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Educational Web Sites
under www.phy6.org
by David P. Stern
http://www.phy6.org/stargaze/Sstern.htm
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(1) "From Stargazers to Starships", home page at: http://www.phy6.org/stargaze/Sintro.htm An extensive illustrated non-calculus course on astronomy, mechanics, the Sun and spaceflight. With Spanish, French and Italian translations, 45 lesson plans, 20-part math course, guidance for teachers, timeline, glossary, 503 Q&A from users, problems, some hands-on projects, etc. Follows historical thread, stresses intuitive understanding, applications (esp. to space), connections with society, culture and technology, stories of discovery and discoverers. Use glossary to access specific topics. Keywords: Course, overview, space, astronomy, spaceflight, Newtonian mechanics, Kepler's laws, Newton's laws, sun, history of science, Satellites, orbits, Spanish, French, Italian, teaching physics, teaching astronomy ----------------------- (2) "The Exploration of the Earth's Magnetosphere" http://www.phy6.org/Education/Intro.html A non-mathematical overview of research on the magnetic space environment around Earth, about 80 files, illustrated, includes Spanish version (MIntro.html) and one in French (incomplete), glossary, timeline, Q&A, teacher guidance, a history overview and articles "Birth of a Radiation Belt" and "Secrets of the Polar Aurora." Stresses history, also conceptual understanding and some basics such as electrons, ions and their motion in space, plasmas and energy. Use glossary to access specific topics. Keywords: Course, overview, history, Spanish, magnetosphere, magnetic field, magnetic field lines, space, satellites, aurora, polar aurora, northern lights, radiation belts, sun, solar wind, Oersted, electromagnetic waves, ions, barium, electrons, plasma, fluorescent lamp, magnetic trapping,, magnetic mirroring, magnetic drift, adiabatic invariants, electron volt, synchronous orbit, Explorer 1, Geiger counter, Schwabe, Carrington, solar flares, sunspot cycle, solar corona, interplanetary magnetic field, solar wind streams, heliosphere, termination shock, magnetopause, polar cusps, Lagrangian points, ring current, sun-synchronous orbit, Chapman-Ferraro theory, substorms, magnetospheric tail, magnetic reconnection, Birkeland, Birkeland currents, dynamo process, frozen-in field lines, parallel electric field, auroral acceleration, plasma sheet, magnetic storms, space weather, Southward magnetic field, Geocorona, Jupiter magnetosphere, planetary magnetospheres, Io, Space tether, cosmic rays, gamma ray bursts, magnetars, solar outbursts, ----------------------- (3) "The Great Magnet, the Earth" http://www.phy6.org/earthmag/demagint.htm A non-mathematical historical overview of the Earth's magnetism, written for the 400th anniversary of William Gilbert's book "De Magnete," covered in some detail. Also discusses electromagnetism, solar magnetism, dynamo theory, ocean floor magnetization, and magnetospheres of Earth and planets. Includes a long review "A Millennium of Geomagnetism," a detailed article on teaching magnetism in high schools and translations to Spanish, German and French. Use glossary to access specific topics. Keywords: Geomagnetism, course, history, Spanish, German, lodestone, William Gilbert, De Magnete, compass, terrella, dip needle, magnetic declination, magnetic inclination, secular variation, induced magnetism, Gellibrand, Halley, Halley's theory of magnetism, Coulomb, torson balance, Oersted, Ampere, Gauss, harmonic analysis, sunspots, sunspot cycle, Schwabe, magnetic pole, reversal, Faraday, dynamo, core, Blackett, poloidal, toroidal, alpha-dynamo, Cowling's theorem, fluxgate, magnetic shielding, cigarette smoking,, Wegener, continental drift, polar wandering, sea-floor spreading, Lawrence Morley, magnetosphere, Birkeland, ring current, radiation belt, polar aurora, Jupiter magnetosphere, planetary magnetism, teaching magnetism ----------------------- (4) An overview of all these is in http://www.phy6.org/readfirst.htm including links to files covering 90+ specific topics, many of which branch out--e.g. nuclear power in http://www.phy6.org/stargaze/Snuclear.htm Keywords: Space, astronomy, Newtonian mechanics, classical physics, spaceflight, magnetosphere, geomagnetism (Note: a version of this also exists under the old name http://www.phy6.org/prospect.htm) ----------------------- Four main Sections of "From Stargazers to Starships ----------------------- 5. Astronomy of the Earth's Motion in Space http://www.phy6.org/stargaze/Sastron.htm An algebra-based overview of elementary and (mostly) pre-telescope astronomy, grades 7-8 (some parts), 9-14 (mostly). Discusses sundials, seasons, calendars, precession, shape and rotation of Earth, Greek astronomy, the path to heliocentric theory and extensive sections on Kepler's laws, also sections on the Moon and how its distance was found. Many history details, stories and applications, also a calculation of the distance to the Sun, based on the Venus transit of 2004. Suitable for independent study and home schooling Part of a wider site "From Stargazers to Starships" which has related lesson plans, glossary, timeline, problems etc., also Spanish French and Italian translations. Keywords: North, celestial sphere, celestial pole, equatorial, zodiac, pole star, constellations, apparent motion, sundial, gnomon, equation of time, seasons, tilt of Earth axis, equinox, solstices, zenial days, moon, lunar month, lunar rotation, gravity gradient, libration, earthshine, lunar craters, project Apollo, latitude, longitude, local time, universal time, international dateline, Time zones, right ascension, declination, navigation, cross-staff, coordinates, Cartesian coordinates, polar coordinates, graphs, azimuth, elevation, calendar, mean solar day, rotation of Earth Julian calendar, Gregorian calendar, metonic calendar, Moslem calendar, Jewish calendar, Naw Ruz, Maya calendar, precession of equinoxes, Milankovich theory, ice ages, Columbus, Eratosthenes, Posidonius, horizon, parallax, Aristarchus, Hipparchus, distance of moon, distance of sun, retrograde motion, Ptolemy, Geocentric theory, epicycles, heliocentric theory, planets, Copernicus, Galileo, Tycho, Kepler. Kepler's laws, semi-major axis, orbital period, ellipses, focus of ellipse, perihelion, aphelion, extrasolar planets, orbital energy, areal velocity, astronomical unit (AU), mean anomaly, orbital inclination, orbit eccentricity orbital elements, Venus transit, Halley's method ----------------------- 6. Newtonian Mechanics http://www.phy6.org/stargaze/Smechopen.htm Grades 9-14 An algebra-based course at the high-school level, oriented towards astronomy and spaceflight. It omits rigid body mechanics, but includes mass measurements in the weightless environment of a space station (with a simple related experiment), synchronous orbits and space trajectories from Earth to Mars. Concepts are stressed-- vectors and applications, mass and inertia, also frames of references, clarifying centripetal vs. centrifugal forces. Suitable for independent study and home schooling Part of a wider site "From Stargazers to Starships" which has related lesson plans, glossary, timeline, problems etc., also Spanish and French translations. Keywords: Gravity, acceleration, free fall, acceleration due to gravity, Galileo