- Boulder, Colorado, United States
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Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose... more
Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose eccentricity and argument of periapse have values close to those of a frozen orbit. We call them "nearly" frozen because their eccentricity vector (a vector whose polar coordinates are eccentricity and argument of periapse) will stay within a bounded distance from the frozen orbit eccentricity vector, circulating around it over time. For highly inclined orbits around the Earth, this distance is effectively constant over time. Furthermore, frozen orbit eccentricity values are low enough that these orbits are essentially eccentric (i.e., off center) circles, so that nearly frozen orbits around Earth are bounded above and below by frozen orbits.
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The NISAR mission is a proposed joint mission of the space agencies of India and the United States. It would use L-band SAR radar interferometry to measure very small changes in the topography of the Earth including ice sheets. The use of... more
The NISAR mission is a proposed joint mission of the space agencies of India and the United States. It would use L-band SAR radar interferometry to measure very small changes in the topography of the Earth including ice sheets. The use of interferometry places more stringent requirements on the orbit design and maintenance of this mission than any earlier robotic mission in either agency has had to meet. This paper discusses how the requirements led to the orbit design and outlines orbit maintenance strategies to meet the orbit requirements.
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Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose... more
Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose eccentricity and argument of periapse have values close to those of a frozen orbit. We call them "nearly" frozen because their eccentricity vector (a vector whose polar coordinates are eccentricity and argument of periapse) will stay within a bounded distance from the frozen orbit eccentricity vector, circulating around it over time. For highly inclined orbits around the Earth, this distance is effectively constant over time. Furthermore, frozen orbit eccentricity values are low enough that these orbits are essentially eccentric (i.e., off center) circles, so that nearly frozen orbits around Earth are bounded above and below by frozen orbits.
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Research Interests: Computer Science and Drag
In order to gain an understanding into the problem of eccentricity (e) and argument of perigee (omega) control for TOPEX/Poseidon, the two cases where the highest latitude crossing time and one of the equator crossings are held constant... more
In order to gain an understanding into the problem of eccentricity (e) and argument of perigee (omega) control for TOPEX/Poseidon, the two cases where the highest latitude crossing time and one of the equator crossings are held constant are investigated. Variations in e and omega cause a significant effect on the satellite's ground-track repeatability. Maintaining e and omega near their frozen values will minimize this variation. Analytical expressions are found to express this relationship while keeping an arbitrary point of the ground track fixed. The initial offset of the ground track from its nominal path determines the subsequent evolution of e and omega about their frozen values. This long-term behavior is numerically determined using an earth gravitational field including the first 17 zonal harmonics. The numerical results are plotted together with the analytical constraints to see if the later values of e and omega cause unacceptable deviation in the ground track.
Research Interests:
Mean Orbit Elements can be chosen such that a desired ground track repeat criteria is obtained when propagating with the secular effects of a central body gravity field. If the proper initial conditions are chosen that correspond to these... more
Mean Orbit Elements can be chosen such that a desired ground track repeat criteria is obtained when propagating with the secular effects of a central body gravity field. If the proper initial conditions are chosen that correspond to these Mean Elements, the orbit can also be propagated with the full gravity field and form another ground track repeat pattern. Further, if the effects of other perturbative forces are compensated for, such that the ground track remains near this pattern, the central body effects can again be considered repetitive. The process of arriving at these conclusions, along with the supporting numerical simulations, are presented.
Research Interests:
The accuracy of solar system tests of gravitational theory could be very much improved by range and Doppler measurements to a Small Mercury Relativity Orbiter. A nearly circular orbit at roughly 2400 km altitude is assumed in order to... more
The accuracy of solar system tests of gravitational theory could be very much improved by range and Doppler measurements to a Small Mercury Relativity Orbiter. A nearly circular orbit at roughly 2400 km altitude is assumed in order to minimize problems with orbit determination and thermal radiation from the surface. The spacecraft is spin-stabilized and has a 30 cm diameter de-spun antenna. With K-band and X-band ranging systems using a 50 MHz offset sidetone at K-band, a range accuracy of 3 cm appears to be realistically achievable. The estimated spacecraft mass is 50 kg. A consider-covariance analysis was performed to determine how well the Earth-Mercury distance as a function of time could be determined with such a Relativity Orbiter. The minimum data set is assumed to be 40 independent 8-hour arcs of tracking data at selected times during a two year period. The gravity field of Mercury up through degree and order 10 is solved for, along with the initial conditions for each arc and the Earth-Mercury distance at the center of each arc. The considered parameters include the gravity field parameters of degree 11 and 12 plus the tracking station coordinates, the tropospheric delay, and two parameters in a crude radiation pressure model. The conclusion is that the Earth-Mercury distance can be determined to 6 cm accuracy or better. From a modified worst-case analysis, this would lead to roughly 2 orders of magnitude improvement in the knowledge of the precession of perihelion, the relativistic time delay, and the possible change in the gravitational constant with time.
