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)

I've calculated the muzzle velocity to be 120sqrt(2) ft/sec based on the acceleration of gravity being 32 ft/s/s and no air drag.

My logic is that the time of flight of the golf ball on earth would be equal to someone dropping a golf ball from a 900 ft. ladder. Using S=vt+(1/2)at^2 with v=0, a=32 and S=300; t is 7.5 sec. With no gravity the ball would have traveled from the cannon to the top of my 900 foot ladder (900 ft. away); a distance of 900sqrt(2) ft.

900sqrt(2) ft. in 7.5 sec is 120sqrt(2) ft/sec.

Edited on February 18, 2006, 4:15 pm

Edited on February 18, 2006, 4:21 pm

Edited on February 18, 2006, 8:38 pm

Posted by Eric on 2006-02-18 16:13:01