The question "at what rate will my clock run?" gets trickier the more you think about it. All your own clocks- your heart rate, your wrist watch, your carbon-14 dating, etc.- run at the same rates with respect to each other as they would anywhere else. In that sense, I guess the answer is "at the usual rate".
The interesting effects come in only when observers look at somebody else's clocks. One meaningful version of your question would be "how fast does somebody on Earth think my clocks run?" That answer depends on two things:
1. Your speed, as measured by somebody on Earth.
2. The pattern of gravitational field between you and the Earth, again as seen by the Earth
I can give a definite answer if we make up some facts for these. You say "zero momentum", I suppose with respect to Earth, so we'll set the speed to zero. That means that there's no Special Relativistic effect on your clock speed, as seen by Earth.
Let's take the simplest reasonable pattern for the gravitational field here: just the Earth's field by itself. It's uphill from Earth to distant space, and that makes the distant clocks run faster. The net effect is a factor of (1+gR/c2
) where g is the gravitational acceleration near the Earth's surface, R is the Earth's radius, and c is the speed of light. That's just a little less than a one part per billion speed-up. This simple approximation is in fact roughly what goes on with the geosynchronous satellites used in GPS systems, which have to correct for the effect.
With regard to the radioactive isotopes, as I mentioned, their decay rates stay proportional to the rates of all other local clocks.
(published on 09/14/11)