Time Dilation Effect on High-Speed Object Orbiting Massive Object

[Pro7ech]

I browsed a lot this forum to find an answer, but it always ends up in the same way : no constant answer.

I understand how time dilation relative to speed or to gravity separately work.

But what about an object orbiting at high speed (natural ans stable orbit) an other object with a significant mass?

How would those two effect would interact? How would you calculate the effect of time dilation, of an object moving in a gravity field, knowing the mass of the central object and the orbit radius?

I have seen a lot of different answers, some pull out equations combining both gravity and relative speed time dilation laws and other say there is no connection but without giving any answer or explaining why, some other say it is the same, but again without answering thr question.

Can anyone help me?

 

[A.T.]

I understand how time dilation relative to speed or to gravity separately work.

They can be calculated separately using some derived formulas. But the combined effect of both can also be obtained by integrating the proper time intervals in the appropriate space-time metric.

 

[jartsa]

Special relativity says that all kinds of moving clocks are time dilated the same way.

For example if clock A has mass 10²⁰kg and clock B has mass 0.1 kg, the masses can be ignored, when calculating kinetic time dilation, because there is no mass term in the time dilation formula of special relativity.

 

[russ_watters]

Google "GPS and relativity" and you should find an example with descriptions and calculations.

 

[George Jones]

For an Earth satellite calculation based on material in the book "Exploring Black Holes" by Taylor and Wheeler, see

https://www.physicsforums.com/threads/how-is-relativity-theory-applied-to-gps.87010/#post-731738

 

[Pro7ech]

Thank you everyone, you all helped me a lot in my quest to conquering the world ) I think it is time for me to get a pencil, a sheet of paper and a calculator!