Geo-stationary Satellite

A satellite placed at a definite height directly above the Earth’s equator and revolves in the same direction as the Earth rotates; so that its orbital time period is same as the Earth’s rotation period (24 hours), is called a Geo-stationary satellite. The observer at the equator views the satellite as stationary, hence such types of satellites are also called geosynchronous satellites. These are used for communication, radio broadcasting, universe related studies & researches and gathering weather information. Communication satellite is also a Geo-stationary satellite.
We know the time period of a satellite,

T = \(\frac{2 \pi r^{3 / 2}}{\sqrt{G M}}\)
∴ r = \(\left[\frac{G M T^{2}}{4 \pi^{2}}\right]^{1 / 3}\) ……………. (1)
Putting G = 6.67 × 10^-11 Nm²/kg², mass of Earth M = 6 × 10²⁴ kg, time period T = 24 hours in above equation.

Orbital radius of the satellite from the equation (1) by putting all values;
r = 4.2 × 10⁴ = 42000 km
but r = R + h
Hence, height of the satellite from the surface of the Earth;
h = r – R
h = 42000 km – 6400 km
or h ≈ 36000 km
Hence, the height of a geostationary satellite from the Earth’s surface is approximately 36000 km.

Angular Velocity of Geo-stationary Satellite
Since, angular velocity ω = \(\frac{2 \pi}{T}=\frac{2 \times 3.14}{24 \times 60 \times 60}\)
ω = 7.3 × 10^-5 rad/s
Orbital velocity v = ωr
∴ v = 3.1 km/s.
For communication system, a satellite transmits signals to only \(\frac{1}{3}\) part of the Earth. Hence, to broadcast information throughout the Earth minimum three satellites are necessary.

Any communication satellite (geostationary) can not be placed over India’s capital New Delhi because it will not be in equatorial line.