The Figure shows six paths by which a rocket orbiting a moon might move from point a to point b. Rank the paths according to the net work done on the rocket by the gravitational force from the moon, greatest first.
I was not able to find the work done. As i think that in the elliptical path, the work done shouldn't be 0, the work done in every path would be different.
Think about how the force from gravity is directed. It's in the radial direction seen from the moon. Since it is radially then when moving perpendicular to the radial direction there is no work done. This means that both the work $W=F_g*h$ done and the potential energy $E=mgh$ is path independent and depends only on the net difference in height $h$. I now leave you to answer the question of the ranking in a and b which should not be a struggle with the previous being stated.