Newton's Law of Universal Gravition.

The force of attraction between two point masses *m1* and *m2* separated by a distance of *r* is:

In a circular orbit, the centripetal force required to keep a satellite of mass *m* traveling at an orbital velocity, *v*, is:

Equating these two forces and solving for the period

At an altitude of about 850 km, polar orbiters, the orbit radiusis 850+6378=7228 km, yielding a period of approximately 102 minutes.

For a geostationary (or geosynchronous) orbit,, the satellite angular velocity must be equal to that of earth. The angular velocity is

so, the orbit radius of a geosynchronous orbit is 42,164 km , or 35,786 km above earth's surface.

Of course satellites do not travel in perfect orbits so the equations are a bit more complicated!

Note: G=6.67259 x 10^{-11} N m^{2} kg^{-2} . me=5.9737 x 10^{24} kg and the angular velocity of earth is 7.29115X10^{-5} rad sec^{-1}

**Perigee** - the point where the satellite is closest to earth

**Apogee** - the point where the satellite is fartherest from earth

The ellipic orbit a satellite takes around earth is

where the angle q
is the true anomaly.

**Ascending node** is the point where the satellite crosses the equatorial plan going north.

**Descending node** is the point where the satellite crosses the equatorial plane going south.

**Ephemeris** is a list of time versus position of a celestial body.

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