Moment of momentum (sometimes called angular momentum) $H = mvr\sin(\theta)$, where $m$, $v$, $r$, and $\theta$ are the mass, velocity, radius from the axis of rotation, and angle between the radius and the velocity, of the satellite. When $dH/dt = 0$, clearly $H$ is not changing, so we can say it is "conserved". $dH/dt = Fr\sin(\theta)$, i.e. moment (where $\theta$ is the angle between the radius and the force). So when there is no moment about the axis of rotation, which is always the case for a satellite since the gravitational force is parallel to the radius, moment of momentum is conserved. When a satellite is at the nearest point of its orbit ("perigee"), and the furthest point ("apogee"), the direction of motion and the radius are perpendicular, so $\theta = 90^{\circ}$, so we can say that $mr_pv_p = mr_av_a$ where subscript $a$ denotes apogee, and subscript $p$ denotes perigee.
The sum of kinetic and potential Energy can also be assumed to be conserved for a satellite. This being the case, show that for those two positions, $v_av_p(r_a + r_p) = 2gR^2$, where $R$ and $g$ are the radius and gravitational field strength at the surface of the body being orbited.