A planet moves around the Sun in an elliptical orbit. Answer the following parts.
(i) State Kepler’s law of equal areas.
(ii) By considering two equal short time intervals, one when the planet is near perihelion and the other when it is near aphelion, explain qualitatively why the planet’s linear speed is greater at perihelion.
(iii) Using the small-sector approximation for the swept area, argue that the linear speed v of the planet at any instant is inversely proportional to its distance r from the Sun.