Gravity distribution in the sphere?

[alpha2cen]

We know well gravity between two objects. The relationship is like this. F_g= G M m / r²

Then, how to calculate gravity at a point in the sphere?

[timo]

Assuming the sphere has a density that is the same everywhere, you formally use the same equation, with r still being the distance from the center, but M now being the mass contained in a sphere of radius r (rather than the total mass contained in a sphere of radius R).

Edited September 29, 2012 by timo

[JohnStu]

you change the distance value, that's it

[imatfaal]

you change the distance value, that's it

No - exactly as Timo said, you use the formula with the radius still being the distance from the centre of mass but you only consider the matter within that radius as adding to the mass. As the volume of the contained sphere (and thus the mass if constant density) varies with r^3 and the attraction varies with 1/r^2 - within the sphere the force varies linearly with r, and thus hits zero when r=0 at the centre.