I am writing something for school where I need to calculate the time dilation difference between Earth and Mars. First I calculated the difference from the gravity of the planets itself + that of the sun on the planets. I got 1.73 seconds in 10 years (so 1,73s slower on earth than on mars). A professor checked it for me and it is correct. Now, this is only when the planets don't move because I haven't calculated the speed difference of the planets with it. Can I calculate the time dilation by the speed of the planets with the formula: dt' = dt/(sqrt(1-v^2/c^2)) for the planets separate, then calculate the difference and adding that result to the 1.73? I am not sure because they move in an orbit but then the orbit is made by gravity (curving spacetime) and I already calculated that. I think that you can also do it in one step by not removing the spacecoördinates from the schwarzschild metric but I don't understand that entirely so it would be harder. So I am not sure if this is correct, can anyone help with this one? Thanks!
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