I Time Dilation Paradox: Geosynchronous Satellites

InquiringMind
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Time moves faster when higher above the earth. Time move slower the faster you are moving. A geosynchronous satellite has to be very high to be geosynchronous so it's time should be fast, but it also has to be orbiting the earth extremely fast to keep up with a geosynchronous position, so it's time should be slow. This seems like a paradox to me.
 
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InquiringMind said:
This seems like a paradox to me.
Why? It's just two competing effects.
 
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InquiringMind said:
A geosynchronous satellite has to be very high to be geosynchronous so it's time should be fast
In that case the gravitational effect wins over the kinematic effect

Time_Dilation_vs_Orbital_Height.png
 
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InquiringMind said:
Time moves faster when higher above the earth. Time move slower the faster you are moving
Just to be sure you are clear, neither one of these statements is true as an absolute statement. What you have left out is "relative to <something>". That is, your time ALWAYS moves at one second per second no matter where you are in a gravity well or how fast you are moving relative to something else.

Time APPEARS, to a different observer, to move a differing rates relative to that observer's rate, depending on relative depth in a gravity well and relative speed.
 
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InquiringMind said:
Time moves faster when higher above the earth. Time move slower the faster you are moving. A geosynchronous satellite has to be very high to be geosynchronous so it's time should be fast, but it also has to be orbiting the earth extremely fast to keep up with a geosynchronous position, so it's time should be slow. This seems like a paradox to me.
If you eat too much food, you put on weight. If you exercise a lot, you lose weight. If you eat a lot and exercise a lot you should put on weight and you should lose weight. Is that a paradox too?
 
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InquiringMind said:
it also has to be orbiting the earth extremely fast to keep up with a geosynchronous position
Free-fall orbital speed decreases with altitude.
 
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