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Research Interests:
Research Interests:
The scientific benefits generated from the synergy of the satellites in the AM and PM (A-Train) Constellations are unprecedented. Constellation Flying in this context refers to each satellite flying independently in their own control box... more
The scientific benefits generated from the synergy of the satellites in the AM and PM (A-Train) Constellations are unprecedented. Constellation Flying in this context refers to each satellite flying independently in their own control box with acceptable minimum buffers ensuring that the control boxes do not intersect each other. Recently it is has been realized that rather than two separate constellations, they should be considered as one entity called the “705-km Fleet” named for their common nominal altitude over the equator. This realization partly comes from the recent events with the USGS satellite Landsat-5 which is in the AM Constellation, but for a period of time was overlapping with the A-Train. A fundamental concept is the Triad consisting of Alongtrack Phasing, Groundtrack and Mean Local Time of Ascending Node. Another related lesson learned is that to maintain the buffers, phasing at the two intersection points where each pair of orbits cross near the poles should be considered, as opposed to the relative phasing of the times they cross the equator. These types of geometric considerations are presented after presenting an introduction and history of the constellations. Other topics include: reference ground tracks, the process of handling the growing concern of conjunctions with other orbiting bodies, CloudSat and CALIPSO satellites performing Formation Flying, and the general ascent and exit methods for satellites entering/leaving a constellation.
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Abstract It was shown earlier that 1× 10− 14 Doppler data and 3 cm accuracy range measurements to a small Mercury Relativity Satellite in a polar orbit with 4-hour period can give high-accuracy tests of gravitational theory. A particular... more
Abstract It was shown earlier that 1× 10− 14 Doppler data and 3 cm accuracy range measurements to a small Mercury Relativity Satellite in a polar orbit with 4-hour period can give high-accuracy tests of gravitational theory. A particular conceptual design has been ...
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Research Interests:
Designs for a laser gravitational wave antenna in space using free test masses and heterodyne (interferometric) detection were investigated. Use of 1 million km baselines between three spacecraft in nearly circular 1 yr solar orbit is... more
Designs for a laser gravitational wave antenna in space using free test masses and heterodyne (interferometric) detection were investigated. Use of 1 million km baselines between three spacecraft in nearly circular 1 yr solar orbit is considered. With milliwatt-transmitted laser power ...
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Progress during the past two years on a proposed Laser Gravitational-Wave Observatory in Space (LAGOS) is discussed. Calculated performance for a 10 6 km sized antenna over the frequency range of 10 −5 to 1 Hz is given. The sensitivity... more
Progress during the past two years on a proposed Laser Gravitational-Wave Observatory in Space (LAGOS) is discussed. Calculated performance for a 10 6 km sized antenna over the frequency range of 10 −5 to 1 Hz is given. The sensitivity from 10 −3 to 10 −1 Hz is expected to be 1 ...
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Research Interests: Space Debris and Debris
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The use of laser ranging to the near-Earth satellite, LAGEOS, to determine two of the post-Newtonian parameters (beta and gamma) of gravitational theory is investigated. In addition to the normal N-body point mass equations of motion, the... more
The use of laser ranging to the near-Earth satellite, LAGEOS, to determine two of the post-Newtonian parameters (beta and gamma) of gravitational theory is investigated. In addition to the normal N-body point mass equations of motion, the equations which describe the effect of a finite-size, rotating Earth on the satellite motion are derived. The method of incorporating relativity into the orbit determination problem is described. The results obtained when either beta or gamma is fixed at unity (the value in General Relativity) and the other parameter estimated are: beta = 1.0009 + or - 0.0005 (0.0107) and gamma = 1.0000 + or - 0.0018 (0.0579). In each case, the first uncertainty is the formal standard deviation, while the parenthesized value is the standard deviation resulting from a consider analysis of the systematic errors in the measurement and force models. Both estimates are within two standard deviations of their values in General Relativity.
