# How to properly combine kinetic and gravitational time dilation effect?

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

• 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. Commented Jul 5 at 3:12
• 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. Commented Jul 5 at 9:10