On 2002-06-30 01:13, beskeptical wrote:
Why would the gravity of a hollow sphere differ from the gravity of a solid one, if we are using that hypothetical perfect sphere? Density shouldn't matter, atmosphere or iron, (excluding the CMB for the moment).
According to the math, gravity is zero G inside. It seems logical that each molecule affected by the gravity would exert pressure on the molecules below thus creating a pressure gradient. But you are saying there is a gravity gradient, which is not consistent with zero G throughout.
If gravity is zero, then the mass just below the surface of the sphere shouldn't experience any further pull toward the center. If the mass continues to be pulled toward the center, it makes better sense to me that gravity within the sphere would be equal to the gravity of the whole sphere, and attraction would have to be oriented toward the center. You cannot have a pressure
gradient without gravity.
Take a small hollow sphere in space, the mass would be weightless. Given equal air pressure inside and out, shouldn't the ball collapse as the interior molecules migrated to the center and created a pressure gradient?
I completely understand the gravity of the bigger side that is farther away is equal to the smaller side that is closer, no need to rehash that. But how do you get a pressure gradient if the gravity isn't centered.
And if it is centered, then it might be equal throughout, but not zero.
And if the sphere is hollow but has an atmosphere, what would stop everything from being pulled toward the center, since air is more compressable than iron? You wouldn't expect to float as if weightless. I don't think you could maintain a breathable atmosphere.
I'll stop here, my head is spinning.