Research Interests:
Research Interests:
Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose... more
Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose eccentricity and argument of periapse have values close to those of a frozen orbit. We call them “nearly” frozen because their eccentricity vector (a vector whose polar coordinates are eccentricity and argument of periapse) will stay within a bounded distance from the frozen orbit eccentricity vector, circulating around it over time. For highly inclined orbits around the Earth, this distance is effectively constant over time. Furthermore, frozen orbit eccentricity values are low enough that these orbits are essentially eccentric (i.e., off center) circles, so that nearly frozen orbits around Earth are bounded above and below by frozen orbits.
Many low-Earth-orbit missions have a policy that if a future conjunction with a secondary object such as a piece of orbital debris is detected, a go/no-go meeting will be held to decide about a risk mitigation action before the time of... more
Many low-Earth-orbit missions have a policy that if a future conjunction with a secondary object such as a piece of orbital debris is detected, a go/no-go meeting will be held to decide about a risk mitigation action before the time of closest approach. Commonly, the policy is that a probability of collision (Pc) above a predetermined action threshold at the time of the meeting means the mission will take action to reduce the risk. The value to which the action threshold is set is a compromise-if it is higher, then there is a higher probability that a collision might occur when action is not taken; if it is lower, then more actions will be taken, increasing the cumulative costs and risks of the actions themselves. This paper shows how a policy using an action threshold affects the overall mission risk of a collision with a large object. We augment this with estimates of action success, expected hard-body radius, and expected covariance to obtain an algorithm for estimating the risk reduction associated with an action threshold policy. We apply this algorithm to the OCO-2 and CloudSat missions as examples, using historical conjunction data for these two missions, and show how this algorithm can guide developing missions in setting an action threshold.
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OSMEAN is sophisticated program that converts between osculating and mean classical orbital elements. Enables engineer to exploit advantages of each approach for design and planning or orbital trajectories and maneuvers. Converts mean... more
OSMEAN is sophisticated program that converts between osculating and mean classical orbital elements. Enables engineer to exploit advantages of each approach for design and planning or orbital trajectories and maneuvers. Converts mean elements to osculating elements or vice-versa. Conversion based on mathematical modeling of all first-order aspherical terrestrial, lunar, and solar gravitational perturbations plus second-order aspherical term based on second-degree central-body zonal perturbation. Written in FORTRAN 77.
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The accuracy of solar system tests of gravitational theory could be very much improved by range and Doppler measurements to a Small Mercury Relativity Orbiter. A nearly circular orbit at roughly 2400 km altitude is assumed in order to... more
The accuracy of solar system tests of gravitational theory could be very much improved by range and Doppler measurements to a Small Mercury Relativity Orbiter. A nearly circular orbit at roughly 2400 km altitude is assumed in order to minimize problems with orbit determination and thermal radiation from the surface. The spacecraft is spin-stabilized and has a 30 cm diameter de-spun antenna. With K-band and X-band ranging systems using a 50 MHz offset sidetone at K-band, a range accuracy of 3 cm appears to be realistically achievable. The estimated spacecraft mass is 50 kg. A consider-covariance analysis was performed to determine how well the Earth-Mercury distance as a function of time could be determined with such a Relativity Orbiter. The minimum data set is assumed to be 40 independent 8-hour arcs of tracking data at selected times during a two year period. The gravity field of Mercury up through degree and order 10 is solved for, along with the initial conditions for each arc and the Earth-Mercury distance at the center of each arc. The considered parameters include the gravity field parameters of degree 11 and 12 plus the tracking station coordinates, the tropospheric delay, and two parameters in a crude radiation pressure model. The conclusion is that the Earth-Mercury distance can be determined to 6 cm accuracy or better. From a modified worst-case analysis, this would lead to roughly 2 orders of magnitude improvement in the knowledge of the precession of perihelion, the relativistic time delay, and the possible change in the gravitational constant with time.
