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 m2 kg-2 . me=5.9737 x 1024 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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