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Orbital Velocity of Satellite is considered one the most difficult concept.
20 Questions around this concept.
An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull FG on the astronaut is :
A satellite of mass m revolves around the earth of radius R at a height x from its surface .If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will :
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Orbital velocity of a satellite is the velocity which is required to put the satellite into its orbit around the earth.
For the revolution of a satellite around the earth, there must be a centripetal force for the circular motion to happen.
The gravitational force which acts towards the center is providing the required centripetal force,
i.e
Where Centrifugal force,;
Gravitational force, ;
So on equating we get
Where
Position of satellite from the centre of earth
Orbital velocity
then:
1. Orbital velocity is independent of the mass of satellite and is always along the tangent of the orbit.
2.It depends upon the mass of the central body and radius of orbit
means, Greater the value of radius of orbit, less be the orbital velocity
As h<<<R or
and using
So
Where
Orbital velocity
Radius of Earth
Angular momentum
mass of satellite
Orbital velocity of the satellite
we know that ;
and
Where
Orbital velocity
Escape velocity
or
Or we can say that
If the speed of satellite is made times the original speed, then it will escape from the gravitational pull of the earth.
If , then satellite does not remain in it's circular path rather it traces a spiral path and falls on earth
Satellite revolves in circular path
satellite move along the parabolic path and will escape from gravitational pull.
satellite will escape but now the of motion will be hyperbolic.
Here,
V= velocity of body
- orbital velocity of a body
- escape velocity of a body
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