Q: An artificial satellite is in an elliptical orbit around the earth with aphelion of 6R and perihelion of 2R ,where R is Radius of the earth = 6400 km. Calculate the eccentricity of the elliptical orbit.

Sol: We know that

Perigee (r_{p} ) = a (1-e) = 2R …(i)

Apogee (r_{a} ) = a(1+e) = 6R ….(ii)

Solving (i) & (ii),

eccentricity (e) = 0.5