(Adopted from Universe, Ch.4, with some modifications)
| 01. | The synodic period of Mercury (an inferior planet) is 115.88 days. Calculate its sidereal period in days. |
| 02. |
A comet orbits the Sun with a sidereal period of 27.0 years.
(a) Find the semimajor axis of the orbit. (b) At aphelion, the comet is 17.5 AU from the Sun. How far is it from the Sun at perihelion? |
| 03. |
One trajectory that can be used to send spacecraft from the Earth to
Venus is an elliptical orbit that has the Sun at one focus,
its aphelion at the Earth,
and its perihelion at Venus. The spacecraft is launched from Earth and
coasts along this ellipse until it reaches Venus, when a
rocket is fired either to put the spacecraft into orbit around Venus or
to cause it to land on
Venus.
(a) Find the semimajor axis of the ellipse. (Hint : Draw a picture showing the Sun and the orbits of the Earth, Venus, and the spacecraft. Treat the orbits of the Earth and Venus as circles.) (b) Calculate how long (in days) such a one-way trip to Venus would take. |
| 04. |
A satellite is said to be in a "geosynchronous" orbit if it appears always
to remain over the exact same spot on Earth.
(a) What is the period of this orbit? (b) At what distance from the center of the Earth must such a satellite be placed into orbit? (c) Can such a satellite stay directly over Taiwan? Explain. |
| 05. | Imagine a planet like the Earth orbiting a star with 4 times the mass of the Sun. If the semimajor axis of the planet's orbit is 1 AU, what would be the planet's sidereal period? |
| 06. |
Suppose a newly discovered asteroid is in a circular orbit with synodic
period 1.25 years. The asteroid lies between the orbits of Mars and Jupiter.
(a) Find the sidereal period of the orbit. (b) Find the distance from the asteroid to the Sun. |