Question

Which of the following physical quantity of a planet that revolves around Sun in an elliptical orbit is constant?

• A. Kinetic energy
• B. Potential energy
• C. Angular momentum
• D. Linear velocity

Answer 1

Answer: (C)

Angular momentum

In an elliptical orbit, the distance between the Sun and the planet changes with time. So the gravitational potential energy $($depends on $r$ $)$ changes, hence the kinetic energy. Since the kinetic energy changes, linear speed is also not constant.
Rate of change in angular momentum of a particle about a centre is:
$\frac{dL}{dt}=r\times F$
In this case $F$ is the gravitational force of attraction, which acts along the radius $r$.
So the cross product of $r$ and $F$ is zero.
$\Rightarrow$ Angular momentum is constant.