experiments, vector, vector addition, vector resolution, components, inclined plane, energy, kinetic energy, potential energy, conservation of energy, conversion of energy, chemical energy, heat, joule, calorie, second law of thermodynamics, Newton's laws of motion, inertia, mass, inertial balance, Skylab, weightlessness, Astronauts, Newton's second law, Newton's third law, Newton (unit of force), reaction force, bicycle balance, Ernest Mach, momentum, conservation of momentum, work, work against electric force, Van de Graaff, static cling, lightning, centripetal acceleration, Universal Gravitation, Newton's apple, lunar period, Kepler's 3rd law, orbital velocity, escape velocity, synchronous period, Mars landing, Hohmann ellipse, Frames of reference, accelerated frame, inertial forces, Bradley aberration, solar wind aberration, relativity (special), aerodynamics, lift, drag, angle of attack, sweepback of wings, propeller pitch, swivel-wing airplane, cruising altitude, Voyager airplane, centrifugal force, Earth rotation, equatorial bulge, vomit comet, Coriolis force, bathroom sink, swirling or atmosphere, Buys Ballot law, ----------------------- 7. The Sun http://www.phy6.org/stargaze/Sunopen.htm Grades 9-14 The Sun helps introduce diverse parts of physics--weather and climate, magnetism (via sunspots and the interplanetary field), color, spectra and the electromagnetic spectrum, the Doppler effect, nuclear energy and its release in stars, stellar evolution, even black holes and non-mathematical introductions to quantum physics and to nuclear power. Non-calculus. Qualitative course, suitable for independent study and home schooling, high school level Part of a wider site "From Stargazers to Starships" which has related lesson plans, glossary, timeline, problems etc., also Spanish and French translations. Keywords: Space, solar physics, history, sunlight, radiation balance, greenhouse effect, ozone layer, weather, water vapor in the atmosphere, atmospheric convection, atmospheric temperature profile, thunderstorm cells, squall line, hail, climate, tropical region, polar region, Hadley cells, Coriolis effect, jet stream, Rossby waves, photosphere, chromosphere, corona, solar layers, coronal heating, solar wind, sunspots, sunspot cycle, Schwabe, magnetism of sun, Hale (George Ellery), solar activity, solar flares, interplanetary magnetic field, freezing of field lines, color, perceived color, three-color theory, spectral color, black-body spectrum, line spectrum, wavelength of light, diffraction grating, helium, fields, electromagnetic field, electromagnetic waves, Maxwell (James Clerk), displacement current, Hertz, photons,Planck, Einstein, photoelectric effect, atoms, electrons, ions, quantum physics, Balmer, Balmer series, Rydberg constant, alpha line of hydrogen, Lyman alpha line, energy levels, Ritz combination principle, Zeeman effect, Planck's constant, black body spectrum, microwave background, fingerprint of God, atomic nucleus, Rutherford, alpha particles, Bohr's model of the atom, adiabatic invariants, Bohr-Sommerfeld model, electron spin, periodic table, wave mechanics, wave function of matter, duality, field, aether, atomic orbitals, quantum tunneling, coronal mass ejections, solar energetic particles, solar energy source, nuclear forces, binding energy, nuclear fusion, evolution of stars, stellar evolution, supernovas, neutrinos, Urca process, neutron star, pulsar, black hole, nuclear physics, nuclear composition, nuclear fission, chain reaction, critical mass, nuclear reactor, neutron moderator, nuclear pile, control rods, nuclear waste, nuclear meltdown, Three mile Island, Chernobyl, nuclear bombs, fast neutrons, uranium enrichment, Hiroshima, H-bomb, nuclear fallout, dirty bombs, galactic center. ----------------------- 8. Spaceflight and Spacecraft http://www.phy6.org/stargaze/Spaceflt1.htm Grades 9-14 A historical overview of spaceflight, stressing the technology of rockets, satellites and orbits, and its use in unmanned missions. Contain sections on rocket motions, Robert Goddard, history of rocketry and the space race, 5 kinds of uses of unmanned spacecraft and various orbits and gravity. Largely narrative, except for detailed derivations of Lagrangian points and gravity-assist maneuvers, it also surveys exotic spaceflight methods--nuclear, cannon, solar sails and ion rockets. Part of a wider site "From Stargazers to Starships" which has related lesson plans, glossary, timeline, problems etc., also Spanish French and Italian translations. Keywords: Space, rocket, rocket staging,, center of gravity, center of mass, Goddard, ballistic pendulum, rocket nozzle, De-Laval nozzle, spaceflight, history of spaceflight, Karman, Korolov, Sputnik,, IGY (International Geophysical Year), Vanguard rocket, Explorer 1, reentry, unmanned spacecraft, space telescopes, scientific satellites, communication satellites, interplanetary spacecraft, Light gas cannon, high-altitude cannon, nuclear spaceflight, solar sails, Project Orion, ion rockets, synchronous orbit, lagrangian point, L1, L2, L4, L5, gravity assist, elastic collisions, Pelton wheel, water turbine ----------------------- Specific topics in "From Stargazers to Starships ----------------------- (9) Sundial http://www.phy6.org/stargaze/Sundial.htm Sundials tell time by the motion of a shadow around a dial, caused by the Sun moving across the sky. This web page introduces users to sundials and has plans for a paper sundial, also formulas and links to a page explaining why the fin is aimed towards the pole star, and to related web pages. The page Lsundial.htm has a related lesson plan. Cultural and historical links included--e.g. Sundial bridge in California, Sundial in Shakespeare's play, etc. Keywords: astronomy, sundial, gnomon, equation of time, ----------------------- (10) Moon http://www.phy6.org/stargaze/Smoon.htm The first of three linked sections on the Earth's Moon, discussing (1) The Moon as observed by the eye from Earth, its orbital period, its phases, appearance and the reason it always presents one face; (2) The Moon as seen through the telescope and Moon landings by astronauts; and (3) (optional) Librations of the Moon, the reason more than 50% of it can be observed from Earth. Part of the collection "From Stargazers to Starships" with French, Spanish and Italian translations, also (English) lesson plans. Keywords: Astronomy, Moon ,lunar month, lunar rotation, gravity gradient, libration, earthshine, lunar craters, project Apollo ----------------------- (11) Latitude, Longitude and Navigation http://www.phy6.org/stargaze/Slatlong.htm An elementary introduction to the concepts of latitude, longitude, local time and time zones, followed by a linked web page on navigation, explaining how latitude can be determined by the elevation angle of the noontime sun above the horizon. It then explains how determining longitude requires accurate time-keeping, and ends with related anecdotal stories about Robert Wood and Fridtjof Nansen. The files Llatlong.gtm and Lnavigat.htm contain related lesson plans, also available in Spanish. The use of the Cross-staff is also explained, and questions by users are answered. Has Spanish, Franch and Italian translations. Keywords: Latitude, longitude, local time, universal time, international dateline, Time zones, right ascension, declination, navigation, cross-staff ----------------------- (12) The Calendar