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Physics, Astronomy & Cosmology / Re: Is time dilation present inside of a hollow sphere?
« on: 26/04/2017 00:05:13 »Then the potential difference and the thus the gravitational time dilation would be greater.- And if the shell is very thin, the clock at the center of the hollow sphere would run at pretty much the same rate as a clock at the outer surface of the hollow shell.
What if the shell is very thick instead? For example, if there was a planet that was completely solid except for a 10-meter-diameter cavity at the very center, how would that affect the time dilation calculation within that cavity?
As the shell becomes thinner, the potential inside at all points equal that to the potential at the surface, assuming the total mass stays the same (ofcourse this means the density of the shell needs to increase.)
At maximum shell thickness (a solid sphere) the potential at the center is
Vc =- {3GM}/{2r}
where r is the radius of the sphere.
and at the surface it is
Vs = - {GM}/{r}
So the difference in potential between center and surface is
[tex] Delta V = {GM}/{2r}
And thus the difference in potential between surface and inside the hollow varies from 0 to Delta V as the hollow shrinks. (Again, while maintaining a constant total mass.)
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