I'm investigating into the angular velocity of a planet in its elliptical orbit.
I have these variables defined:
- speed of planet.
- speed of planet at perigee and apogee.
- length of orbit.
- time of orbit.
- distance away from center at apogee and perigee.
Is there a way from this data that I can calculate the angular velocity of the planet in this orbit ?.
$\tt\mbox{I need the angular velocities of all the 8 planets.}$
I've already done this all for a circular orbit which is quite easy but I can't figure out how to do it for elliptical orbits. Any help will be appreciated !. Thank you in advance.
According to Kepler's laws of planetary motion, "a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time". This gives you the angular velocity:
$$ {dA\over dt}=r^2{d\theta\over dt}=k $$ You can work out the velocity vector from that and the direction of motion. Note this assumes the sun is at one focus of the ellipse.