http://www.phy6.org/stargaze/Scalend.htm A short overview of the common (Gregorian) calendar and some less-common ones--Julian, Jewish (leap months), Moslem, Persian (New Year on the spring equinox), Ethiopian and Maya. Explains first why the period of the Earth's rotation is shorter than 24 hours, then recounts the history of the common calendar. With many cultural tidbits, also an optional section #6a on the Jewish calendar (taken from the ancient Babylonians--a good student project), lesson plans, answered questions by users, and translations into Spanish, Italian and French. Keywords: Astronomy, time, calendar, history, rotation of Earth, sidereal day, mean solar day, Julian calendar, Gregorian calendar, metonic calendar, Moslem calendar, Jewish calendar, Naw Ruz, Nowruz, Maya calendar, zenial day ----------------------- (13) Precession http://www.phy6.org/stargaze/Sprecess.htm About 2000 years ago the Greek astronomer Hipparchus discovered that the position of the Sun at any season, measured against the background stars, migrates in a slow cycle of about 26000 years. This "precession of the equinoxes" also shifts the position of the celestial pole (so that our pole star would not have been a good guide for the ancient Greeks) and is caused by the rotation axis of the Earth slowly moving around a cone. Precession may be one of several astronomical processes contributing to the ice ages, as proposed by the Serbian astronomer Milutin Milankovich. The file Lprecess.htm has a related lesson plan. Has Spanish, Franch, Italian versions, also answered questions. Keywords: Precession of equinoxes, precession, Hipparchus, pole star, Thuban, Milankovich theory, ice ages, nutation, nutation dampers, ----------------------- (14) Greek Astronomy http://www.phy6.org/stargaze/Shipprc2.htm Over 2000 years, long before the invention of the telescope, the Greek astronomer Aristarchus accurately estimated the Moon's distance from the length of a lunar eclipse. Hipparchus, a century later, confirmed it by a different method (following section #8d). Aristarchus went on to estimate the distance of the Sun (#9a), and his result (though very inaccurate) convinced him that the Earth went around the Sun, a conclusion accepted only 1700 years later. Lesson plans at Lhipprc2.htm, Lhupparc.htm and Larist.htm.Translations to Spanish, Italian, French, many answered questions Keywords: Astronomy, moon distance, heliocentric theory, Aristarchus, Hipparchus, lunar eclipse, solar eclipse ----------------------- (15) Columbus and the Size and Shape of Earth http://www.phy6.org/stargaze/Scolumb.htm The round shape of the Earth may be inferred from the existence of a horizon at sea (whose distance is derived in linked section #8a). Ancient Greeks deduced it from the shape of the Earth's shadow when the Moon is eclipsed (linked page) and from stars visible only in southern countries. Eratosthenes (and later the Arabs) accurately estimated the size of the Earth, but Columbus based his plans on an incorrect value, by which India would be much closer to Spain. A lesson plan is at Lcolumb.htm, Spanish, Franch and Italian translations exist. Keywords: Columbus, horizon, Eratosthenes, Earth radius, Al Mamun ----------------------- (16) Parallax http://www.phy6.org/stargaze/Sparalax.htm A parallax is the shift in the viewing direction when an object is seen from two separated locations, and it allows the object's distance to be derived. A simple ("pre-trig") method is developed for distance estimation, with a related "extended thumb method" useful outdoors. The page ends by discussing the use of the "stellar parallax" to estimate the distance of nearby stars. A lesson plan is at Lparalax.htm Keywords: Astronomy, parallax, distance estimation, parsec ----------------------- (17) Kepler's laws http://www.phy6.org/stargaze/Skeplaws.htm A collection of 8 connected web pages discussing Kepler's laws. Included are equations and properties of conic sections, the scale of the solar system, the energy equation for Keplerian motion, Newton's "Universal Gravitation" (even the apple) and derivation of the 3rd law for circular orbits. Also why spring and fall equinox are unevenly spaced, and how to derive the duration of spaceflight to Mars. Part of the collection "From Stargazers to Starships," where Spanish translations are linked to page Mintro.htm, French ones to Fintro.htm and 7 lesson related plans to Lintro.htm. Includes the text of a one-hour talk to teachers about presenting Kepler's laws to a class. Many answered questions from users. Keywords: Astronomy, Tycho, Galileo, Kepler, Kepler's laws, graph, ellipse, focus of ellipse, law of areas, areal velocity, semi-major axis, extrasolar planets, center of gravity, astronomical unit (AU), mean anomaly, orbital inclination, orbital eccentricity, orbital elements, ----------------------- (18) Flight to Mars http://www.phy6.org/stargaze/Smars1.htm A calculation of flight to Mars and back, using a Hohmann transfer ellipse between two circular orbits, in 3 linked sections of "From Stargazers to Starships." Only algebra is used, with Kepler's laws and the equation for the energy of Kepler motion, covered in Skepl2nd.htm *sect. #12). The boosts at launch and arrival are derived, also the flight's duration and the delay before the return trip can start. A good project for advanced high-school students; also available in French, Spanish, Italian.. Keywords: astronomy, Mars, interplanetary flight, Hohmann ellipse, transfer orbit, synodic period, ----------------------- (19) Airplane Flight http://www.phy6.org/stargaze/Sflight.htm This web page and one linked to it contain a very elementary discussion of the physics of airplane flight. Concepts of lift and drag are used to apply vectors and frames of reference to wings swept back (or forward!), also to propellers. The linked file discusses dependence of lift and drag on speed and altitude, using as example the "Voyager" non-stop flight around the world. A lesson plan on the first page only is at Lflight.htm Keywords: Aerodynamics, lift, drag, angle of attack, sweepback of wings, propeller pitch, swivel-wing airplane, cruising altitude, Voyager airplane, ----------------------- (20) Mass Measurement in Weightlessness and the Inertial Balance http://www.phy6.org/stargaze/Smass.htm This is the first of three linked web pages. The one listed introduces the concept of mass and the question of how it may be measured without recourse to gravity, e.g. in the weightless environment of a space station. The second tells how such measurements were actually conducted in 1973 aboard "Skylab," and the third describes a simple experiment of comparing masses without using gravity, requiring only a hacksaw blade, clamps, bolts and a watch. Keywords: Mechanics, mass, mass comparison, weightlessness, inertial balance, astronauts, Skylab, space station, astronaut health, Eotvos ----------------------- (21) Work performed against an Electric Force http://www.phy6.org/stargaze/Svandgrf.htm In classes on elementary mechanics, work is usually illustrated by motions with overcome either gravity or friction. This web page, completely qualitative, makes the case for work against electrical forces. Examples include the Van de Graaff voltage generator, the production of lightning in thunderstorms and the separation of clinging sheets emerging from a copying machine. Keywords: