# Homework Help: Falling through the earth

1. Jan 20, 2010

### fondah

1. The problem statement, all variables and given/known data
You drill a narrow hole through the center of the earth and drop a ball of mass m into it. Describe its motion qualitatively.

2. Relevant equations
F=-G*M*m/r^2

3. The attempt at a solution
I was thinking that the ball would fall toward the center of the earth and then stop at the center since there would be no more acceleration due to gravity at the center of the earth. Would this be right?

2. Jan 20, 2010

### Staff: Mentor

No. Think about it. If there's no acceleration at the center (which is correct), how can it stop?

3. Jan 20, 2010

### fondah

OK, so the acceleration is 0 but the ball keeps moving toward the other side because of inertia, and as the acceleration gets stronger towards the center, it turns around and falls back down the other way. Without friction, can it oscillate forever?

4. Jan 20, 2010

### Staff: Mentor

Sounds good to me.

5. Jan 20, 2010

### fondah

Thanks so much

6. Jan 20, 2010

### DaveC426913

...assuming the hole is drilled through the poles. Otherwise, the rotation of the Earth will bring the ball in contact with the wall of the hole.

Indeed, the ball is in orbit. And what's awesome is that the period of its orbit is 90 minutes, the same length of time it would be if its orbit were circular like a low-alt satellite.

7. Jan 21, 2010

### fondah

So could I use the simple harmonic motion equations with this oscillation?

8. Jan 21, 2010

Sure.