This question appears in Mumbai University > Satellite Communication and Network subject

Marks: 5 M

Year: May 2015

Apogee is the farthest point in an orbit from the Earth’s surface whereas perigee is the nearest point.

Apogee and perigee

As per Kepler’s second law, a satellite will sweep out equal areas in its orbital plane, focused at the barycentre (a point in space around which two objects orbit. In our specific case, because of the enormous difference between the masses of the earth and the satellite, the centre of mass coincides with the centre of the earth).

Now, consider figure 2 where the satellite is orbiting around Earth in an elliptical fashion (Kepler’s first law). Assuming the satellite travels distances $S_1$ and $S_2$ meters in one second, then the areas $A_1$ and $A_2$ will be equal. For these areas (shaded in grey in the figure) to be equal, and because of the equal area law, the velocity at $S_2$ is less than that at $S_1$.

An elliptical orbit

In other words, the satellite velocity at the apogee point $(S_2)$ should always be less that the velocity at the perigee point $(S_1)$ because the area covered by a satellite in these points should be equal for a given fixed period of time. And to satisfy this, the satellite moves at a less speed at apogee.