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Geostationary satellites orbit at a height of above the Earth's surface and orbit with the same period as the Earth (so they always stay above the same spot, i.e. geostationary). If you stand on the Earth's surface what is the ratio of a geostationary satellite's speed to your speed?
Details and assumptions
- Assume the earth is a perfect sphere of radius 6370 km.
- We're asking about tangential speeds in this question (in m/s), not angular velocities.
The answer is 6.618.
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1 solution
Your speed on the surface of the earth is given by v = 6 3 7 0 ω where ω is the angular velocity of the earth. The speed of the satellite is given by v s = ( 3 5 7 8 6 + 6 3 7 0 ) ω . Hence the ratio of speeds v s / v = ( 3 5 7 8 6 + 6 3 7 0 ) / 6 3 7 0 = 6 . 6 1 8 .