# Gravitation on three uniform spheres

1. Jan 29, 2004

### stunner5000pt

Lets say we have three spheres all of uniform density and equal mass, However, sphere A has a rotational period of 16h, B has period of 24h and C has period of 48h.
So which one has the greatest acceleration (g value) at the poles and at the equator.

2. Jan 29, 2004

### HallsofIvy

Staff Emeritus
I am sorely tempted to say that, since they all have the same size and density, they all have the same GRAVITATIONAL acceleration.

A mass on a sphere of radius R, rotating with angular velocity &omega;, requires an inward (centripetal) acceleration of R&omega;2 just to stay on the surface. If you were to drop a mass at the surface of each of those spheres, the acceleration you would observe would be the "gravitational" acceleration (the same for all these spheres) minus the centripetal acceleration. Since that is proportional to R, you would observe the greatest acceleration on the sphere with least rotational speed: largest period- 48 hours.

I just noticed that you said "uniform density", not same density or same size. However, since uniform or non-uniform density is not really relevant to the problem, I going to assume you meant that the three spheres were all the same size and stick with my answer.

Last edited: Jan 29, 2004