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The Virial Theorem ties both effects to each other where the
gravitational effect is stuck being twice the kinetic effect for a
fixed-radius orbit.
Oops! It looks like I made an error in my previous post concerning the
threshold orbital radius for the time dilation effect on the Earth to
exceed the time dilation effect on an Earth-orbiting satellite (in a
circular orbit). I had claimed that that threshold orbital radius was
twice the radius of the Earth. Today I rechecked my math from last night
and I found an error. The correct threshold orbital radius is 3/2 times
the Earth's radius (rather than 2 times). It seems I don't do my best
work after midnight.
Sorry about the confusion.
David Bowman
David_Bowman@georgetowncollege.edu