Extra Problems - Kepler's laws
Recall that Kepler's Third law is
P2 = a3, where P is in years and a is in astronomical units.
You may find the following numbers useful.
The speed of light is 3x105 km-sec-1.
1 AU is 1.5x108 km.
One year = about 3x107 seconds.
- Comet Borrelly has an orbital period of 6.8 years. What is the semi-major axis of its orbit in astronomical units? If its orbit is a circle, between which two planets does its orbit lie?
- A new and very large "asteroid" has been found. It's orbital period is about 250 years, what is the semi-major axis of its orbit? If its orbit is circular, near what planet does it move?
- How long does it take a planet following a circular orbit at 10 AU to circle the Sun?
- Kepler's Law as written above applies to planets moving around the Sun. It can be modified to apply to any two orbiting objects. For example, if a star is orbiting in the Milky Way, the law can be written (approximately) as P2 = (a3)/1012.
Use this law to figure out how roughly the distance from the center of the galaxy in astronomical units a star is orbiting if its orbital period is 3x108 years.