In order that a satellite keeps revolving in an orbit, the

gravitational force should be balanced by the centripetal force

where GM = 3.986 1014 (m3 /s2 ), G is the gravitational

constant, M is the Earths mass, m is the mass of the satellite, v is the

tangential velocity of the satellite and r denotes the distance between the

Earths center and the satellite. Inserting v = wr = 2_r T into the above

equation, one can write the orbital period T, the time required for one

complete revolution around earth in terms of h, the height above Earth, is as

follows

In order that a satellite keeps revolving in an orbit, the

gravitational force should be balanced by the centripetal force

where GM = 3.986 1014 (m3 /s2 ), G is the gravitational

constant, M is the Earths mass, m is the mass of the satellite, v is the

tangential velocity of the satellite and r denotes the distance between the

Earths center and the satellite. Inserting v = wr = 2_r T into the above

equation, one can write the orbital period T, the time required for one

complete revolution around earth in terms of h, the height above Earth, is as

follows

where r = h + R and R = 6371 km denotes the radius of the

Earth.

a. Plot the variation of T as a function of h, the height of

the satellite above Earths surface and show that T increases with increasing

height and becomes equal to 24 hours at a height of h = 35870 km. What is the

period of a satellite at an orbital height of 900 km?

b. Plot the variation of the tangential velocity v as a

function of h and show that the velocity decreases with increasing orbital

height.

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