JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Geostationary Satellite

The satellite which appears stationary relative to earth is called geostationary or geosynchronous satellite, communication satellite.

A geostationary satellite always stays over the same place above the earth such a satellite is never at rest. Such a satellite appears stationary due to its zero relative velocity w.r.t. that place on earth.

The orbit of a geostationary satellite is known as the parking orbit.

(i) It should revolve in an orbit concentric and coplanar with the equatorial plane.

(ii) Its sense of rotation should be same as that of earth about its own axis i.e., in anti-clockwise direction (from west to east).

(iii) Its period of revolution around the earth should be same as that of earth about its own axis.          

\[\therefore \] \[T=24\ hr=86400\ \sec \]          

(iv) Height of geostationary satellite     

As  \[T=2\pi \sqrt{\frac{{{r}^{3}}}{GM}}\] \[\Rightarrow \] \[2\pi \sqrt{\frac{{{(R+h)}^{3}}}{GM}}=24hr\]

Substituting the value of \[G\] and \[M\] we get \[R+h=r=42000\ km=7R\]

\[\therefore \] height of geostationary satellite from the surface of earh \[h=6R=36000\,km\]            

(v) Orbital velocity of geo stationary satellite can be calculated by \[v=\sqrt{\frac{GM}{r}}\]     

Substituting the value of \[G\] and \[M\] we get \[v=3.08\ km/\sec \]