If the earth were more elliptical rather than so close to spherical, would those standing on the edge of the ellipse feel more gravitational pull than those standing near the center of the ellipse? How do you calculate the gravity of a non-spherical object?
It has been said that the gravitational force between 2 objects is proportional to the product of their masses and inversely proportional to the square of the distance between them (F=m1m2/r^2), the distance being measured from the center of mass of each objects. And force is a vector quantity so it has a magnitude and a direction and is additive. But most of what we know about gravity comes from large spherical objects (planets and stars) with a symmetrical mass distribution.
Now consider a binary star system. If you were feeling the net gravitational effect of a binary star system, you would feel more gravity when the two stars were in line with each other than you would feel when they were next to each other because the vectors would be in line with each other and one of the stars would be closer to you thereby magnifying its gravitational effect.
Now consider a non-spherical object like a galaxy or a nebula. If I were standing some distance away from a galaxy perpendicular to its axis (so the galaxy looks like a circle), I would feel a certain gravitational pull toward its center. But if that galaxy were to rotate 90 degrees without changing the location of its center (so now it looks like a long narrow ellipse), then I would feel a much greater gravitational force from the stars that rotated closer to me.
In both examples, the masses have not changed, nor have the distances between the observer and the centers of mass, but the gravitational force on the observer has changed.
So the question is, how do you calculate the gravity of a non-spherical object taking into account its shape and orientation, short of adding up the gravitational pull from each molecule or each atom? Has a formula been worked out for a thin disk or ellipse or a cube or any other 3-dimensional object other than a sphere? Do any objects exist close enough to us such that we can test these formulas or can we test them using smaller scale objects here on earth?
I’m sure these questions have been asked by much smarter people (such as yourself) and probably at least partially answered, but I cannot find them addressed in basic physics books. Can you help increase the understanding of gravity by the Teeming Millions? Thank you.
R.M., Seattle, WA