A spacecraft is to be put into a circular orbit about a spherical planet. The planet may be considered to be isolated in space. The mass of the planet, assumed to be concentrated at its centre, is 
. The radius of the planet is 
. One possible path of the spacecraft as it approaches the planet is shown in the figure below.
The spacecraft enters the orbit at point A with speed 
. At point B, a distance of 
from the centre of the planet, the spacecraft has a speed of 
. The mass of the spacecraft is 
. For the spacecraft moving from point B to point A, show that the change in gravitational potential energy of the spacecraft is 
.
