Let's say there's a satellite orbiting earth. At some random point in its orbit, it is observed with a tangential velocity, a radial velocity and some altitude.
Given only this information (along with known values for earth radius, standard grav. parameters etc.), is it possible to determine the eccentricity of the satellite's orbit?
My approach was to determine the specific orbital energy and the specific relative angular momentum at the point observed in its orbit. The former can be found using the vis-viva equation (taking the magnitude of the radial and tangential velocities) but the latter cannot be determined since the random point cannot be assumed to be the peripasis or apoapsis.