Theoretical gravity question?

Question

Suppose one had an object capable of passing frictionlessly through the planet and resists all pressure without collapsing. A ball or something. Since we're taught that gravity pulls all things toward the earth, once the object got to the center of the planet would it just hover there? Possibly it's momentum would fire it through the other side of the planet? What does newtonian physics dictate this object would do?

Answer 1

The are objects like that -- they're called neutrinos, and they mostly come from the Sun. But ... they have very little mass, and they're moving _very_ fast. So they just go through the Earth like a bullet through smoke, without bothering the Earth at all.

I guess you mean something that starts at the surface of the Earth with no speed. Then, yes, its momentum would carry it up to the other side of the Earth, then it would drop back to the center and keep going, etc. It would take about 1.5 hours for each cycle. Without friction, the amplitude of the oscillation would NOT get smaller and smaller.

Answer 2

In side the planet, the acceleration due to gravity decreases and becomes zero at the center.

When the body reaches the center, because of its momenum will go to the other side of the planet.

But gravity increases as it moves away from center.

Hence the body oscillates to and fro between the opposite surfaces of the planet through the center.

Answer 3

This problem was first discussed by Galileo Galilei in his "Two World Systems" back in the 16 century. Give it a shot there is an edition with a prologue by Einstein. It's a good read you'll love it!