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I developed a time dilation calculator that includes both kinetic (Lorentz Factor) and gravitational (Schwarzschild Metric Formula) factors to assess the time difference between Earth and satellites. My calculations match the expected ≈38 microseconds time adjustment per 24 hours for satellites relative to Earth. However, when I factor in Earth's angular velocity, the adjustment drops to ≈33 microseconds. I am trying to determine if this discrepancy is due to a flaw in my logic or potential inaccuracies in the commonly cited data.

Calculation used

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    $\begingroup$ As it turns out, if you use the "time dilation factor" $\gamma=\frac{\mathrm{d}t}{\mathrm{d}\tau}$ in curved spacetime, i.e. for a nontrivial metric. this actually handles itself. Special relativity follows directly from general relativity; in Minkowski spacetime, the classic formulation of $\gamma$ appears when $\frac{\mathrm{d}t}{\mathrm{d}\tau}$ is calculated, and when the same is done in Schwarzschild spacetime the $\gamma$ factor accounts for it. $\endgroup$ Commented Jul 5 at 3:12
  • $\begingroup$ If you haven't seen this article, it should explain everything much more clearly: mathpages.com/rr/s6-05/6-05.htm. More information in the following chapter: mathpages.com/rr/s6-06/6-06.htm. Basically the relationships are fundamentally nonlinear, and intertwined, so adding stuff together is only an approximation. $\endgroup$
    – m4r35n357
    Commented Jul 5 at 9:10

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Simply multiply the gravitional time dilation with the kinematic time dilation for both the earth and the GPS and then divide the earth's total by the GPS's. Of course on the poles the v on the surface of the earth is 0, while on the equator it is 460 m/s, but that is almost neglible, so you must have messed up the earth's angular velocity since that shouldn't make that much of a difference.

GPS time dilation

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