Research Interests:
The present design concepts for a Laser Gravitational Wave Observatory in Space are described. Laser heterodyne distance measurements are made between test masses located in three spacecraft separated by roughly 106 km. The major... more
The present design concepts for a Laser Gravitational Wave Observatory in Space are described. Laser heterodyne distance measurements are made between test masses located in three spacecraft separated by roughly 106 km. The major technology issues are: the reduction of spurious acceleration noise for the test masses to below 2 x 10-15 cm/sq sec/Hz(0.5) from 10-5 to 10-3 Hz; and
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Abstract The requirements for determining the existence and size of the suspected fluid outer core of Mercury are discussed. The moment of inertia Cm of Mercury's solid mantle and crust can be calculated from the amplitude of the 88... more
Abstract The requirements for determining the existence and size of the suspected fluid outer core of Mercury are discussed. The moment of inertia Cm of Mercury's solid mantle and crust can be calculated from the amplitude of the 88 day forced libration in longitude and some auxiliary information, since the fluid core will not follow this motion unless its viscosity is much higher than expected. The libration amplitude can be determined from camera observations of the surface near periherm during the Mercury Orbiter mission, provided that the spacecraft location and the camera attitude are measured sufficiently well. The accuracies required are roughly 15 m in the spacecraft coordinate normal to the (polar) orbit plane and 15 arcsec in the camera attitude for 10% accuracy in Cm. The fluid core radius follows from Cm plus the total moment of inertia C and models for the composition and thermal history of the planet. Since maintaining a fluid core appears to require having perhaps 2 or 3% sulfur in the core, determination of the existence and size of the core will provide vital information on mixing of materials between different parts of the solar nebula. In this paper, the accuracy achievable for determining the spacecraft location with an X-band transponder system, as is planned for the mission, is investigated. A very preliminary covariance analysis was carried out based on 65 independent arcs starting every 10 days during the mission, with 6 h of tracking data around periherm for each arc. Gravity field coefficients up to degree and order 26 were solved for, and the effects of uncertainties in the other coefficients up to degree and order 36 were “considered”, along with the effects of uncertainties in some additional parameters. Six of the eight parameters included in the radiation pressure model were “considered” rather than solved for in order to make sure that model uncertainties were allowed for adequately. The 1 m assumed range measurement uncertainty was treated as a bias for each arc rather than a random error. The spacecraft location determination accuracy was found to be consistent with the requirements for measuring Cm to 10% or better accuracy if C m C is about 0.5, as suggested by current models.
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ABSTRACT
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Translocation studies of LAGEOS laser range data from Quincy and Monument Peak in California observed during 1984–1987 suggest that plate tectonic motion across the San Andreas fault system in the direction of the baseline between the two... more
Translocation studies of LAGEOS laser range data from Quincy and Monument Peak in California observed during 1984–1987 suggest that plate tectonic motion across the San Andreas fault system in the direction of the baseline between the two stations is uniform at a rate of −30(±3) mm/a. Changes in the components of the baseline vector were inferred from repeat determinations using
Research Interests:
Research Interests:
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Research Interests:
The use of laser ranging to the near-Earth satellite, LAGEOS, to determine two of the post-Newtonian parameters (beta and gamma) of gravitational theory is investigated. In addition to the normal N-body point mass equations of motion, the... more
The use of laser ranging to the near-Earth satellite, LAGEOS, to determine two of the post-Newtonian parameters (beta and gamma) of gravitational theory is investigated. In addition to the normal N-body point mass equations of motion, the equations which describe the effect of a finite-size, rotating Earth on the satellite motion are derived. The method of incorporating relativity into the orbit determination problem is described. The results obtained when either beta or gamma is fixed at unity (the value in General Relativity) and the other parameter estimated are: beta = 1.0009 + or - 0.0005 (0.0107) and gamma = 1.0000 + or - 0.0018 (0.0579). In each case, the first uncertainty is the formal standard deviation, while the parenthesized value is the standard deviation resulting from a consider analysis of the systematic errors in the measurement and force models. Both estimates are within two standard deviations of their values in General Relativity.
