Wolfgang **Demtröder:**

Experimentalphysik 4, Kern- Teilchen- und Astrophysik, Heidelberg 1998

Experimentalphysik 1, Mechanik und Wärme, Heidelberg 1994

The **C**onsortium for **U**pper Level **P**hysics **S**oftware,
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")

[Back to Homepage][Back to seminar site] [Other Gravity Applets]

**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: Armagedon , Deep Impact ) (English reviews: Armagedon , Deep Impact more DI )

ESA European Space Acency and its Missions

International Space Station Virtual tour

Lunar and Planetary Institute (LPI) Home Page

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

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

Saturnimages Cassini, Voyage to SaturnThe Cassini Mission to Saturn

Skyweek-site (German but English links)

Sterne und Weltraum (German Astronomy Magazine)

**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.