Quote:
Originally Posted by grav
Of course, I've already got the one for uniform density and height. In terms of using rings for the reverse problem, I was thinking I could just find for a disk with a radius equal to the outer rim of a ring with that program and subtract it from a disk with a radius equal to the inner rim of the ring, using the height and density for each ring, to find for a series of rings, using the rotation speeds for the resulting mass distribution. But then, that would require two integrations per ring all the way from the center to the radius of the ring, for each ring, so it might actually turn out to be less precise when running over the same number of points as your program would for the reverse problem, I don't know yet.
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Oh, wait. If I'm thinking about this correctly, I should just be able to find for the acceleration of gravity at the edge of a ring using that last integration over x program by finding for the disk to rr + dr/2 and subtracting that for rr - dr/2, and just record those for a particle placed at the edge of every ring in respect to every other ring in the disk, for say, a 20 by 20 grid for every position and for every ring in a 20 ring disk, but I would need to do that only once. After that, the acceleration should vary in direct proportion with the mass density of the rings, so I would just add up the accelerations already found for a constant density disk by whatever their individual densities are multiplied for each ring as the iteration is performed to gain the rotation speeds. I hope I said that in a clear way.
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Let's put together the pieces of
The Grand Puzzle . (website)
"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
"It may be true that zero equals zero -- and that is certainly an equality -- but I don't want to go into the details at this time."