A planet revolves around the Sun in an elliptical orbit. If $v_P$ and $v_A$ are the speeds of the pl

Question

A planet revolves around the Sun in an elliptical orbit. If $v_P$ and $v_A$ are the speeds of the planet at perihelion and aphelion respectively, and $r_P$ and $r_A$ are the corresponding distances from the Sun, which of the following relations is correct?

Professor PC Thomas Classes · Answer

According to the law of conservation of angular momentum, the angular momentum of the planet about the Sun remains constant. Thus, $m r_P v_P = m r_A v_A$, which gives $v_P r_P = v_A r_A$.