Mechanics, electricity, work, electricity, work against electric force, Van de Graaff, static cling, lightning,, electrification of rain clouds, xerography ----------------------- (22) Robert H Goddard and his Rockets http://www.phy6.org/stargaze/Sgoddard.htm A web page devoted to the story of Robert H. Goddard and his contributions, in particular the introduction of the DeLaval nozzle, a story not often told . Without going into calculations, it explains how Goddard used a ballistic pendulum to derive the efficiency of his rockets. Also tells of Goddard's inspirational moment at age 17 (19 October 1899) and on his work with liquid-fueled rockets. Keywords: : Goddard, ballistic pendulum, rocket nozzle, De-Laval nozzle, rocket efficiency, liquid fuel rockets, spaceflight ----------------------- (23) Unconventional Spaceflight http://www.phy6.org/stargaze/SSHARP.htm This web page is the first of 6 linked ones, describing 4 unconventional methods of accelerating spacecraft: cannon, nuclear energy, solar sails and ion rockets. A fifth approach, gravity-assist maneuvers near moving planets or moons, is described further in this sequence (section #35). Keywords: Light gas cannon, high-altitude cannon, Paris siege gun, Big Bertha, nuclear spaceflight, solar sails, Project Orion, ion rockets, ----------------------- (24) Climate and Weather ("Sunlight and the Earth") http://www.phy6.org/stargaze/Sun1lite.htm Climate and weather are driven by the processes by which earth returns to space the heat it receives from sunlight. This web page, continued on two linked sections, traces the processes involved. Radiation and reflection of light (both visible and infra-red) return heat to space directly, but run into the greenhouse effect. Convection and the role of water vapor are discussed in the 2nd section, including the generation of thunderstorms, and then the 3rd one describes global-scale air flows, explaining why wind in the continental US usually blows from the west, while near the equator it comes from the east (e.g. migration of hurricanes across the Atlantic). (24a) Energy Exchanges in the atmosphere ("Atmospheric Energy and Climate") http://www.phy6.org/stargaze/SenergyA.htm Discussion of the above processes from the point of view of energy flow in the atmosphere, from sunlight warming the ground to the tropopause returning energy to space. Discusses vertical heat transport by IR and convection, global heat flow and the role of latent energy of evaporation. Evidence for global climate change is briefly reviewed. Keywords: Sunlight, radiation balance, greenhouse effect, ozone layer, weather, water vapor in the atmosphere, humidity, atmospheric convection, atmospheric temperature profile, thunderstorm cells, squall line, hail, climate, tropical region, polar region, Hadley cells, Coriolis effect, jet stream, Rossby waves, ----------------------- (25) Electromagnetic Waves http://www.phy6.org/stargaze/Sun4spec.htm This section and the one following, linked to it (part of "From Stargazers to Starships") try to explain electromagnetic waves. Starting by distinguishing physiological and spectral color, they tell of spectral lines, the electromagnetic field work by Maxwell (omitting the math!) and the discovery of radio waves by Hertz, ending with photons and Einstein's relation. (A following section deals with X-rays in space.) "Stargazers" also has detailed lesson plans accompanying these sections, at Lsun4spe.htm and Lsun5wav.htm . Keywords: Color, rainbow colors, color dispersion by a prism, perceived color, three-color theory, black-body spectrum, line spectrum, spectral lines, light waves, diffraction grating, absorption spectra, fields, electromagnetic field, electromagnetic waves, Maxwell (James Clerk), displacement current, Hertz, photons, Planck, Einstein, photoelectric effect ----------------------- (26) Nuclear Power http://www.phy6.org/stargaze/Snuclear.htm An introduction to nuclear fission, its controlled release in power stations, also problems of nuclear waste and nuclear accidents. A following web page discussed nuclear weapons their effect, their ban--even "dirty bombs" discussed in recent news. Part of "From Stargazers to Starships" where the preceding section discussed nuclear fusion (as applied to the Sun) and the curve of binding energy. A French translation also exists (Fnuclear.htm). Added March 2009: Nuclear Energy. http://www.phy6.org/stargaze/SnucEnerA-1.htm A series of linked 5 web sites (preceded by introductory summary), covering the subject of commercial nuclear power in greater detail than the preceding item. Part of a free "Flexbook" for Virginia State Schools, meant to cover recent subjects not found in standard texts, it includes problems and answers. Keywords: Nuclear physics, nuclear energy, nuclear composition, nuclear fission, chain reaction, critical mass, nuclear reactor, neutron moderator, nuclear pile, control rods, nuclear waste, nuclear meltdown, Three mile Island, Chernobyl, nuclear bombs, fast neutrons, uranium enrichment, Hiroshima, H-bomb, nuclear fallout, dirty bombs ----------------------- (27) Lagrangian Points http://www.phy6.org/stargaze/Sorbit.htm The combined gravities of Earth and Sun give spacecraft at certain locations the same one-year period as Earth, so viewed from Earth they seem to hang motionless in interplanetary space. Such "Lagrangian points" are used by monitoring spacecraft, as described in this section of "From Stargazers to Starships." The three sections that follow there derive the equilibrium properties of Lagrangian points: the calculations only involve algebra and trig, but are rather lengthy. Translations to French and (in part) Spanish are also provided. Keywords: Space, orbits, Lagrangian point, L1, L2, L4, L5, space colonies ----------------------- Specific topics in "Exploration of the Earth's Magnetosphere" ----------------------- (28) Folding Paper Model of the Earth's Magnetosphere http://www.phy6.org/Education/wfold.html Instructions and an image which can be downloaded, printed on a regular page, copied by a xerox machine (preferably, onto stiff paper), cut and folded to produce a model of the Earth's magnetosphere. A supplement to "Exploration of the Earth's Magnetosphere" whose index page is linked at the beginning and the end of the above page. Versions of the model with Spanish or French captions are also available. Keywords: Space, magnetosphere, paper model, magnetopause, magnetotail ----------------------- (29) Oersted and the Discovery of Electromagnetism http://www.phy6.org/Education/wmfield.html This section and a linked one explain how in 1820 scientists suddenly realized that magnetism was not just a strange property of specially treated iron, but was basically the interaction of electric currents. This section gives the physics (very elementary, no math), and the one linked to it tells of Oersted's discovery and describes a way of demonstrating it in the classroom, using a vu-graph projector. Later sections #5, #5a and #6 extend this to magnetic field lines and electromagnetism. Keywords: Oersted, Ampere, magnetic force, force on electric currents, electromagnetism, history of physics, Halley, Maxwell ----------------------- (30) Electricity as a Fluid http://www.phy6.org/Education/welectrc.html A short non-mathematical description of the analogy between fluid flow in pipes and electricity flow in circuits, comparing batteries to