Satellites

Satellites

A satellite may be defined as a body that moves continuously around a comparatively large body. The satellite may be natural or artificial.

Natural Satellite:

The celestial body which revolves around the planet is called a natural satellite. For example, the moon is a natural satellite of the earth.

Artificial Satellite:

The human-made bodies that are placed in specific orbits and are made to revolve around the earth are called artificial satellites

Geostationary Satellite

A geostationary satellite will revolve around the earth with the same angular velocity and in the same direction as that of the earth around its axis.

Escape Velocity

The minimum velocity of projection of a body for which it will escape the gravitational attraction of earth is known as escape velocity.

Substituting the value of ‘g’ and ‘G’ we get

ve = 11.2 km/s

Orbital Velocity

If the satellite is at a height h above the surface of the earth, then r = R + h

Relation between Escape Velocity and Orbital Velocity

v0 =ve/√2 (if h < R)

Time Period of Satellite

The time period of the satellite is the time taken by the satellite to complete one revolution around the earth.

Time period = circumference of circular orbit/orbital velocity

T = 2πr/v0

= 2π (R+h)/v0

But orbit velocity,

T = [2π (R+h)]/ [√GM/R+h]

The time period of the satellite depends only on its height from the surface of the earth.

Energy of Orbiting Satellite

Kinetic Energy of a Satellite

The satellite makes a pure rotational motion. In a pure rotation, the kinetic energy of the satellite is given by

​Potential Energy of a Satellite

Potential energy is the energy possessed by the body in a particular position.

​Total Energy of a Satellite

The total energy of the satellite is the sum of all energies possessed by the satellite in the orbit around the earth. As only the mechanical motion of the satellite is considered, it has only kinetic and potential energies.

Total energy of the satellite = kinetic energy of the satellite + potential energy of the satellite

E = KE + U

Binding Energy

The energy required to remove the satellite from its orbit to infinity is called the binding energy of the system.

Binding Energy of the satellite = -E

= GMm/2r