Answer :

Given


Radius of earth = R = 6400 km


Aphelion earth - satellite distance ra = 6R


Perihelion earth - satellite distance rp = 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 vp and va 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 vp and va above we have



Putting the values of rp and ra 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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