A geostationary satellite orbits directly above Earth's equator at an altitude of 35,786 kilometers, moving in the direction of Earth's rotation with an orbital period equal to Earth's rotational period (23 hours, 56 minutes, 4 seconds).
By balancing gravitational acceleration with centripetal force ($G\frac{M}{r^2} = \omega^2 r$), Kepler's laws dictate that only at an orbital radius of 42,164 km (altitude 35,786 km) will a circular orbit exactly synchronize with Earth's sidereal day.
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