How To Find Angular Momentum of Elliptical Orbits

[carbon_mc]

Hey there is one question I have that has been burning in my mind. I know that in elliptical orbits of satellites/ spacecraft s/planets around a planet, angular momentum and energy is conserved, but how do we find that angular momentum only knowing the velocity of the orbiting object, its mass and its distant from Earth's surface? thank you

 

[jtbell]

In classical (non-relativistic) mechanics, you find the angular momentum using the definition in terms of vectors:

$$\vec L = \vec r \times m \vec v$$

Do you know about vectors and the vector cross product? Are you specifically looking for a relativistic version of this equation?

 

[mikelepore]

There are two points, the apogee and the perigee, where the angle between v and r is 90 degrees, so if you know the magnitudes of v and r at either one of those two points, the magnitude of the cross product simplifies to the scalar expression mvr. I don't know if that will be helpful, but I happen to remember reading about it.