Page 47 - Intro to Space Sciences Spacecraft Applications

Introduction to Space Sciences and Spacecraft Applications
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This represents an appreciable change in distance for an orbit considered
almost circular and would certainly have to be taken into account if plan-
ning a trip to the moon.

Newton’s Laws

Kepler’s laws were empirically derived relationships describing plane-
tary motions based on years of observations. Newton’s laws more pre-
cisely defined the mechanics of motions and, combined with his idea of
universal gravitation, allowed a more complete description of general
orbital motions. In a dedicated course in orbital mechanics, Newton’s laws
of motions are studied in great depth, and in fact, Kepler’s laws are usu-
ally derived from these relationships. For our purposes, the next few sec-
tions will merely state some of the important results of Newton’s laws.

Angular Momentum. The angular momentum of an orbit is represented
by a vector quantity perpendicular to the orbital plane (the plane contain-
ing the satellite position and velocity vectors) as shown in Figure 2-4. One
of the results of Newton’s laws shows that the angular momentum of a
satellite’s orbit is constant, which for a vector means constant in both
magnitude and direction. This implies that an orbit lies in a plane which
remains inertially fixed in space.
Consider, in Figure 2-5, that the vector h shown represents the angular
momentum of a satellite in orbit around the earth. (We are looking edge-
on to the satellite’s orbit so its orbital plane looks like just a line across the

- orbit
satellite
position h angular
vector

satellite
velocity
vector

Figure 2-4. The angular momentum vector of an orbit is perpendicular to the
orbital plane.