Answer :

Given

Radius of earth = R = 6400 km

Aphelion earth - satellite distance r_{a} = 6R

Perihelion earth - satellite distance r_{p} = 2R

We know for an ellipse

Where e is the eccentricity of the ellipse, and the semi major axis.

Now, the angular momentum of the satellite is conserved we then, we have

Where m is the mass of satellite and v_{p} and v_{a} are the velocities at the perigee and apogee respectively

Now from conservation of energy at the apogee and perigee

Where K and U are the kinetic and gravitational potential energy of the satellite

Where M is the mass of earth. Using the relation between v_{p} and v_{a} above we have

Putting the values of r_{p} and r_{a} we have

To transfer the satellite to a circular orbit of radius 6R the satellite’s velocity has to be maintained at a value of

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