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 Originally Posted by CoccoBill
Moon's mean orbital velocity: 1.022 km/s
GPS satellites move at 3.9 km/s.
Now someone calculate how much of the time dilation disparity is due to gravity and how much due to velocity.
This relative velocity is so tiny compared to c.
The gamma factor (the multiplier that tells the difference in relative time / space measurements) is
[gamma] = 1/SQRT(1-[beta]^2)
where [beta] is the ratio of a measured velocity to the speed of light,
i.e. [beta] = v/c
Note that all measured velocities are relative velocities.
3.9(10)^3 m/s - 1.022(10)^3 m/s = 2878 m/s ~= 3(10)^3 m/s
[beta] ~= 3(10)^3 / 3(10)^8 = 10^-5
[gamma] = 1/SQRT(1-[beta]^2)
= 1/SQRT(1-10^-10)
=1.000 000 000 05
= 1 + 5(10)-11
So the time dilation multiplier for a delta-v of ~3 km/s is "not 1" by about 5 seconds per hundred billion.
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