- #1
Robin04
- 260
- 16
Homework Statement
We drill a hole from the surface of the Earth to the other side through the center, drop a test particle and measure the time it takes to come back. How does this time depend on the radius and density of the Earth?
Homework Equations
The Attempt at a Solution
The gravitation field inside a sphere is ##g=\frac{4\pi G\rho}{3}r##, where ##G## is the gravitational constant, ##\rho## is the density, ##r## is the distance from the center.
Now I have to find the function ##r(t)##. I already found ##v(r)=r\sqrt{4\pi G \rho}## (the initial velocity is zero). How can I bring time into the equation?