Page 50 - Satellite Communications, Fourth Edition

30 Chapter Two

Figure 2.1 The foci F 1 and F 2 , the semimajor axis a, and the
semiminor axis b of an ellipse.

The eccentricity and the semimajor axis are two of the orbital param-
eters specified for satellites (spacecraft) orbiting the earth. For an ellip-
tical orbit, 0 e 1. When e 0, the orbit becomes circular. The
geometrical significance of eccentricity, along with some of the other geo-
metrical properties of the ellipse, is developed in App. B.

2.3 Kepler’s Second Law

Kepler’s second law states that, for equal time intervals, a satellite will
sweep out equal areas in its orbital plane, focused at the barycenter.
Referring to Fig. 2.2, assuming the satellite travels distances S and
1
S meters in 1 s, then the areas A and A will be equal. The average
2
2
1
velocity in each case is S and S m/s, and because of the equal area law,
2
1
it follows that the velocity at S is less than that at S . An important
1
2

Figure 2.2 Kepler’s second law. The areas A 1 and A 2 swept
out in unit time are equal.