Geo-stationary satellites and Polar satellites

Geo-stationary satellites

A geo-stationary satellite is a particular type used in television and telephone communications. A number of communication satellites which appear to remain in fixed positions at a specified height above the equator are called synchronous satellites or geo-stationary satellites. Some television programmes or events occuring in other countries are often transmitted 'live' with the help of these satellites.

For a satellite to appear fixed at a position above a certain place on the Earth, its orbital period around the Earth must be exactly equal to the rotational period of the Earth about its axis.

Consider a satellite of mass m moving in a circular orbit around the Earth at a distance r from the centre of the Earth. For synchronisation, its period of revolution around the Earth must be equal to the period of rotation of the Earth (ie) 1 day = 24 hr = 86400 seconds.

The speed of the satellite in its orbit is

v = Circumference of orbit / Time period

v = 2π r / T

The centripetal force is F = mv²/r

F = 4mπ²r /T²

The gravitational force on the satellite due to the Earth is

F = GMm/r²

For the stable orbital motion 4mπ²r / T²  = GMm / r²

We know that, g = GM/R²

r³ = gR²T² / 4 π²

The orbital radius of the geo- stationary satellite is, r = [gR²T² / 4 π²]^1/3

Substituting T = 86400 s, R = 6400 km and g = 9.8 m/s², the radius of the orbit of geo-stationary satellite is calculated as 42400 km.

The height of the geo-stationary satellite above the surface of the Earth is h = r - R = 36000 km.

If a satellite is parked at this height, it appears to be stationary. Three satellites spaced at 120^o intervals each above Atlantic, Pacific and Indian oceans provide a worldwide communication network.

Polar satellites

The polar satellites revolve around the Earth in a north−south orbit passing over the poles as the Earth spins about its north - south axis.

The polar satellites positioned nearly 500 to 800 km above the Earth travels pole to pole in 102 minutes. The polar orbit remains fixed in space as the Earth rotates inside the orbit. As a result, most of the earth's surface crosses the satellite in a polar orbit. Excellent coverage of the Earth is possible with this polar orbit. The polar satellites are used for mapping and surveying.