Literature for Gravity-Applet

Wolfgang Demtröder:
Experimentalphysik 4, Kern- Teilchen- und Astrophysik, Heidelberg 1998
Experimentalphysik 1, Mechanik und Wärme, Heidelberg 1994

The Consortium for Upper Level Physics Software, Classical Mechanics Simulations, New York

DTV-Atlas zur  Astronomie,10th edition, München 1990

Richard Greenberg und Donald Davis: 'Stability at potential maxima: The L4 and L5 points of the restricted three-body problem' in American Jornal of Physics, 46, Vol 10, Oct. 1978 (Trojan motion)

William K. Hartmann, Moons and Planets, Belmont (California) 1993 (overview, easy to understand))

Hans-Ulrich Keller, Kosmos Himmelsjahr 1999, Stuttgart 1998 (German, for astronomy-amateurs, easy to understand)

Kenneth R. Lang, Planeten: Wanderer im All, Heidelberg 1993

Sir Harrie Massey, Space travel and exploration, London 1966

David Morrison, Planetenwelten, Heidelberg 1995

Press et al., Numerical Recipes in Pascal (or C), Cambridge Univ. Pr ( Programming of Runge Kutta algorithm)

Ernst A. Steinhoff, Weltraumfahrt, Darmstadt 1973

Josef Stoer, Numerische Mathematik 1(&2), 7. Auflage, Heidelberg 1994 (Regula/Falsi Zerosearching, adaptive stepsize for numerical integration)

Stumpf, Himmelmschanik, VEB Verlag der Wissenschaften, Berlin 1965 ("Hard food")

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Related  Internet-Links

Asteroid 3753 coorbiting with Earth (three body-problem)

Australian Spacewatch for asteriodes

CASS Home Page (Center for advanced space studies)

Dangerous Asteroides (Map of real inner solar system with Asteroides)Asteroid conference

Deep Impact (Nasa-Space Probe)

What Hollywood created about motion in the solar system ( German: ArmagedonDeep Impact ) (English reviews:  Armagedon , Deep Impact  more  DI )

ESA European Space Acency and its Missions

Galileo Mission to Jupiter

International Space Station Virtual tour

Lunar and Planetary Institute (LPI) Home Page

Mars Exploration

NASA (nationl aeronautic and space administration)NASA headquarters  Space flights

Near spaceprobe to Eros

Welcome to the NSSDC! (National space science data center)

Orbital Plots

Planetary science meeting

Saturnimages Cassini, Voyage to SaturnThe Cassini Mission to Saturn

Skyweek-site (German but English links)

Space Science Missions

Sterne und Weltraum (German Astronomy Magazine)

Solar System Simulator (Nasa, Chose the Planets etc you want to watch static views, planetary images and  prepared animations such as Galileo's arrival at Jupiter)


Exercises concerning Gravitation (Summary of Physics)
(Some ones  taken from Wolfgang Demtröder: Experimentalphysik 1, Mechanik und Wärme, Heidelberg 1994 and Experimentalphysik 4, Kern- Teilchen- und Astrophysik, Heidelberg 1998)

1. Conclude Newton's gravity law from Kepler's laws and vice versa. (see Wolfgang Demtröder: Experimentalphysik 1, Mechanik und Wärme, Heidelberg 1994). Use the Applet's item [Sun and One] to see an example ellipse. Add Objects [+] and change values and/or directions of the preset speeds (or they would only create circular orbits.). Use [A] (adaptive stepsize) for creating narrow ellipses.

2. How fast has a spacecraft  (Mass 10000 kg) to be a) to escape from Earth at Moon's Distance b) to escape from Solar System at Earth's distance from the Sun. You can approximatly find out the values by selecting [Inner Solar System], getting Earth or Sun as center by [CE] and using the add object [+] procedure of the Applet, but you better compute exactly:-)

3. Halley's Comet has an orbiting period of 76 years. It's shortest distance to Sun is 0.59 Astronomical units. How fast is it at this distance, how long is it's semiaxis and it's greatest distance to Sun. Use the Applet's procedure [Define new System]  to visualize your results. (Start the comet at  its perihel and scale its speed.)

4. Why can little objects get accelerated or slowed down by passing heavy planets (Jupiter!!!) during the so called swing-by-maneuvers. Use [Sun Jupiter Comet] to see an example of a swing-by-comet-capture to the solar System by Jupiter. [Swingby] to watch how Voyager left the Solar System using Jupiter's and Saturn's gravity force. Why dit it have to fly past the planets?

5. At what distance to the center of Earth has a satellite to be placed to orbit it in exactly one day? How far is this geostationary orbit form Earth's surface. Select [Inner Solar System] and Earth as center to verify your results. Pay attention to "integrating stepsize"! Why do you need finer steps than for computing the Moon's orbit? What happens if the stepsize is to large? Consider numerical effects.

6. Why do the Trojans keep their relative location on the triangle with equal edges Sun-Jupiter-Tojan? (see Richard Greenberg und Donald Davis: 'Stability at potential maxima: The L4 and L5 points of the restricted three-body problem' in American Jornal of Physics, 46, Vol 10, Oct. 1978 ) Why is there a mass-ratio-limit for "Jupiter" relative to "Sun" to allow Trojans? What happens to objects placed at different distances to the Lagrangian Points or on Jupiter's Trace? Use the [Trojan Traces] Menu-item. Where are further stable orbits in the Sun-Jupiter-System. What results to planetary orbits  if masses of Sun and Jupiter were similar? You can explore that by the [Double Star System], [Two equal Masses] and [Alpha Centauri] item, too.

7. Try to build a System yourself with two equal or similar masses orbiting each other. It won't work if you don't let actualize the speed of the center.Why? It's no numerical problem! What is wrong when one object is seen as not moving? At what mass-ratio between center and satellite this effect can be ignored? Consider the energy-shift of an electron and a proton orbiting their center of mass.

8. What additional speed has to be given to a spacecraft starting from Earth (so that it has already Earth's orbiting speed) to reach the orbit of Mars. (look for Hohmann transfer traces) How long is the semiaxis of the transfer trace? What is the optimum constellation (shortest flight) of Earth and Mars to start. The Applets procedure [Mars Mission] was found by "try and error"-method, varying start conditions. If you find a better solution you can apply for NASA's Mars-missions.