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1. Homework Statement

1. Homework Statement

Explain why the orbit of a geostationary satellite is circular and in the equatorial plane.

## Homework Equations

None provided.

## The Attempt at a Solution

"For a satellite to be geostationary its position vector and the position vector of the planetary surface point above which the satellite is stationed must lie along the same line at every point in time, so since a position vector rotating with time describes a plane the two must lie in the same plane. Since a satellite's orbital plane must be focused at the centre of mass of the planet the surface point must also rotate on a plane focused at the centre of mass of the planet, and since a point fitting that condition may only be found along the equator the satellite must orbit in the equatorial plane in order to be geostationary.

From Kepler's 2nd law (1/2 r

^{2}dθ /dt = constant) the angular frequency of the orbiting body about the centre of its orbit must vary as the inverse of the square of the radial distance of that body from the centre of its orbit, so since a geostationary satellite must have a constant angular frequency to match the constant angular frequency of the point on the planetary surface above which it is stationed it follows that the radial distance must also be constant, in which case the trajectory must be circular."