Two satellites $A$ and $B$ are revolving around the earth in circular orbits of radius $r_1$ and $r_2$ respectively with $r_1 < r_2$. Plane of motion of the two are same. At position $1$, $A$ is given an impulse in the direction of velocity by firing a rocket so that it follows an elliptical path to meet $B$ at position $2$ as shown.Focal lengths of the elliptical path are $r_1$ and $r_2$ respectively. At position $2,$ $A$ is given another impulse so that velocities of $A$ and $B$ at $2$ become equal and the two move together.

For any elliptical path of the satellite time period of revolution is given by Kepler's planetary law as $T^2 \alpha r^3$ where a semi - major axis of the ellipse which is $\frac{r_1+r_2}{2}$ in this case. Also angular momentum of any satellite revolving around the earth will remain a constant about earth's centre as force of gravity on the satellite which keeps it in elliptical path is along its position vector relative to the earth centre.