Recall that Kepler's Third law is

P^{2} = a^{3}, where P is in years and a is in astronomical units.

You may find the following numbers useful.

The speed of light is 3x10^{5} km-sec^{-1}.

1 AU is 1.5x10^{8} km.

One year = about 3x10^{7} 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 P
^{2}= (a^{3})/10^{12}.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 3x10

^{8}years.