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I'm writing a story which involves civilisations across multiple planets, and I've been trying to work out the impact of time dilation between them. I'm hoping someone can help me out here (thanks in advance!).

(I'm not sure if this exact question may be applicable to one of the 'real' science areas in the forum, but I thought I'd at least start here and a moderator can tell me if I'm wrong..)

Essentially, I'm trying to ascertain the exact difference between 2 planets, taking into account their velocity and gravity calculations. (I should also say that I'm not amazing with maths or physics - I have a 'roughly college level' understanding of physics - so please be gentle...) Anyway:

I found the calculation for time dilation due to velocities;

- T=1 / SQRT(1 - (V^2 / C^2 ))

And I found the calculation for time dilation due to gravity;

- T=1 / SQRT(1-(2*G*M / R*C^2))

I found this thread (post # 35) where some forum members have proved that you use the product of these two calculations (rather than the sum) to get the true time dilation factor (everything in those threads is *way* over my head to be honest).

So I've been using details about Earth and Jupiter (taken from Nasa planetary fact sheets) just so that I can get the calculations in order, and I've made myself a crude spreadsheet with the various calculations. I'm not 100% sure of the rules of posting links to files here, but if it's okay to post it and anyone wants to see it, let me know and I'll link it.

The values I've been working with, and the results of the calculations (incidentally, I'm basing these calcs on individual seconds) I have are as follows;

Earth: Mass = 5.9724E+24, Radius = 6371008, Velocity = 29780

Dilation from Velocity = 1.0000000049337600

Dilation from Gravity = 1.0000000006961300

Product = 1.0000000056298900

Jupiter: Mass = 1.89819E+27, Radius = 69911000, Velocity = 13060

Dilation from Velocity = 1.0000000009488900

Dilation from Gravity = 1.0000000201624900

Product = 1.0000000211113800

So now I have a couple of questions

Do I just subtract one product from the other, and if so, how do I know which order to do that subtraction? I.e. I subtracted the Jupiter Product from the Earth product, and I have the result -0.0000000154814885, showing that Jupiter experiences less time ... but I could just as easily subtract Earth's from Jupiter's. Feeling quite frustrated at being this clueless.

- Firstly, are these calculations correct?
- Secondly, what's the correct method to compare these two?

(I also understand that when using these values that the differences we're talking about are so ridiculously small that it would really never be a problem to any space-faring civilisation, but these are just some real figures that we can all agree on so that I can get the right calculations worked out.)

Any help or advice would be appreciated - thanks!

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# Time dilation/difference between 2 planets

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