Gravitation up close and personal?

Question

what is the % difference in terms of their masses between the actual force of attraction between two sperical masses the size and mass of the sun Ms
and the force of attraction as approximated by GMM/d^2
when the two planets' surfaces are less than 1 inch apart.

if your answer contains the double integral of:

[density(r1)].[density(r2)].[dV1].[dV2] /(r1-r2)^2

explain how this can be integrated.

Answer 1

Gravity is a conservative field and by gauss' theorem it can be shown that the gravitational field of a spherical body is identical to the gravitational field that would result if all the mass were confined to a point at the field's center.

Newton himself had trouble proving this fact but managed it eventually.

So the force is independent of the radii of the two masses and hence independent of how near to each other their surfaces are, only the distance between their centers matters and the formula GMM/r^2 is exact and the % difference is 0.

Answer 2

Why did you close the question I answered before? Here it is again.
F = Gm1m2/d^2 is exact for spherical, rigid, uniform-density bodies as long as they don't touch. Whether two real suns satisfy those conditions is another question.

Answer 3

http://www.wwu.edu/depts/skywise/a101/milkyway.jpg

JUST LOOK @ HOW SMALL THE SUN IS ON THAT CHART...when you think about how SMALL we are...it really makes you wonder...why is all this space needed? whats beyond space? these are brain hurtersss