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ASTRONOMY
Spring 2009
If ~ ') N 2010
1. A satellite is said to be in a "geosynchronous" orbit if it appears always to remain over
the same exact spot on Earth.
(a) What is the period of this orbit?
(b) At what distance from the center of the Earth must the satellite be placed into orbit?
(c) Explain why the orbit must be in the plane of the Earth's equator.
(a) What is the distance (in km) from the center of the Sun to the center of mass of
Earth-Sun system?
(b) What is the distance (in km) of from the center of the Sun to the center of mass of
Jupiter-Sun system?
(c) Compare the results from a) and b) to the solar radius (R0).
3. (Problem
5.15) We observe two stars that are 1 and 2 arcsec, respectively, from
center of mass. The system is 10 pc from us. The period is 33 yr. What are
masses of the two stars, assuming that i=900? (Hint/aside:
The i=90° means we
observing the stars from the direction perpendicular to their orbital plane. Also, while
explicitly stated in the textbook's version, you have to assume the orbits are circular
the information given to be sufficient to solve this problem.)
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(a) Jupiter's orbital period around the Sun is P=1l.9 years. Calculate its orbital radius.
(b) Jupiter's moons were observed at Jupiter's closest approach to the Earth. Ganymede's
greatest angular separation from Jupiter was measured to be 5' 50.25". What is
Ganymede's orbital radius around Jupiter?
(c) Ganymede's period is 7.15 days. Assuming that its mass is negligible compared to
Jupiter, calculate the mass of Jupiter in solar masses (M0).
5. Consider a comet in our Solar System with an aphelion distance of 5x 104 AU and an
orbital eccentricity of 0.995.
(a) What are the perihelion distance and orbital period?
(b) What is the comet's speed at perihelion and at aphelion?
(c) What is the escape speed from the Solar System at the comet's aphelion? What do
you conclude from this result?