pumps, current to flow rate (liters-per-second) and voltage to pressure. At the end the electric field is introduced as the 3-dimensional distribution of voltage in space. Keywords: Electricity, Electric currents, Ohm's law, field, electric field, ----------------------- (31) Electrons, ions and plasmas http://www.phy6.org/Education/welect.html We all believe electrons and ions exist, but what do students know about that? The above is the first in a series of non-mathematical linked sections, in which "Exploration of the Earth's Magnetosphere" introduces such particles, later focusing on their role in space. The section cited here describes the Edison effect, the next one gives J.J.Thompson discovery of the electron, sections #7 define plasma and illustrate its use in fluorescent lamps (also give the history of the word "plasma"), and sections #8 (wposion.html and whposion.html) give the story of positive ions, including ions in chemical solutions and in radioactivity. Keywords: Electrons, ions, plasma, history of physics, Edison effect, photoelectric effect, J.J. Thomson, history of "electron", ionization, electroscope, positive ions, proton, ions in solutions, space, barium vapor, radioactivity ions, alpha rays, beta rays, history of "plasma," Langmuir, fluorescent lamp, gas discharge, non-ohmic behavior, ballast coil, ----------------------- (32) Motions of Ions and Electrons in Magnetic Fields http://www.phy6.org/Education/wtrap1.html The first of 5 linked web pages describing in non-mathematical terms the "guiding center motion" which determines the motion of ions and electrons trapped in the Earth's magnetic field (and also in laboratory plasma devices). Covered are gyration and mirroring, later also adiabatic invariance and drifts due to an electric field and due to gradients in the magnetic field intensity. Keywords: Ions, electrons, charged particles, particles in a magnetic field, gyration around field lines, magnetic guiding of particles, magnetic mirroring, magnetic drift, ring current of Earth, electric drift, trapped particles, radiation belts, trapping in plasmas, adiabatic invariants, parallel electric field, ----------------------- (33) The Discovery and Early History of the Earth's Radiation Belts http://www.phy6.org/Education/wexp13.html The first of 6 linked web pages on how the inner radiation belt was discovered in 1958 by Van Allen, on the type of instrument used (Geiger counter), on the belt's explanation based on neutron albedo, on radiation belts created by nuclear bombs and on the discovery of the outer belt. Nonmathematical and short; a longer exposition (with references) is in file bh2_1.html of the same collection. Keywords: Space, history, space race, Explorer 1, Sputnik, satellites, inner radiation belt, neutron albedo, outer radiation belt, artificial radiation belt, Geiger counter, Van Allen, Christofilos, project Argus, project Starfish ----------------------- (34) Secrets of the Polar Aurora http://www.phy6.org/Education/aurora.htm Grades 9-14 The polar aurora ("northern lights")--rare to most of us, but not in Alaska--is our window to the magnetic environment of Earth in space. The very detailed review tells where and when it is seen, its relation to the Earth's magnetic field, to the electric currents which accelerate its electrons, to radiation belts and sunspots, to magnetic storms and "substorms," even its history and "artificial aurora" created by humans. Part of the non-mathematical exposition "Exploration of the Earth's Magnetosphere", its Spanish translation is on http://www.phy6.org/Education/Msecrets.html Keywords: Space, electrons, aurora, polar aurora, northern lights, auroral zone, auroral substorm, magnetic storm, red aurora, green aurora, aurora and magnetic field lines, Birkeland, auroral currents, solar wind, magnetosphere, magnetotail, mirroring, energy of aurora, sunspots, Schwabe, artificial aurora, project Argus, Jupiter aurora ----------------------- (35) Tracing Interplanetary Magnetic Field Lines http://www.phy6.org/Education/wimfproj.html A graphical exercise for students, tracing a typical interplanetary magnetic field line, dragged out of a location on the Sun by the radial flow of the solar wind. This illustrates the way magnetic field lines are "frozen to the plasma." Keywords: Space, magnetic field lines, lines of force, interplanetary magnetic field, solar wind, spiral field in space, freezing of field lines in a plasma, stretching of sunspot fields, classroom project on space ----------------------- (36) Solar Activity http://www.phy6.org/Education/wsun.html The first of 4 linked files giving a very brief and elementary overview of sunspots, flares and coronal mass ejections, including some early history and the articles by Schwabe (1843) and Carrington (1859). Keywords: Space, sun, solar physics, sunspots, magnetic field, magnetic energy, eruptions on the sun, Schwabe, Carrington, history of solar physics, sunspot cycle, solar corona, solar flares, magnetic storms, coronal mass ejections, Hale (George Ellery), magnetism of sunspots, ----------------------- (37) The Solar Wind http://www.phy6.org/Education/wsolwind.html An elementary introduction to the solar wind,, starting with evidence from comet tails and continuing to Parker's theory of the Sun's corona. Two linked web files follow in the same collection, the first a graphic exercise (suitable for the classroom) for tracing interplanetary magnetic field lines "dragged out" of the Sun by the solar wind, the second, a quick summary of the observational discovery of the solar wind. A recent file also describes the discovery (late 2004) of the "termination shock" where the solar wind starts reaching its outer limits. Keywords: Space, sun, Sun-Earth connection, solar physics, corona, coronal heat, comets, ion tails of comets, Biermann (Ludwig), Parker (Eugene), solar wind , interplanetary magnetic field, solar wind streams, heliosphere, termination shock, classroom project on interplanetary field ----------------------- (38) Magnetic Substorms, Storms and Space Weather http://www.phy6.org/Education/wsubstrm.html Keywords: Space, magnetosphere, solar activity, space weather, magnetic energy, magnetotail, aurora, auroral substorms, particle acceleration, ring current injections, magnetic storms, flares, interplanetary shocks, open magnetosphere, reconnection, substorm electric currents, ----------------------- (39) Cosmic Rays http://www.phy6.org/Education/wcosray.html see also http://www.phy6.org/Education/wenpart1.html An elementary discussion of cosmic rays (on the high school level), followed by two linked sections on high energy particles in the universe and high-energy particles from the Sun. The common thread is the unexpected existence in our universe of atomic particles (ions) whose velocity approaches that of light. They bombard the Earth in a constant drizzle, and their origin poses interesting questions. Includes recent observation of X-ray origins by the HESS array in Namibia Keywords: Space, energetic particles, electron volt, cosmic ray protons, cosmic ray energy, cosmic ray showers, air showers, supernovas, celestial gamma ray sources, HESS experiment, Cherenkov radiation, shock acceleration. ----------------------- (40) Magnetospheres of other Planets http://www.phy6.org/Education/wotherms.html http://www.phy6.org/earthmag/mill_8.htm Most large planets in the solar system