A planet of mass m moves around the Sun in an elliptical orbit.
(a) State the law that governs the area swept by the radius vector of the planet in equal intervals of time.
(b) Give a qualitative explanation to show how this law implies that the angular momentum of the planet about the Sun remains constant in the absence of external torque.
(c) Derive an expression for the areal velocity dtdA of the planet in terms of its instantaneous distance r from the Sun and its linear speed v.
(d) When the planet is at a point P such that its distance from the Sun decreases continuously, explain whether its speed will increase, decrease or remain unchanged as it approaches the nearest point of the orbit. Justify your answer on the basis of the ideas developed in parts (a)–(c).