Assume the moon is a perfect sphere and a straight tunnel has been drilled through the center. How long would it take a 1kg ball dropped from one end of the tunnel to reach the center? Ignore all resistances.
If a second 1kg ball is dropped 10 seconds after the first one, when and where in the tunnel would they first meet?
Idealized Moon Stats:
- Diameter: 3480 kilometers
- Mass: 7.38x10^22 kilograms (uniform density)
(In reply to part 1: another method; another answer
Acceleration due to gravity is not proportional to the cube of the distance from the center of the moon.
I had stated in my solution that the acceleration is proportional to the distance from the center of the moon. I had stated that it was based on symmetry, which isn't wrong but hard to see.
For those who have learned E&M (Electromagnetism), this is exactly the same as Coulomb's Law and Gauss's Law. Coulomb's law says that electric force is proportional to 1/r^2 for point charges. Gauss's Law (although universally correct) is useful only for symmetrical shapes. It is actually used to prove something similar to the given situation.
If you have a sphere of charge and you have a point charge inside the sphere of radius R at a distance r. Only the charge contained in the smaller sphere (radius r) exerts a net force equivalent to that of a point charge carrying a charge equivalent to the smaller sphere. In other words, all charges contained between r and R don't count.
By defining gravitational field lines (similar to electric field lines), you can define a "Gauss's Law" for gravity and use that to prove the same thing.
AND YES, I'M A SCIENCE GEEK. CHEMICAL ENGINEER. AND I'M 100% SURE THIS IS CORRECT.
Edited on November 22, 2004, 11:25 pm
Posted by np_rt
on 2004-11-22 23:24:06