have magnetic fields, probably produced quite differently from ours. The giant planets also have trapped radiation belts--indeed, those of Jupiter and Saturn are far more intense than Earth's, and their polar auroras have been observed by telescopes from Earth. Keywords: Jupiter magnetosphere, Saturn magnetosphere, Uranus magnetosphere, Neptune magnetosphere, Mercury magnetic field, Io dynamo ----------------------- Specific topics in "The Great Magnet, the Earth" ----------------------- (41) Discovery of the Magnetic Compass http://www.phy6.org/earthmag/upto1600.htm First of several linked files, telling the early history of the compass (discovered in China) and how Robert Norman in 1581 showed the magnetic force was not horizontal but slanted downwards. He was followed by William Gilbert's demonstration that the Earth behaved like a giant magnet; two reviews of Gilbert's 1600 book "De Magnete" follow, as well as a modern version of one of Gilbert's experiments. The web collection also includes several sections for science teachers. Keywords: Geomagnetism, history, magnetism, compass, lodestone, Robert Norman, William Gilbert, De Magnete, compass, terrella, dip needle, magnetic declination, magnetic inclination, induced magnetism, ----------------------- (42) Lodestones http://www.phy6.org/earthmag/lodeston.htm Naturally occurring magnets or "lodestones" gave humans their first experience with magnetism, making possible the magnetic compass and its use by seafarers. What are these strange minerals and how were they formed? A proposed explanation is described. Keywords: History, geomagnetism, lodestone, magnetite, magnetization, lightning, Curie point ----------------------- (43) Magnetometers--and Cigarette Smoking http://www.phy6.org/earthmag/magmeter.htm A short non-mathematical web page (with links) about modern magnetometers, in particular, fluxgate instruments, which depend on the saturation of magnetic materials. When placed aboard spacecraft, these are sensitive enough to observe the very weak magnetic fields in space. Includes an application--a 1979 experiment on the effects of cigarette smoking which suggested the reason why the damage caused by asbestos inhalation is amplified by smoking. This is part of the site "The Great Magnet, the Earth" where it is also available in Spanish, German and French. Keywords: Magnetism, magnetometer, fluxgate, magnetic saturation, ring cores, proton precession magnetometer, magnetic shielding, David Cohen, cigarette smoking, cilia in trachea, carcinogens, tobacco, asbestos. ----------------------- (44) Dynamos, Magnetic Reversals and Plate Tectonics http://www.phy6.org/earthmag/dynamos.htm http://www.phy6.org/earthmag/mill_5.htm A "dynamo process" creates the magnetic fields of the Earth of the Sun: flows of electrically conducting through existing magnetic fields produces electric currents, which maintain the magnetic field. Michael Faraday in 1832 first tried to observe the process in a flowing river, Larmor in 1919 suggested it made sunspots magnetic, and today's computers can simulate it. Dynamos in the Earth's core may reverse the north-south polarity, a process recorded by sea-floor magnetization, which confirms the slow motion of continents. Three linked sections of "The Great Magnet, the Earth" (starting with the above) give the details. More is found there in "A Millennium of Geomagnetism," as well as instructions to teachers and translations to Spanish, French and German. Keywords: Geomagnetism, history, Faraday, dynamo, fluid dynamo, solar magnetism, solar rotation, frozen-in field lines, interplanetary magnetic field, Earth core, Blackett, poloidal, toroidal, alpha-dynamo, Cowling's theorem, Wegener, continental drift, polar wandering, sea-floor spreading, Lawrence Morley, plate tectonics ----------------------- Separate web pages ----------------------- (45) Proposed K-12 Science Standards http://www.phy6.org/outreach/edu/standard.htm In 1998 the State of Maryland issued a call for inputs on a statewide science syllabus, and this (somewhat ambitious) "set of standards" was submitted. Although not adopted, it might provide some guidance to other school systems. Following a short list of guiding principles, this web page lists goals for grades K-3, 4-5, 6-8 and 9-12, in each of the following areas: mechanics, heat, electricity and magnetism, light and sound, space, geology, weather and climate, and modern physics/nuclear power. Keywords: Science curriculum, science education, teaching of science, syllabus, education goals, education standards, grades K-3, grades 4-5, grades 6-8, grades 9-12, high school physics, mechanics, heat, electricity, magnetism, light, sound, space, geology, weather, climate, modern physics, nuclear power ----------------------- More recent additions to the web collections" ----------------------- (46) Deriving solar system dimensions using the 2004 transit of Venus http://www.phy6.org/stargaze/Svenus1.htm On June 8, 2004, the planet Venus passed between the Earth and the Sun. As Halley had noted about 300 years earlier, by measuring the time required by Venus to cross the Sun's disk, as seen from different locations on Earth, one can deduce actual distances in the solar system in kilometers. In contrast, Kepler's laws of planetary motion only give relative distances, e.g in terms of the "Astronomical Unit" (AU), the mean Sun-Earth distance. The above web page is the first of 3 linked ones deriving the AU, using predicted transit times at Cairo and Durban. The calculation is approximate, involving only simple algebra and trigonometry, but is still accurate to within 5%. Factors taken into account include the rotation of the Earth, the finite distance of the Sun, the eccentricity of the Earth's orbit and the obliqueness of the Earth's axis. A related introductory page "The Scale of the Solar System" is also linked. Keywords: Astronomy, Venus, Venus transit, astronomical unit, AU, Halley's method, parallax, solar parallax, first contact ----------------------- (47) How Things Fall http://www.phy6.org/stargaze/Sfall.htm A freely falling object (if air resistance can be neglected) increases its fall velocity by about 9.81 meter/sec each second, its acceleration. This section calculates such accelerated motion, with or without an initial velocity, and discusses how Galileo examined such motions and how a similar experiment can be performed in class. A lesson plan is linked. Keywords: Mechanics, free fall, gravity, acceleration, acceleration due to gravity, Galileo, history, velocity, final velocity, time of fall, intuitive view of fall, false concepts of fall, rifle sight, air resistance ----------------------- (48) Vectors http://www.phy6.org/stargaze/Svector.htm Velocity, as well as acceleration and force, are vectors--quantities with both magnitude and direction, in a way a new family of number-like objects. This section shows how vectors are added, also how any vector (on a plane) can be resolved into the sum of two vectors having standard directions, and how that allows the motion of an object of a friction-free slope to be calculated. With linked lesson plan Keywords: Mathematics, vector, vector addition, velocity addition, vector resolution, components, Cartesian components, mechanics, inclined plane ----------------------- (49) Energy http://www.phy6.org/stargaze/Senergy.htm Energy in physics is something like money