# Satellite Motion

### Polar Satellite Orbit

Polar satellites travel around the Earth in an orbit that travels around the Earth over the poles. The Earth rotates on its axis as the satelitte goes around the Earth. Thus over a period of many orbits it looks down on every part of the Earth.

Geostationary satellites, orbit around the equator in the same direction as the Earth rotates. They are positioned at a height above the Earth such that the same time for the satellite to complete its orbit is the same as the time it takes for the Earth to rotate once about its axis, ie. 24 hours.

Using the relationship derrived earlier which showed that *r*^{3}/*T*^{2}=*GM/4π* we can calculate the height of a satellite above the Earth*h* necessary to achieve a geostationary orbit. (The height above the Earth's surface is the distance r minus the radius of the Earth). Since the satellite is orbiting the Earth the mass we must use in this formula is the mass of the Earth.

The time in seconds for the Earth to rotate is 24x60^{2}=86400 seconds and the mass of the Earth is 6 x 10^{24}kg.

r^{3}=6.67 x 10^{-11} N.kg^{2}.s^{-2} x 6 x 10^{24}kg x (86400 s)^{2}/(4x π^{2})

r=(9.34 x 10^{17})^{1/3}

4.23 x 10^{7} m=4.23 x 10^{4} km

The radius of the Earth is 6400 km. Therefore the height of the satellite above the Earth necessary to maintain a geostationary orbit is 4.23 x 10^{4}-6.4 x 10^{4} km = 3.58 x 10^{4} km

A nice links that tracks the orbits of satellites in 3D.