May I ask a dumb question? What if the sun, with all its mass, were shaped like a cube, instead of a sphere. What would orbits look like? What would happen at the interfaces/sides of the cubes as a planet transit-ed that point?
parsy, who has been trying to keep the shortest distance stuff he read in Bertrand Russells(?) book on relativity. (Dang I wish I had my books with me!!!)
What an interesting thought experiment you posit!
Well, to begin with, it is not in the nature of gravity to allow a massive cube with the mass of the Sun to exist...
But, I suppose that one could grow a giant diamond sun cube that might somehow withstand the natural tendencies of the gravitational forces collapsing the sharp edges and corners. But, I digress... Back to the question at hand:
A hypothetical “diamond sun cube” would exhibit the same gravitation constant as a spherical object of equal mass and would not alter the orbits of the planets orbiting around it...
However, since gravity is dependent on the distance from the center of the object, if you were able to don some hyper-asbestos space suit, grab a scale, and walk out onto the “surface” of the “diamond sun cube” then you would weigh more when you walked on the face of the cube than you would if you were walking at the corners of the cube.
Remember, at the corners, you are farther from the center gravitational point of the cube than you are when on the face of the cube. Newton’s formula for the Force of gravity is:
F=GMm/r^2.
We can apply this formula to our cubic sun.
The value of r (radius) is the distance from the center of the sun, M is the mass of the sun, and m is your mass. Ignore the “G” for this discussion.
As r goes up, F (Force) goes down.
Basically, the amount of gravitational pull due to mass from corner to corner is largely offset by the increased distance you are from the center of the cube.
It’s kind of a counter-intuitive concept, but that’s the math behind it.
Cheers