in society: every process must be paid for by energy. Pendulum motion is an exchange of kinetic and potential energy, and other types include electric energy, heat (measured in calories) chemical energy (also measured in calories, in the case of food) and light. The total energy is always conserved, but heat is a "soft currency"--you can convert other energies into it, but you can never convert all of it back. With linked lesson plan and related file on work. Keywords: mechanics, energy, kinetic energy, potential energy, conservation of energy, conversion of energy, work, chemical energy, food energy, energy conversion, heat, joule, calorie, second law of thermodynamics, ----------------------- (50) Newton's laws http://www.phy6.org/stargaze/Snewton.htm Newton formulated the first fundamental laws of motion: motion is causes by forces, which act in pairs (if object A pushes B, then B pushes A with equal and opposite force), and causes acceleration. Every object also has mass, which resists acceleration: heavy objects fall no faster than light ones, because they also have proportionally greater mass (also called "inertia"), which resists the motion. With linked lesson plan, and several consecutively linked related web pages. Keywords: Mechanics, force, Newton, Newton's laws, inertia, mass, motion against resistance, balanced forces, freely accelerated motion, inertia of ships, inertial balance, Skylab, weightlessness, Astronauts, Newton's second law, Newton's third law, Newton (unit of force), reaction force, bicycle balance, Ernest Mach, momentum, conservation of momentum, Eotvos (Roland or Lorand), ----------------------- (51) Newton's Universal Gravitation http://www.phy6.org/stargaze/Sgravity.htm Newton allegedly wondered if the force of gravity which caused apples to fall down (the story is traced here) was the reason the Moon orbited the Earth and did not break free from it. His calculation is given (assuming the formula for centripetal acceleration). With linked lesson plan. Keywords: Mechanics, astronomy, gravity, gravitation, Newton, Newton's apple, inverse squares law, moon motion, lunar motion, lunar period, Cavendish, gravitational constant, galaxy, Kepler's third law, Kepler's 3rd law, orbital velocity, escape velocity, synchronous period ----------------------- (52) Work http://www.phy6.org/stargaze/Swork.htm Work is overcoming a force along a distance, e.g lifting a brick from the floor to the table. Energy is needed for performing it, as is illustrated by an example, With linked lesson plan, also linked section giving a qualitative discussion of 3 examples of work done against electric forces. Keywords: Mechanics, energy, work, friction, funicular railroad, electric forces, work against electric force, Van de Graaff, static cling, electrification of rain clouds, lightning, ----------------------- (53) Inertial forces http://www.phy6.org/stargaze/Sframes2.htm Newton's laws hold in the universe at large, but sometimes our frame of reference, relative to which all our measurements are done, is itself accelerating--e.g. the rotating Earth, or a rapidly decelerating car. To calculate the forces needed to create equilibrium there, extra "fictitious" or "inertial" forces need to be added. With linked lesson plans, also linked with section on the centrifugal force, the most common example. Keywords: Mechanics, frames of reference, inertial frame of reference, accelerated frame of reference, deceleration, rotating frame of reference, centrifugal force, equatorial bulge of Earth. ----------------------- (54) Motion in a circle http://www.phy6.org/stargaze/Scircul2.htm Motion in a circle is accelerated motion, and the "centripetal" force required to maintaining a circular path can be calculated using the Pythagoras theorem. It is directed to the center of the circle. With linked lesson plan. Keywords: Mechanics, uniform rotation, acceleration, centripetal acceleration, centripetal force, Pythagoras theorem ----------------------- (55) Introduction to rotating frames of reference http://www.phy6.org/stargaze/Srotfram.htm The inertial force in an orbiting spaceship or an airplane following a free-fall trajectory can explain the "weightlessness" observed there on objects at rest. Objects that move in a rotating frame experience an additional "Coriolis force", given a qualitative explanation. The Coriolis force dictates the swirling of hurricanes, but not of water draining from a sink! With linked lesson plan; also, a preceding section on physics of the rotating Earth. Keywords: Mechanics, rotating frame of references, weightlessness, vomit comet, Coriolis force, bathroom sink, swirling of atmosphere, Buys Ballot law, hurricanes ----------------------- (56) Introduction to Quantum Physics http://www.phy6.org/stargaze/Q1.htm First in a series of 8 linked non-mathematical web pages, tracing the ideas of quantum physics and their history from the discovery of atoms, to the Balmer series (1885), to Plank's radiation formula(1900), to Bohr's model (1913), to expansions by Sommerfeld and Pauli, wave mechanics (1925-6) and quantum tunneling. Part of a broader section on the Sun and its physics, in a large course on astronomy, physics and space. Keywords: Planck's constant, atoms, photons, line spectra, electrons, Balmer series, Rydberg's constant, Lyman series, energy levels, Ritz principle, ground state, Zeeman effect, black body spectrum, solar spectrum, primordial fireball, microwave background, Bohr's model, atomic nucleus, Rutherford, quantum numbers, adiabatic invariants, sodium spectrum, allowed transitions, quantization of angular momentum, electron spin, periodic table, wave mechanics, wave-particle duality, fields, duality of light, orbitals, wave function, tunneling, alpha radioactivity, Gamow ----------------------- (57) At the edge of the solar system http://www.phy6.org/Education/wtermin.html On December 16, 2004, the space probe Voyager 1 apparently crossed the termination shock of the solar wind. Encountered at a distance of 94 AU (nearly 3 times the distance of Pluto), the termination shock is the first sign of the interstellar medium, stopping the solar wind from expanding into space without limit. Keywords: Astronomy, solar system, solar wind, interstellar medium, interstellar plasma, interstellar magnetic field, interplanetary, magnetic field, shock front, termination shock, heliosphere, heliopause, Voyager 1. ----------------------- (58) A Frying Pan Electrophorus http://www.phy6.org/outreach/edu/electrph.htm How can you tell that static electricity, usually at a fairly high voltage, and the charge produced by a chemical cell, are one and the same fluid? Alessandro Volta, who introduced the latter, also designed an instrument to boost a low voltage to a much higher level. Using a frying pan, aluminum and saran foils, a neon-light tester and some wires, you can build one, too. Keywords: Electricity, capacitance, electric cell, Alessandro Volta, electrophorus, voltage, ----------------------- (59) The Grease Spot Photometer http://www.phy6.org/outreach/edu/greaspot.htm A simple tabletop experiment, using very simple equipment, demonstrating quantitatively that light intensity decreases as the inverse square of the distance from the source. It also underscores that many measurements are really comparisons to a standard. Keywords: Light, photometry, calibration, comparison to standard, candle