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
Thank you. I think you are saying the center of the cube is more or less where the effect would be measure from. So, if there were a planet, like Mercury in close orbit, and assume in an orbit perpendicular to a face of the suncube....
Would gravity be stronger at the center of each face and then weaken as the planet approached the interface of the sides, and how would this affect the orbit? Would it tend to flare out a little at each of the four corners?
And, may we assume that the suncube is not rotating as it is actually a big square block of neutron star or something, because I understand that rotating gassy things like the Sun would tend to sphere up?
For some reason I just keep thinking one would get a basically circular orbit with four rounded corner points.
parsy, who isn’t asking you to spend a lot of time on this.