Angular momentum of a planet about its apogee is maximum at __________
Now, I do know that
- Angular momentum of a planet around the focus of the elliptical orbit (the sun) is conserved due to gravity being a central force. (Side note: this gives Kepler’s second law.)
- The formula of speed of a planet at any point on its orbit which is a distance $r$ away from the star ($a$ is the length of the semimajor axis): $$v(r)=\displaystyle\sqrt{\frac{GM(2a-r)}{ar}}$$
- Angular momentum about a point is defined as $\vec L=m\vec v\times \vec r$.
So I can’t see any easy way out to determine the answer. I was thinking that it may be at perigee because of the large distance but got confused because of the decreasing speed as the planet moves from apogee to perigee. So is the only way out for me now to do some coordinate-bashing of the ellipse? Or is there any easier way? Intuitive (but convincing) reasoning is more than welcome.