# Gravity at an arbitrary location near a disc

1. Sep 5, 2011

### bumpkin

1. The problem statement, all variables and given/known data

calculate the gravity acceleration at an arbitrary location due to a disc of thickness h, radius r and density p

2. Relevant equations

g=Gm/r^2

3. The attempt at a solution

define r in terms of the vector magnitude from the measurement point to some point on the disc, then hit it with a volume integral? Is there an easier way, say using symmetry?

2. Sep 5, 2011

### Hootenanny

Staff Emeritus
Welcome to Physics Forums.

I'm assuming that rho and h are constant.

It may well be easier to tackle this problem in two separate cases: (a) When the point of interest is outside the body; and (b) when the point of interest is inside the body. For the former case, the gravitational field of the disc is identical to that of a point source of equivalent mass, located at the centre of the disc.

3. Sep 5, 2011

### bumpkin

rho and h are constant. I hadn't even thought of b. But for a, I would assume the acceleration at the edge of the disc would be different to the gravity long the axis of the disc? Ie if the disc was in the xy plane, the gravity at (r,0,h) would be different to (0,0,sqrt(r^2+h^2))?

4. Sep 5, 2011

### Staff: Mentor

That would be true for a uniform sphere, but not for a disk.

5. Sep 5, 2011

### Hootenanny

Staff Emeritus
Oh, sorry. I assumed that you were working in 2D, in the plane of the disc. My bad.

The best option then is to transform into cylindrical coordinates. Apologies for the confusion.