Figure $17\mathrm{.}35$ shows a planet orbiting the sun.

Figure $17\mathrm{.}35$: For question $35.$

a Explain why at points A and P of the orbit the potential energy of the planet assumes its minimum and maximum values, and determine which is which.

b Hence determine at what point in the orbit the planet has the greatest speed.

c Explain why the angular momentum of the planet is constant.

d Hence determine the ratio of the speeds at P and A in terms of the distances of $\backslash ($ P $\backslash )$ and $\backslash ($ A $\backslash )$ to the sun.