Quote:
Originally Posted by grav
Well, this is astonishing. In response to Cougar's post, I changed the dimensions of the disk in the program from 100,000 light years across and 12,000 light years thick for the Milky Way to 100,000 light years across and 1,000 light years thick, which accounts only for the stars themselves and not the dust and gas which extends out further, to see what that would give for a lesser thickness. Well, the force still comes out to almost twice as great as that of a sphere and the energy 1.2 times as great. I even found for twice as many points along each axis, for eight times as many points in all, and it comes out the same. If that continues with smaller thicknesses, then the gravity of a disk plane is finite. I'm not sure what that means yet, unless the integration must somehow be performed in a much different than the ordinary way or something. It might also have something to do with the natural "clumping" that is done when considering the mass over a finite number of points in the program instead of an even spreading out of the mass throughout the disk, as would be the case when performing integrations for it. I will also recheck the program. This sort of clumping does definitely seem to be the way to go with this.
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Whoops. I rechecked the program and it appears I changed the numbers of points found for along the z axis, but not the actual thickness of the galaxy itself, so it was still finding for the same thickness, but just using a lesser number of points along it. Sorry. So for a thickness that is 3/25 that of the diameter of the galaxy, the force at the rim is about 1.9 times greater than that of a sphere of the same mass and the energy is 1.2 times greater. For a thickness that is 1/12 as great, or 1/100 of the diameter, the force at the rim is 2.75 times as great as that of a sphere of the same mass and the energy is 1.25 times as great. I'm still going to try working with a "clumping" variable in the integrations, though.
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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."