Answer Right? Calculate Satellite Slow-down, Find Relativity Speed-up

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SUMMARY

The discussion focuses on calculating the gravitational time dilation experienced by a satellite at an altitude of 27,000 km, using the equation sqrt(1 - GM/Rc²). The user attempted to compute the time dilation but obtained a result of 0.9999999994, indicating that the satellite's clock is nearly synchronized with ground clocks. Participants clarified that the terms "slow down" and "speed up" refer to gravitational time dilation, and the user was advised that their equation may not be appropriate for this context.

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  • Understanding of gravitational time dilation
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  • Basic knowledge of orbital mechanics
  • Concept of general relativity
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Homework Statement


calculate the slow down on a satellite at height 27,000 km
how find the amount of speed up due to general relativity

Homework Equations


sqrt(1-GM/R/c/c)

The Attempt at a Solution


ok sqrt(1-(6.67*10^-11)*(6*10^24)/(27000000)/(3*10^8)/(3*10^8))

Why do i get .9999999994? it makes sense right? The M is right right?
 
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What do you mean by "slow down" and "speed up" - you don't seem to be talking about tidal drag or orbital speeds here.

Do you mean the gravitational time dilation?
In which case you seem to have the wrong equation.

The number real close to 1 usually means that the satellite and ground clocks are very nearly in agreement. Would you expect this to happen? Or would you expect the satellite clock to be much slower (or much faster) than a ground-based clock?
 

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