typical
at S-band, with the exception of 50 kHz for Saturn, because of the wider bandwidth
required for the adjacent occultation of its rings (Lindal et al., 1981, 1983, 1985a, b,
1987, Lindal, 1992).
2.5.3. Major Requirements
As in the case of ring occultations, the quality of atmospheric and ionospheric
occultation data depends on the phase and amplitude stability of the three radio
links, the signal-to-noise ratio available on these links, and the orbital geometry
which defines the occultation locations on the target body and their characteristics.
Since atmospheric and ionospheric occultations will be conducted only in the oneway mode, the discussion of the USO stability and the SNR in Section 2.4.3 applies
equally here. The requirements on the orbital geometry are given below.
The requirements for Saturn occultations are as follows:
1. A sufficient number of Saturn occultations well spaced in latitude in both the
Northern and the Southern hemispheres. This is needed to provide data on zonal
wind speeds at different altitudes and latitudes, as well as to sample the ionosphere structure and the ammonia abundance at different latitudes.
52
A. J. KLIORE ET AL.
The requirements for Titan occultations are:
1. A sufficient number of Titan occultations well spaced in latitude in both hemispheres to provide data for the derivation of the global zonal circulation of Titan’s
atmosphere.
2. An adequate sampling of the ionosphere at different locations relative to the
magnetospheric ram direction.
3. Occultations that are not fast enough to require the use of thrusters to carry out
the limb-tracking maneuvers (Section 2.5.2.2).
3. Radio Science Instrument
3.1. OVERVIEW
Among the Cassini instruments, the radio science instrument is unique in that is
not confined to the spacecraft, and that part which is on the spacecraft is distributed
among several subsystems. It can be regarded as a solar-system-sized instrument
observing at microwave frequencies, with one end of the radio path on the spacecraft
and the other end at DSN stations on the ground.
3.1.1. Functional Description
Figure 10 shows a functional block diagram abstracting those elements of the
Cassini orbiter and the DSN that make up the radio science instrument. The instrument operates in two fundamental ways, distinguished by whether the microwave
optical path has one or two legs.
For two-way measurements, the uplink can be a single carrier signal at either
X-band (∼7.2 GHz) or Ka-band (∼34 GHz), or both carriers can be transmitted
at the same time. These signals are generated by the DSN receiver/exciter system,
using as a reference the local frequency and timing system. The DSN frequency
standard is a combination of a Hydrogen Maser and a Sapphire Cavity Oscillator.
The uplink signals are amplified, radiated through feed horns, and collimated by a
large parabolic ground antenna, which is continuously aimed at the Cassini spacecraft. The actual transmission frequencies can be adjusted to allow the spacecraft
receivers to lock to the uplink signals and to compensate, finite steps, for the main
part of the Doppler effect between the earth and the Cassini Orbiter. In this mode
spacecraft radio equipment forms a repeater, collecting the carrier signal with the
spacecraft’s high gain antenna (HGA), transforming it to one or more downlink
frequencies (2.3 GHz, 8.4 GHz, or 32 GHz) that are coherent with the uplink, amplifying and re-collimating it, and sending it back to earth. The returning signal is
detected using DSN ground receiving equipment, amplified and downconverted,
and recorded for later analysis. In a variant of the two-way mode, the downlink is
received at a different ground station; this three-way technique has been found very
CASSINI RADIO SCIENCE
53
Figure 10. The distributed radio science instrument.
useful to isolate anomalous noise sources and to improve the science return from
most of the radio science experiments.
For one-way measurements, the signal source is on board the Cassini orbiter.
The output from on-board ultrastable oscillator (USO) is transformed to downlinks at S-band (2.3 GHz), X-band (8.4 GHz), or Ka-band (32 GHz) by elements
in the radio frequency subsystem (RFS) and radio frequency instrument subsystem (RFIS). These signals are amplified and radiated through the HGA toward
earth. After passing through the medium of interest, the perturbed signal is collected by a DSN antenna, amplified and downconverted, and recorded for later
analysis.
