# How long does it take to fall to the center of the earth?

1. Nov 8, 2006

### raul_l

Let's assume that there are no other forces acting besides the gravitational pull of the earth. If a body started falling from the surface how much time would it take before it reached the center of the earth?
It seems like an easy problem, but so far I have had no luck. So far I have only found acceleration as a function of distance (which is quite easy), which would be $$a=\frac{4G\pi \rho}{3}(r-s)$$ (rho: earth's density, r: earth's radius, s: traveled distance)
But that doesn't help me since I need acceleration (or velocity) as a function of time and I have no idea how to proceed.

2. Nov 8, 2006

### Staff: Mentor

Write the gravitational force as a function of distance from the center. Then see if it reminds you of anything.

3. Nov 8, 2006

### raul_l

$$F=\frac{4G\pi \rho m}{3}s$$

still thinking...