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.

  1. 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?
  2. 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?
  3. How long does it take a planet following a circular orbit at 10 AU to circle the Sun?
  4. 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.