3.1.2. Measurements
The scientific observables are phase, frequency, and amplitude perturbations on the
S-, X-, and Ka-band signals that are transmitted between the spacecraft and the
ground. These perturbations are induced by:
– passage through atmospheres, ionospheres, plasmas, and populations of particles
(rings);
– gravitational accelerations of the spacecraft caused by nearby masses;
– relativistic effects.
Because the perturbations induced by the phenomena under investigation are
very small, it is essential that sources of obscuring noise be minimized. The
54
A. J. KLIORE ET AL.
contribution of the Doppler effect due to the spacecraft and ground antenna motions
must be removed, which is a key step in the processing of the data. In the spacecraft
and ground equipment, this means that all components have to preserve as much
dimensional and electrical stability as can be accomplished within mass, power,
and environmental constraints. The key characteristics of the radio frequency (RF)
signals have to be maintained over short and long integration times. Short-term stability is generally measured as phase noise. Stability over longer integration times
is described by the so-called Allan deviation parameter σ y , a statistical measure of
contiguous differences of frequency measurements. In general, the requirements
are that phase noise be ≥60 dB below the carrier in the frequency bands where
radio science measurements are made, and that the Allan deviation range from
2 × 10−13 at 1-second integration time to 1 × 10−15 at 1000-second integration
time.
Investigations dealing with the composition, chemistry, and dynamics of planetary atmospheres and ionospheres use the instrument in its one-way mode at
all three downlink frequencies. Ring studies and measurement of general relativistic time delay during solar conjunction are also conducted using the noncoherent mode. Data samples for these experiments are integrated over short
times (≤1–100 s), where the USO-driven signal provides the best stability. In
the one-way mode, measurements can be started immediately after the spacecraft
emerges from behind a planet or satellite. Using the one-way mode avoids potential lock up problems associated with a deep egress atmospheric occultation.
The one-way path also avoids complications that would be introduced into data
analysis by two passages, separated in time and space, through the target under
study.
Two-way Doppler experiments in cruise and during the tour use the same link
system, X-band and Ka-band (when available) uplink and downlink. An additional
observable is provided by the possibility of locking to the X–band uplink an additional Ka-band carrier downlink as shown in the Riley report (Riley et al., 1990).
This will allow essentially complete calibration of the plasma contribution to the
noise, which is the crucial factor in two way experiments, especially during conjunction experiments, when the signal propagates through the heavily ionized and
turbulent medium of the solar corona. This is a necessary condition for the coherent
reconstruction of the signal over the long duration of the experiment.
3.2. SPACECRAFT E LEMENTS
On the Cassini Orbiter, the radio science instrument is encompassed in the radio
science subsystem (RSS). RSS is really a virtual subsystem in that it is composed
of elements from three spacecraft subsystems, two of which have other functions
to perform as well. The subsystems that participate in RSS are the RFIS, the RFS,
and the Antenna Subsystem. Figure 11 illustrates the elements of the subsystems
that make up RSS, and the RF paths through the instrument that are involved in
CASSINI RADIO SCIENCE
55
Figure 11. Radio frequency paths through the Cassini Orbiter radio science subsystem for two-way
configuration (a) and one-way configuration (b).
its various operational modes. Figure 11a shows the signal paths available when
the instrument is in two-way configuration, while Figure 11b shows those for the
one-way configuration. In each case the active signal paths and subassemblies are
depicted in bold.
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A. J. KLIORE ET AL.
3.2.1. Radio Frequency Subsystem
The primary function of the RFS, a redundant critical engineering subsystem, is
to support spacecraft telecommunications. RFS receives commands and transmits
telemetry at X-band; its carrier is also the source of the X-band downlink signals
used by radio science. For radio science purposes, the key components are the USO,
the deep space transponders (DSTs) and the X-band traveling wave tube amplifiers
(X-TWTAs).
