Geostationary satellites orbit at a height of \(35,786~\mbox{km}\) 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.

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