Page 41 - Intro to Space Sciences Spacecraft Applications

Introduction to Space Sciences and Spacecraft Applications
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between any two bodies in the universe! In the following sections we will
look at these relationships and how they describe the motions and other
characteristics of bodies in orbits around the earth.

ORBITAL PRINCIPLES

Kepler’s Laws

Kepler’s First ,aw. Kepler’s first law reveals that :aptive” satellites
(those with closed orbital paths) will travel around the earth in elliptical
(or circular) paths with the center of the earth located at one of the foci, as
depicted in Figure 2- 1.

Orbital Parameters. Figure 2-1 defines some of the terms with which we
will be dealing, and the geometry of the ellipse reveals some useful relation-
ships between these orbital parameters. From the figure it is obvious that:

a = semi-major axis b = semi-minor axis
Note: a circle is simply an ellipse with a = b
r = radial distance between bodies’ mass centers
ra = apoapsis radius (maximum distance between bodies)
rp = periapsis radius (minimum distance between bodies)
v = true anomaly (measured in same direction as movement in the orbit)

Figure 2-1. The ellipse. Many orbital terms can be defined simply by the
geometry of an ellipse.