The RFS has three modes of operation:
– two-way coherent mode, where the receiver in the DST is locked to the uplink
and the downlink is referenced to, or coherent with, that uplink;
– two-way noncoherent mode, where the receiver is locked to the uplink and the
exciter in the DST is referenced to either the USO or the transponder’s auxiliary
oscillator; and
– one-way mode, where there is no uplink and the exciter is referenced to either
the USO or the transponder’s auxiliary oscillator.
When RSS is operating in two-way mode, RFS is in its two-way coherent mode.
The active DST receives a 7.2 GHz uplink signal from the HGA or one of the
two low gain antennas (LGAs), amplifies it, and translates it by the ratio 880/749
into an 8.4 GHz downlink. The precise frequency of the uplink of course depends
on the Doppler shift experienced in its transit from the ground. The DSTs are
capable of locking onto a signal as low as -155.8 dBm. The DST also generates
input signals, coherent with the uplink, for the S-band transmitter (SBT) and the
Ka-band exciter (KEX) in the RFIS. For the SBT, a single input at 115 MHz
is supplied. The KEX receives input at 8.4 GHz and a reference signal at 115
MHz.
For one-way radio science experiments, RFS will be in either one-way or twoway noncoherent mode. The USO (the DST’s auxiliary oscillator is not stable
enough to use for radio science) provides a 115 MHz input to the DST exciter,
which multiplies it to 8.4 GHz for the X-band downlink and for the 8.4 GHz input
to the KEX. The SBT input and the 115 MHz reference signal for the KEX are sent
directly from the USO.
Cassini’s USO is a crystal oscillator based on a carefully selected 4.8 MHz
quartz resonator, which is housed along with its oscillator circuit and oven control
circuit in a titanium Dewar whose internal temperature is maintained constant to
within 0.001◦ C by a proportionally controlled oven. The USO’s 114.9 MHz output
provides a reference signal for the DST, SBT, and KEX that has exceptional shortterm phase and frequency stability.
The X-band downlink from the DST is amplified by the X-TWTA to 15.8 W,
and radiated to earth through the HGA or whichever of the two LGAs is active.
X-band is the only frequency available to radio science when the spacecraft is not
using the HGA.
CASSINI RADIO SCIENCE
57
3.2.2. Radio Frequency Instrument Subsystem
The elements in the RFIS are devoted exclusively to radio science. They include the
SBT, the KEX, the Ka-band Translator (KAT) and the Ka–band TWTA (K-TWTA).
Primary application of the SBT and the KEX is in one-way experiments, though the
KEX will also be used in two-way (X-up, Ka-down) mode. The SBT transmits a
13.5W, 2.3 GHz carrier derived from the 115 MHz reference provided by the DST,
through a diplexer contained in the probe receiver front end (RFE), to the HGA.
The KEX multiplies its 115 MHz reference by 11/3, mixes the result with its 8.4
GHz input, and multiplies by 4 to produce 32 GHz. That output is routed through
a hybrid coupler contained in the KEX subassembly to the K-TWTA.
Used only in two-way mode, the KAT turns a 34 GHz uplink signal from the HGA
into a coherent 32-GHz downlink using a 14/15 translation ratio. The translator is
capable of generating a downlink with 1000-second Allan deviation of 3 × 10−15
from input signals as low as −132 dBm. KAT output goes through the hybrid coupler
in the KEX subassembly and then to the K-TWTA . Amplification of Ka-band
output from both the KEX and the KAT, singly or simultaneously, is accomplished
in the K-TWTA. The amplifier produces a total output power of 7.2 W when
operating with one carrier and 5.7 W in dual-carrier mode. Like the SBT, it feeds the
HGA only.
3.2.3. High Gain Antenna
While all the Cassini Orbiter antennas are usable at X-band, only the HGA transmits
all the radio science frequencies. In addition to supporting telecommunications and
radio science, the HGA also serves as the transmit and receive antenna for the
Cassini Radar and for the probe relay link. It is the most complex antenna ever
flown on a planetary spacecraft, functioning at S-band, X-band, Ka-band, and Kuband. Its functions are illustrated in Figure 12 . The portions used for radio science
experiments or in-flight tests are highlighted.
