Undergrad Time Dilation Paradox: Geosynchronous Satellites

[InquiringMind]

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.

 

[Ibix]

This seems like a paradox to me.

Why? It's just two competing effects.

 

[Dale]

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

 

[phinds]

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.

 

[PeroK]

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?

 

[PeterDonis]

it also has to be orbiting the earth extremely fast to keep up with a geosynchronous position

Free-fall orbital speed decreases with altitude.