Time Dilation Paradox: Geosynchronous Satellites

In summary: This is because the Earth's gravitational pull decreases the closer you get to the center of the Earth.This is because the Earth's gravitational pull decreases the closer you get to the center of the Earth. 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 is because the satellite's orbit is tilted so that the earth's gravity is always pulling on it at the same rate, no matter how fast it's moving.
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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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  • #3
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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  • #5
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.
 

1. What is the Time Dilation Paradox?

The Time Dilation Paradox is a phenomenon in which time appears to pass slower for an observer in a higher gravitational field compared to an observer in a lower gravitational field. This is due to the effects of general relativity, where gravity can bend both space and time.

2. How does this relate to geosynchronous satellites?

Geosynchronous satellites orbit the Earth at a height of approximately 35,786 kilometers, where the gravitational pull is weaker compared to the surface of the Earth. This causes time to pass slightly faster for the satellite compared to an observer on the surface, resulting in a time dilation effect.

3. How much of a time difference is there between a geosynchronous satellite and the Earth's surface?

The time difference between a geosynchronous satellite and the Earth's surface is approximately 45 microseconds per day. This may seem insignificant, but it is crucial for accurate timekeeping and communication systems.

4. How do scientists account for this time difference in satellite communication?

To account for the time difference, scientists use a concept known as gravitational time dilation, which is a correction factor applied to the satellite's clock to ensure it stays synchronized with clocks on the ground. This correction factor takes into account the difference in gravitational potential between the satellite and the Earth's surface.

5. Are there any other factors that can affect time dilation in geosynchronous satellites?

Yes, there are other factors that can affect time dilation in geosynchronous satellites, such as the satellite's velocity and the Earth's rotation. However, these effects are relatively small and can be accounted for in the correction factor used for time synchronization.

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