A golf ball cannon is made that shoots the ball at a 45 degree angle to the horizontal, and consistently achieves 300 yards.

That cannon is transported to a spherical asteroid which has the same density as the Earth. A golf ball is fired in a horizontal direction and just reaches the velocity for a stable circular orbit.

What is the radius of the asteroid?
What is the time of one orbit?

Assume the radius of the Earth is 4000 miles.
(Inspired by The Longest Drive)

(In reply to solution by Charlie)

Nice work, Charlie.  But, if the golf ball is fired "horizontally" at orbital velocity, what would keep it from hitting the back of the cannon instead of making it all the way around the asteroid?

Here's another thought.  Is there a reaction to firing the cannon that would make the asteroid start spinning in the direction opposite to that of the golf ball?  That would reduce the orbital period slightly.  Probably negligible.

Posted by Mindrod on 2006-02-18 23:47:53