Question

A satellite of mass orbits earth in an elliptical orbit having apehelion distance is ra

Answer 1

For a satellite, moving in a circular orbit, to remain in equilibrium around the Earth it is required that the centripetal force acting outwards equals the gravitational force acting between them.

So,

mv2/r = mw2r = GMm/r2 

 

here

m is the mass of the satellite

M is the mass of the Earth

r is the radius of separation

and 

w is the angular velocity

 

so, by multiplying both sides of the equation by 'm' and by  'r3', we get

(mwr)2 = GMm2r 

or

 as L = mrw

 

we have

L2 = GMm2r 

 

or finally, the angular momentum of a satellite in a circular orbit would be

L = [GMm 2 r]1/2