Question

A planet is moving around the sun in an elliptic orbit. Its speed

• A. is the same at all points of the orbit
• B. is maximum when it is farthest from the sun
• C. is maximum when it is nearest to the sun
• D. is maximum at the two points in which the orbit is intersected by the line which passes through the focus of the orbit and which is perpendicular to its major axis

Answer 1

Answer: (C)

is maximum when it is nearest to the sun

Answer 2

According to Kepler's II law of planetary motion, the areal velocity of the planet around the sun is constant ie, $\frac{d \vec{A}}{d t}=\frac{\vec{L}}{2 m}=$ constant where $\vec{L}$ is the angular momentum of the planet and $m$ is its mass. But $L=m v r$ $\therefore \frac{d A}{d t}=\frac{m v r}{2 m}=\frac{v r}{2}=$ constant or $v \propto \frac{1}{r}$ Therefore, the speed of a planet is maximum when it is nearest to the sun.