Period of Revolution or time period of a Satellite
It is the time taken by a satellite to complete one revolution around the Earth.
If T be the time period, v the velocity and h the height of the satellite above the Earth's surface.
T = 2π (R + h)/v
v = √GM/R + h
Substituting in the equation, we get
T = 2π (R + h)3/2/GM
= 2π ((R + h)3/ gR2)1/2 (GM = gR2)
T2 = 4π2/ R2 (R + h)3/g
T2 = (4π2/gR2)r3 (where r = R + h)
This expression is consistent with Kepler's III law.
(R + h)3 = T2R2g/4π2
h = g R2 T2/4 π2]1/3 - R
This is the required expression for height of a satellite.
Geostationary Satellite
These are used in meteorological study and produce the signal interventions.
A satellite, whose period of revolution is 24 hours, hence appearing stationery is called a geostationary satellite.
Its orbital velocity is 3.1 km/s, its plane of orbit is the equatorial plane.
It revolves from west to east like Earth.
Its orbital radius of geostationary satellite is nearly 42200 km and above earth’s surface is (4200 – 6400) km = 35800 km.
Polar satellites are other types of satellites used for environmental and earth resources' survey moving over the polar regions.
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