Research Interests:
Research Interests:
In order to gain an understanding into the problem of eccentricity (e) and argument of perigee (omega) control for TOPEX/Poseidon, the two cases where the highest latitude crossing time and one of the equator crossings are held constant... more
In order to gain an understanding into the problem of eccentricity (e) and argument of perigee (omega) control for TOPEX/Poseidon, the two cases where the highest latitude crossing time and one of the equator crossings are held constant are investigated. Variations in e and omega cause a significant effect on the satellite's ground-track repeatability. Maintaining e and omega near their frozen values will minimize this variation. Analytical expressions are found to express this relationship while keeping an arbitrary point of the ground track fixed. The initial offset of the ground track from its nominal path determines the subsequent evolution of e and omega about their frozen values. This long-term behavior is numerically determined using an earth gravitational field including the first 17 zonal harmonics. The numerical results are plotted together with the analytical constraints to see if the later values of e and omega cause unacceptable deviation in the ground track.
Research Interests:
Mean Orbit Elements can be chosen such that a desired ground track repeat criteria is obtained when propagating with the secular effects of a central body gravity field. If the proper initial conditions are chosen that correspond to these... more
Mean Orbit Elements can be chosen such that a desired ground track repeat criteria is obtained when propagating with the secular effects of a central body gravity field. If the proper initial conditions are chosen that correspond to these Mean Elements, the orbit can also be propagated with the full gravity field and form another ground track repeat pattern. Further, if the effects of other perturbative forces are compensated for, such that the ground track remains near this pattern, the central body effects can again be considered repetitive. The process of arriving at these conclusions, along with the supporting numerical simulations, are presented.
Research Interests:
Research Interests:
The scientific benefits generated from the synergy of the satellites in the AM and PM (A-Train) Constellations are unprecedented. Constellation Flying in this context refers to each satellite flying independently in their own control box... more
The scientific benefits generated from the synergy of the satellites in the AM and PM (A-Train) Constellations are unprecedented. Constellation Flying in this context refers to each satellite flying independently in their own control box with acceptable minimum buffers ensuring that the control boxes do not intersect each other. Recently it is has been realized that rather than two separate constellations, they should be considered as one entity called the “705-km Fleet” named for their common nominal altitude over the equator. This realization partly comes from the recent events with the USGS satellite Landsat-5 which is in the AM Constellation, but for a period of time was overlapping with the A-Train. A fundamental concept is the Triad consisting of Alongtrack Phasing, Groundtrack and Mean Local Time of Ascending Node. Another related lesson learned is that to maintain the buffers, phasing at the two intersection points where each pair of orbits cross near the poles should be considered, as opposed to the relative phasing of the times they cross the equator. These types of geometric considerations are presented after presenting an introduction and history of the constellations. Other topics include: reference ground tracks, the process of handling the growing concern of conjunctions with other orbiting bodies, CloudSat and CALIPSO satellites performing Formation Flying, and the general ascent and exit methods for satellites entering/leaving a constellation.
Research Interests:
Designs for a laser gravitational wave antenna in space using free test masses and heterodyne (interferometric) detection were investigated. Use of 1 million km baselines between three spacecraft in nearly circular 1 yr solar orbit is... more
Designs for a laser gravitational wave antenna in space using free test masses and heterodyne (interferometric) detection were investigated. Use of 1 million km baselines between three spacecraft in nearly circular 1 yr solar orbit is considered. With milliwatt-transmitted laser power ...
Research Interests:
submitted to the AAS/AIAA Astrodynamics Conference August 4-7, 1997 Sun Valley, Idaho Mark A. Vincent Jet Propulsion Laboratory M/S 301-165 4800 Oak Grove Drive Pasadena CA 91109 (818) 354-3224 Mark. A. Vincent@jpl.nasa. gov In order to... more
submitted to the AAS/AIAA Astrodynamics Conference August 4-7, 1997 Sun Valley, Idaho Mark A. Vincent Jet Propulsion Laboratory M/S 301-165 4800 Oak Grove Drive Pasadena CA 91109 (818) 354-3224 Mark. A. Vincent@jpl.nasa. gov In order to fulfill Surveyor (MGS) the planetary protection requirements for the Mars Global mission a capability to predict the probability of various orbita~ lifetimes was needed. This pap-er presents a new method of solving the inherent problem of modeling the long-term behavior of the Martian atmosphere. The simple case of one solar cycle will be discussed before tackling the more complicated approach to the many n-year solar cycles situation. The former has the benefit of establishing the relationships between solar flux, atmospheric density and orbital lifetime requirements. The nominal solar flux incident upon Mars has been previously modeled as a combination of several sinusoidal functions. The basis of this study is the statistical nature of the variati...