Geo-stationary satellite:

When a satellite revolves around the earth at a suitable height from the surface of the earth, with the same velocity in the same direction as the earth revolves around its own axis, then the satellite is called geo-stationary satellite.

The relative velocity of a geo-stationary satellite with respect to the earth is \( zero \). So the apparent position of the geo-stationary satellite appears stationary to an observer on the surface of the earth.

The time period of geo-stationary satellite is the same as that of the earth about its own axis. Is the same as the length of the day, i.e, 24 hrs.

Altitude of a geo-stationary satellite:

The height of an artificial satellite from the surface of the earth is,

\( \displaystyle{ h= {\left[\frac{gR^2{T}^2}{4{\pi}^2}\right]}^{\frac{1}{3}} -R } \)

where, \( R \) is the radius of the earth and \( g \) is the acceleration due to gravity.

Calculate The Height Of An Artificial Satellite. Read In Detail.

Here \( T=24\times{60}\times{60}=86400\ sec \)

Substituting the values of \( g \), \( R \), \( T \) in the above equation we get,

\( \displaystyle{h={\left[\frac{9.8\times{(6400\times{10}^3)}^2\times{86400}^2}{4{\pi}^2}\right]}^{\frac{1}{3}} \\-6400\times{10}^3} \)

or, \( h=35950 \ km \)

This satellite is placed at a distance of 35950 km is said to be in a synchronous orbit at the equator. If it is placed over the Atlantic then it could be seen by the American continent. Europe and Africa and thus can be used for communication purposes for all the 24 hours. Three such satellites placed at 120-degree intervals about the equator can effectively cover the whole globe except for some regions at the north and the south poles. The height of a geo-stationary satellite is constant.