Carrier signals transmitted between the spacecraft and the ground are all circularly polarized. X-band signals are received and transmitted with right-hand circular
polarization through the RFS A-string diplexer and with left-hand circular polarization through the B-string diplexer. The Ka-band uplink is left-hand circularly
polarized, the downlink right-hand circularly polarized. The S-band downlink is
right-hand circularly polarized. The S-band transmit signal path is shared between
the probe relay link and radio science.
3.3. G ROUND ELEMENTS
3.3.1. Deep Space Network
The DSN comprises three complexes around the globe, called the deep space communication complexes (DSCC), located in the desert of Southern California, near
Madrid, Spain, and near Canberra, Australia. Each complex is equipped with several tracking stations of different aperture size and different capabilities. Each
58
A. J. KLIORE ET AL.
Figure 12. The Cassini antenna subsystem, with radio science functions emphasized.
complex has one 70-m diameter station, one 34-m high-efficiency (HEF) station,
and at least one 34-m beam-wave-guide (BWG) station. Though their primary
functions are to send commands to and to receive telemetry from space probes,
these complexes have been designed to be an integral part of the radio science
instrument (Asmar and Renzetti, 1993). As such, their performance and proper
calibration directly determine the accuracy of Radio science experiments. The following subsystems of the DSN stations are relevant to acquisition of radio science
data (see Figure 13): the monitor and control subsystem, the antenna mechanical
subsystem, microwave subsystem, receiver–exciter subsystem, transmitter subsystem, tracking subsystem, spectrum processing subsystem, and frequency and timing
subsystem.
The monitor and control subsystem receives and archives information sent to the
complex from the control center at JPL. It also handles and displays responses to directives for configuration or information. Operator control consoles at the complex
central processing center allow centralized control of all station subsystems within
that complex. The center receives and distributes schedules of activities, sequence
of events, prediction files for pointing the antennas and tuning the receivers, and
other information.
The antenna surface performs two functions. As part of the receiving function, it
acts as a large aperture to collect incoming energy transmitted from a spacecraft and
CASSINI RADIO SCIENCE
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Figure 13. DSN subsystems relevant to the acquisition of radio science data.
focus it onto the feed horns. The subreflector is adjustable in the axial and angular
positions in order to correct for gravitational deformation due to the motion of
the antenna between zenith and the horizon. The primary surface is a paraboloid,
modified for optimized illumination and signal stability. As part of the transmitting
function, the antenna surface is used to form a narrow microwave beam that is
directed to the spacecraft.
The electronics handles the received signal in two main steps. First the microwave subsystem accepts the S-, X-, and/or Ka-bands (depending on the station)
and directs them via polarizer plates and microwave mirrors to low-noise amplifiers. Then the amplified signals are downconverted by local oscillators and routed
to the receivers. These two processes set the electronics contribution to the overall amplitude sensitivity (usually measured as system noise temperature) and frequency/phase stability (generally quantified in terms of Allan deviation and phase
noise respectively).
Two types of receivers (part of the receiver–exciter system) can be used: closedloop and open-loop. (The distinction is that the closed-loop receiver estimates
parameters such as phase and amplitude in real time with standardized values of
receiver bandwidths and time constants; the open-loop receivers record the predetection electric field for subsequent non-real time processing.) The closed-loop
receiver (Block V Receiver) is the primary DSN receiver for telemetry and tracking
data. It phase-locks to the signal carrier and demodulates science data, engineering
data, and ranging signals transmitted by the spacecraft. The tracking subsystem
measures Doppler shifts and ranging information based on the closed-loop receiver
output.
The open-loop receiver (called the radio science receiver) downconverts and
digitizes a selected bandwidth of the spectrum centered around the carrier signal.
