A satellite is in an elliptic orbit around the earth with an aphelion of 6R and perihelion of 2R where R = 6400 km is the radius of the earth. Find eccentrically of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R?

Solution:

Radius of perigee is given as

Radius of apogee is given as

And we know,

and,

From the above equations, we get

From the law of conservation of angular momentum, we have,

Let be the mass of satellite

So,

From conservation of energy we get,

The velocity at the apogee will be,