# In order that a satellite keeps revolving in an orbit, the gravitational force should be balanced by

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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