It utilizes a fixed first local oscillator and a tunable second local oscillator that is
driven by a tuning “predict set” (predicted downlink frequency versus time) that
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A. J. KLIORE ET AL.
takes into account the relative motion between the spacecraft and ground station.
The predict set can also take into account the atmospheric effects of the planet
under study. With no real-time signal detection requirements, the open-loop system
provides flexibility in post–processing of the data. It is also designed with stringent
requirements on amplitude, frequency and phase noise stability. Additional advantages of the open-loop reception include the simultaneous handling of signals in two
polarization states as well as capturing multiple signals resulting from multipath
propagation between the spacecraft transmission and the earth reception.
The transmitter subsystem utilizes a frequency reference to synthesize the uplink
frequency channel assigned to a specific spacecraft. It also has the capability to tune
the uplink to account for the Doppler shift on the uplink. The DSN can transmit at S-,
X- or Ka-bands depending on the transmitting station and the receiving spacecraft.
A record of the transmitted frequencies is saved for post-processing of the two-way
Doppler observable, as necessary.
The frequency and timing subsystem provides a reference that drives the local oscillator devices throughout the complex. Global positioning system (GPS) satellites
are utilized for inter-complex timing calibration. Currently centered on hydrogen
masers, the frequency and timing system will be upgraded to include additional
devices to meet the Cassini requirements including a linear trapped ions standard
with a cryogenic local oscillator and a feedback-stabilized frequency distribution.
Performance of the frequency and timing subsystem to fractional frequency stabilities of order 10−15 for integration times of 1000 s, as well as phase noise lower than
−75 dBc at 100 Hz from a Ka-band carrier, is fundamental to many radio science
observations.
3.3.2. 70-m Stations
The 70-m diameter stations of the DSN (DSS-14, DSS- 63, and DSS-43) are currently equipped for transmission at the S-band frequencies and reception at S- and
X-band frequencies. Future upgrades to transmit at X-band are possible. The microwave subsystem allows reception at both polarizations such that the right circular
polarization (RCP) and left circular polarization (LCP) components of each band
can be received via the radio science System. Accurate pointing of the 70-m stations
is achieved by either active conical scanning or via blind pointing, driven by predicts of the spacecraft’s position on the sky. It is anticipated that the 70-m stations
will be used for occultation and other experiments requiring S-band reception from
the Cassini spacecraft. The new BWG stations in Spain and Australia also may be
used for occultation measurements.
3.3.3. Beam Wave-Guide Stations
The 34-m diameter BWG stations have been recently added to the DSN. Several
BWG stations will exist at the California DSCC and one station each will be at
the Spanish and Australian complexes. It is anticipated that only one BWG station
will be instrumented for transmission and reception at Ka-band frequencies. This
CASSINI RADIO SCIENCE
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station in California (DSS-25) was developed to meet stringent Radio Science
requirements on all of its components, including special structural and pointing
requirements unique to a high-precision two-way Ka-band capability. In time for
Saturn’s tour, it is expected that Ka-band downlink will be available at 34-m BWG
stations DSS-54 and DSS-34 in Spain and Australia, respectively.
3.3.4. High-Efficiency Stations
The 34-meter diameter high-efficiency DSN stations (DSS-15, DSS-65, and DSS45) are equipped for transmission at X-band and are optimized for reception at
X-band. The microwave and receiver subsystems allow for the reception of two
channels simultaneously. The station pointing capabilities and strategies are similar
to those of the 70-m stations.
3.3.5. Media Calibration System
The earth’s atmosphere contributes phase and amplitude noise to a spacecraft radio
signal received at a ground station. A system to calibrate the effects of the atmosphere on the phase of the microwave signal is under development especially for
Cassini radio science experiments utilizing Ka–band, where excellent end-to-end
frequency and phase stability is required. The purpose of this media calibration system is to provide a line-of-sight calibration of the water vapor delay (responsible
for most of the atmosphere induced phase fluctuations at microwave frequencies)
during DSS-25 radio science experiment passes. It will also provide estimates of the
total zenith delay and delay fluctuation. This will be accomplished via several components of the system. An advanced water vapor radiometer will sense the number
of water vapor molecules along the line-of-sight, a microwave temperature profiler
will sense the vertical temperature distribution, a surface meteorology package will
measure the temperature, pressure, and humidity, and a GPS receiver will provide
the total zenith delay estimates.
