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Energy of a Satellite
Definition: The minimum
energy that must be provided to a satellite to free it from the
gravitational influence of the earth is called its binding energy.
1. Expression for binding energy when body is at rest on the
surface of the earth
Total Energy of the body = K.E. + P.E.
K.E. of rotation = 0
P.E. = gravitational potential × mass
necessary to free the body from the gravitation field
2. Expression for binding energy when body is orbiting
When a body is revolving around the earth at height 'h'
above the surface of the earth
\ Total energy of the satellite = K.E. + P.E.
= mass ´ gravitational
= m ´
\ Total energy,
The negative sign indicates that the satellite is bound to
the earth by the gravitational force.
Binding energy = Energy necessary to free the satellite from the
\ Binding energy = - (T.E.) =
\ B.E. =
2(R + h)
Velocity of a Body from the Surface of the Earth
minimum velocity with which a body should be projected from the surface
of the earth so that it escapes the gravitational field of the earth is
called the escape velocity of the body.
Expression for Escape Velocity (Ve)
When body is at rest on the surface of the earth:
Binding energy =
For a body projected from the surface of the earth with
escape velocity Ve , the kinetic
energy of projection is equal to the binding energy.
\ Ve =
Alternate expressions for Ve:
Ve = =
Ve = =
When a body is revolving around the earth at height 'h' above the
surface of the earth:
in a Satellite