Exploring the Earth's Center: Ball Drop Speed vs Distance Plot

[Molydood]

If I drilled a hole all the way through the earth, and then dropped a ball down one end, what do you think the speed versus distance plot would look like?

I am interested in the centre point of the Earth primarily - instinct tells me it would overshoot by quite a bit, but how far?

assume no wind resistance

 

[ZapperZ]

If I drilled a hole all the way through the earth, and then dropped a ball down one end, what do you think the speed versus distance plot would look like?

I am interested in the centre point of the Earth primarily - instinct tells me it would overshoot by quite a bit, but how far?

assume no wind resistance

And if other assumptions to be made include the Earth as a sphere with uniform density, no spinning, etc... then if you solve for the gauss's law equivalent for the gravitational field, you'll get a mass-spring system!

This is a common question in undergraduate mechanics course.

Zz