3.3.6. Other Stations
The utility of stations other than those of NASA’s DSN has been proven for several radio science experiments on past missions. For example, arraying of different
antennas has improved the signal strength coming from an extremely distant spacecraft (as during the Voyager Neptune encounter, where Australian and Japanese
stations also recorded the received signals in collaboration with the ight project and
science team.)
More recently, the contribution of an Italian station and a Japanese station has
proven valuable to the radio science experiments on the Ulysses mission. These
stations are normally equipped with a dual S- and X-bands receiver and a hydrogen
maser frequency standard in order to perform very long baseline interferometry
studies. Adding a dedicated instrument to these radio telescopes made it possible to
measure the phase and amplitude of the S- and X-band carrier signals transmitted
from Ulysses. This instrument, called a digital tone extractor, has been used at
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both the Medicina 32-m parabola in Italy and at the Kashima observatory in Japan.
Medicina successfully participated in the three measuring campaigns of the 1991,
1992 and 1993 opposition and conjunction experiments made with Ulysses. The
operation started with the transfer of trajectory information from JPL to the station
where pointing coordinates and the downlink Doppler shifts were computed. The
acquired data were comparable in quality to the DSN data for those experiments.
The information collected at these two stations enabled the sampling of a propagation path across a substantially different region of the troposphere and ionosphere
than those of the DSN stations. Furthermore, the data were useful in understanding
the DSN-acquired data at times of unusual behavior of the signal or equipment.
The availability of non-DSN stations, capable of operation up to Ka-band and
available for limited times during specific mission events, has become crucial since
existing plans allow for only one DSN station (DSS-25, discussed earlier) expressly
dedicated to the Cassini radio science experiments at Ka-band. The possible future availability of an Italian station, located more than 120◦ away in longitude
from Goldstone, would almost double the tracking time at Ka-band for Cassini.
This could significantly improve the integration time for gravitational wave experiments, as well as benefit other radio science research. Availability of such
non-DSN stations might open new opportunities during the cruise and tour phase
of the Cassini mission, in addition to reducing the tracking load on the DSN under
critical conditions.
4. Conclusion
At the time this paper is being written, a partial check-out of the radio science
instrument indicates very good performance, and scientific data were obtained
during the flybys of Venus and Earth. The investigators are working at planning
future observations and looking forward to successful cruise and tour experiments.
Acknowledgments
The Radio Science instrumentation on the Cassini Orbiter represents a truly global
effort, with contributions from organizations all over the world. The DST was developed for JPL by Motorola. Both X-band and Ka band TWTAs were provided by
Hughes Electronics; the Ka band TWTA utilized a design developed from research
done at NASA Lewis Research Center. The USO was designed and built by the
Johns Hopkins University Applied Physics Laboratory. The KEX was designed and
built at JPL. The SBT and KAT were provided by the Italian firm Alenia Spazio
for our partner, the Italian Space Agency (ASI), and Alenia Spazio integrated and
tested the RFIS. The Radio-Science Team wishes to particularly thank B. Bertotti,
now retired from the Radio Science Team, for his important efforts leading to
Cassini’s superb radio system, his work on the cruise experiments, and his work in
preparation for the Tour.
CASSINI RADIO SCIENCE
63
We also thank the Cassini engineers in JPL’s Radio Science Systems Group:
Aseel Anabtawi, Elias Barbinis, Don Fleischman, Gene Goltz, Randy Herrera,
Trina Ray, and the personnel of the DSN for their efforts and support of the experiments described in this paper. The Radio Science Team thanks G. Comoretto, F. B.
Estabrook, J. Lunine, M. Tinto, and R. Woo for discussions and collaborations.
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