teclontz
Quick question:

If a satellite is traveling at a fixed velocity, how do you calculate the differential in velocity as observed from the earth and as observed from the satellite?

That is, their respective clocks are at different speeds, with the gravity well of the earth suppressing time at one rate and the velocity of the satellite suppressing time at another rate.

The net effect should show the satellite traveling "faster" from the frame of reference of sea level than from its own reference, but I'd like a source for the actual equation involved.
rpenner
GR questions will not be answered here because this forum lacks any facility for the display of the relevant mathematics. Sensible GR questions may be answered at sciforums.com. It's not clear that you understand the nature of non-local measurement in GR, and the sciforums.com posters may agree with me that your question lacks evidence that the answer would be meaningful without long and careful instruction.
brucep
QUOTE (teclontz+May 3 2012, 01:52 PM)
Quick question:

If a satellite is traveling at a fixed velocity, how do you calculate the differential in velocity as observed from the earth and as observed from the satellite?

That is, their respective clocks are at different speeds, with the gravity well of the earth suppressing time at one rate and the velocity of the satellite suppressing time at another rate.

The net effect should show the satellite traveling "faster" from the frame of reference of sea level than from its own reference, but I'd like a source for the actual equation involved.

Equation 12 is derived from the Schwarzschild metric solution to the EFE as a weak field approximation for the GPS. It includes the gravitational and relative velocity time dilation components. The Student Project A for the GPS.

http://www.eftaylor.com/pub/projecta.pdf

You can use it for any

dt_satellite / dt_earth = .....

In geometric units:

M_earth = .00444 meter

v_orbit = is dimensionless and a fraction of c [c = 1].

The following v^2_orbit equations are derived from the same metric. Specifically the effective potential component of the equation of motion.

v^2_shell = M/r(1-2M/r)

v^2_bkkpr = M/r

The Schwarzschild bookkeeper is the remote observer. Since r is very large for your case the ratio:

v^2_shell / v^2_bkkpr = 1 [as far as experiments conducted in the weak field are concerned].
brucep
QUOTE (rpenner+May 3 2012, 02:36 PM)
GR questions will not be answered here because this forum lacks any facility for the display of the relevant mathematics. Sensible GR questions may be answered at sciforums.com. It's not clear that you understand the nature of non-local measurement in GR, and the sciforums.com posters may agree with me that your question lacks evidence that the answer would be meaningful without long and careful instruction.

Really? He isn't completely confused and what I wrote down should answer his questions.

Edit: It seems to me that many folks think these delta's are large. Going through the GPS project shows relative dt1/dt2 = ... and dr1/dr2 = ..., in the weak field, is infinitesimal and generally can be ignored when doing experiments. Not the GPS so it can be instructive.
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