Aspacecraft in a low-earth elliptic orbit is described by the orbit equation

r =((17000)/(1+0.15 cos( km

in its orbital plane. it is desired to transfer the spacecraft into a co-planar circular orbit of radius 7,000 km using two impulsive horizontal engine burns. the first burn is to occur at perigee of the original elliptic orbit and should place the spacecraft onto an elliptic transfer orbit whose radius of perigee is 7,000 km. the second burn is to occur at perigee of the elliptic transfer orbit and should circularize the orbit at the desired radius of 7,000 km.

(a) sketch (not necessarily to scale) the original elliptic orbit, the final circular orbit, and the transfer orbit.
(b) what is the ∆v magnitude required by the first engine burn on the original elliptic orbit? is it a posigrade burn or a retrograde burn?
(c) what is the ∆v magnitude required by the second engine burn that circularizes the elliptic transfer orbit? is it a posigrade burn or a retrograde burn?