Effect of gravity on time dilation.

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SUMMARY

The discussion focuses on the relationship between the orbital radius of satellites and time dilation effects due to gravity. It highlights that the International Space Station (ISS) experiences a time loss of approximately 3.5 x 10-10 seconds per second due to its altitude, derived from the gravitational potential difference between the Earth's surface and the ISS orbit. Additionally, the discussion mentions that GPS satellites gain time relative to Earth, influenced by their orbital motion and gravitational effects, as described by the equations of Newtonian mechanics and general relativity.

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  • Understanding of Newtonian mechanics and orbital motion
  • Familiarity with general relativity concepts
  • Knowledge of gravitational potential and Schwarzschild radius
  • Basic mathematical skills for interpreting equations
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  • Research the effects of gravitational time dilation on GPS satellites
  • Study the mathematical derivation of the Schwarzschild radius
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Physicists, aerospace engineers, satellite communication specialists, and anyone interested in the effects of gravity on time perception in orbital mechanics.

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Can anyone tell me What is the relationship between the orbital radius of a satellite and the time gained per second due to its weaker gravity at its altitude?
In relation to that how much time does the International Space station lose per-second due to weaker gravity at its altitude?
Also What about a GPS? How much time does it gain if it is on Earth?

I have read some articles but i have yet to found the exact value. Very interested in the values. Please help. Thanks
 
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The apparent clock rate of a satellite will be affected firstly by its orbital motion. From Newtonian mechanics and assuming a circular orbit, mv2/r = GMm/r2, implying the orbital velocity is v2/c2 = GM/c2r and γ = 1/√(1-v2/c2) ≈ 1 + GM/2c2r.

According to Wikipedia the Schwarzschild radius of the Earth is 2GM/c2 = 8.9mm. The radius of the Earth is r = 6378 km, so for a surface-skimming satellite, γ ≈ 1 + 3.5 x 10-10.

Secondly, the effect of the gravitational potential. ds2 = (1-2GM/c2r) dt2, so ds/dt = √(1-2GM/c2r) ≈ 1 - GM/c2r. Larger by a factor of two, but what matters here is that you must take the difference between the gravitational potential at the surface vs the potential at the orbit.
 

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