experiment, grease spot, inverse squares law ----------------------- (60) Keplers 3 Laws--Overview for Science teachers http://www.phy6.org/stargaze/Kep3laws.htm A lecture given to science teachers, guiding them in teaching Kepler's laws, including applications, calculated examples and the history surrounding Kepler's work. Keywords: Mechanics, astronomy, Kepler's laws, lesson plans, history, scientific revolution, ellipse, galactic center, planets, perihelion, aphelion, Kepler's second law, Kepler's 3rd law, fall to the Sun, Halley's comet ----------------------- (61) Teaching about Magnetism http://www.phy6.org/earthmag/MagTeach.htm A presentation for teachers about presenting elementary facts about magnetism, including 3 tabletop demonstrations (or experiments) which can also be done on top of a vu-graph projector, for the entire class to see. They involve the magnetic compass (with a floating needle), induced magnetism and magnetism produced by an electric current in a straight wire. Keywords: Magnetism, teaching magnetism, classroom demonstrations, history, compass, surface tension, projector, floating needle, Norman (Robert), Gilbert (William), induced magnetism, electroscope, Oersted, Ampere, lodestones, lightning ----------------------- (62) Timeline of Astronomy, Physics and Spaceflight http://www.phy6.org/stargaze/Stimelin.htm A timeline of astronomy, physics and spaceflight (red entries) interleaved with a history of human society and technology (black). Part of a wider site "From Stargazers to Starships," With scientific entries linked to corresponding web-pages in "Stargazers." Keywords: History, astronomy, physics, space, spaceflight, history of science, chronology, timeline, world history ----------------------- (63) Timeline of studies of the Earth's Magnetic Field in Space http://www.phy6.org/Education/whchron2.html A timeline of studies of the Earth's Magnetic Field in Space (red entries) interleaved with a history of human society and technology (black). Part of a wider site "Exploration of the Earth's Magnetosphere." Keywords: Apace, magnetosphere, history, radiation belts, magnetic storms, chronology, timeline, world history ----------------------- (64) Introduction to the Doppler effect: The Velocity of Light http://www.phy6.org/stargaze/Sun4Adop1.htm The discovery of the velocity of light in 1676 by Ole Romer actually applies an idea which later expanded into the Doppler effect observed in sound and light. Keywords: Astronomy, Doppler, Romer, longitude, Io (satellite of Jupiter), velocity of light, c ----------------------- (65) The Doppler Effect and the Expanding Universe http://www.phy6.org/stargaze/Sun4Adop2.htm The apparent shift in frequency of a wave when source or observer are moving was proposed by Christian Doppler in 1842 and was tested by Buys Ballot using a musician aboard a moving train. Today is is observed in light of binary stars, in broadening of spectral lines and most notably, in the red-shift of distant galaxies, demonstrating the expansion of the universe. That expansion seems faster for near stars than for distant ones, emitting light from the early universe suggesting the expansion is accelerating--perhaps due to some "dark energy" added to the universe. Keywords: Astronomy, Doppler, light, sound, wavelength, double stars, Doppler broadening, red-shift, Big Bang, expanding universe, dark energy. ----------------------- (66) Rotating Galaxies and Dark Matter http://www.phy6.org/stargaze/Sun4Adop3.htm Most galaxies seem to rotate, and the rotation rate as function of distance depends on the distribution of mass, e.g. if most mass is at the center, we expect Kepler's 3rd law. If instead mass is distributed in proportion to the distribution of luminous stars in the galaxy, a different distribution of rotation rate can be derived. The rate can also be observed using the Doppler effect--one side of the galaxy approaches, the other recedes. The observed variation deviates from either result, and is closer to uniform rotation. Astronomers have proposed that this is due to unseen "dark matter" in the galaxy, distributed more uniformly. What this matter might be no one knows. Keywords: Astronomy, galaxy, Andromeda galaxy, galaxy rotation, Kepler's 3rd law, dark mass ----------------------- (67) Logarithms--introduction http://www.phy6.org/stargaze/Slog1.htm http://www.phy6.org/stargaze/Slog2.htm http://www.phy6.org/stargaze/Slog3.htm Just as division is the inverse of multiplication, "taking a logarithm" may be viewed as the inverse of "raising to a power." The problem is--when the power exponent is whole, like 2, 3, 4 etc., we simply multiply that many times, but to invert, we need also powers which are negative, fractional or any other type of number. After this is accomplished in the early 1600s, tables of decimal logarithms became a useful calculation tool, and today's electronic calculators can replace those tables. Logarithms also simplified the handling of very big and very small numbers, by means of the "scientific notation" and helps one derive relations like Kepler's 3rd law. (No calculus is used.) Keywords: Logarithms, powers of numbers, exponents, base, Napier, Briggs, decimal logarithms, common logarithms, scientific notation, power law, Kepler's 3rd law ----------------------- (68) Deriving Logarithms http://www.phy6.org/stargaze/Slog4.htm Tables of logarithms have their limit--sometimes one must "interpolate" between tabulated values, like estimating a length that falls between two divisions on a ruler. Here approximate logarithms are derived, without requiring calculus. The fact that the tenth power of 2 is 1024, close to 1000, gives an estimate of decimal log 2, and similar methods can be applied to other integers up to 10. The slide rule is then described--a pre-electronic aid to calculation, based on logarithms, and examples are given of logarithmic effects in nature--magnitude of stars, Weber-Fechner law, the Richter scale of earthquakes and the velocity attained by rockets. Keywords: logarithms, interpolation,approximate values of logarithms, slide rule,stellar magnitude, Weber-Fechner law,Richter scale, rocket motion. ----------------------- (69) The number "e" http://www.phy6.org/stargaze/Slog5.htm "Simple" interest of (say) 6% can be calculated annually--but collecting 3% twice a year yields more, 0.5% every month even more. This process of "compound interest"leads to a limit however, related to a universal mathematical constant e = 2.7182818.. , important in calculus and more advanced math. Keywords: simple interest, compound interest, the number e, limits ----------------------- (70) Natural Logs and more accurate approximate Logarithms. http://www.phy6.org/stargaze/Slog6.htm Approximate values of logarithms using base "e" (or "natural logs") are relatively easy to derive, and if we know how to switch logarithms from one base to another, it also helps derive decimal or "common" logs. We need then the binomial theorem, and we need the decimal log of "e" which is 0.434294... . With these, much more accurate approximations are obtained, even without calculus. Keywords: Natural logarithms, binomial theorem ----------------------- The Solar System, sections P-1 through P-14 of |
Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: david("at" symbol)phy6.org .
Last updated 20 February 2008
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