Satellite and planetary motion Assignment Help

Assignment Help: >> Gravitation >> Satellite and planetary motion

Orbital Velocity of Satellite: Satellites are natural or artificial bodies describing orbit around a planet under its gravitational attraction. Moon is a universal satellite while INSAT-1B is an artificial satellite of earth. Condition for creation of artificial satellite is that the centre of orbit of satellite must coincide with centre of earth or satellite must move around great circle of earth.

Orbital speed of a satellite is the velocity required to put the satellite into its orbit around the earth.

For motion of satellite around the earth, the gravitational pull provides the required centripetal force.


2258_Satellite and planetary motion.png

1167_Satellite and planetary motion1.png

                                 [As GM = gR2 and r = R + h]

1791_Satellite and planetary motion2.png

Angular Speed: The corresponding angular speed is,

            w = v0/r

Putting  2328_Satellite and planetary motion4.png , we obtain,

           123_Satellite and planetary motion5.png

1928_Satellite and planetary motion3.png

Time Period of Revolution: The period of revolution

                  T = 2p/w

Putting,       464_Satellite and planetary motion6.png         

 

Potential Energy: The Gravitational potential energy of the planet satellite system is,

            PE = -GMm/r  .

The negative sign shows that the satellite is subjected to planet's gravitational field.

Kinetic Energy: KE of a satellite in orbit is given by , KE = 1/2 mv02, where   2426_Satellite and planetary motion7.png ,

            KE = GMm/r.

Total Energy: The total mechanical energy of the satellite is equal to the sum of its potential and kinetic energies.

Total energy 693_Satellite and planetary motion8.png

The total energy is negative because the satellite is bound by the planet's gravitational field.

 

Angular Momentum: The angular speed of the satellite is shown by, L = mv0r.

Putting  1804_Satellite and planetary motion9.png  , we obtain,    305_Satellite and planetary motion10.png .

 

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