Page 42 - Intro to Space Sciences Spacecraft Applications

ra+rp=2a or a=- ra + rp Orbital Principles 29
2

where ra and rp represent the upoapsis (maximum) and periapsis (mini-
mum) distances between the bodies, respectively. These distances will be
better defined shortly. The quantity a is defined as the semi-major axis of
the ellipse.
The eccentricity e describes the shape of an ellipse, sort of in terms of
how fat to wide with respect to the semi-major axis and semi-minor axis b:

A more useful form for the eccentricity equation can be derived from
geometry as:

e=- ra - (2 - 3)
‘p
ra + rp

The orbital parameters a and e together define the size and shape of an
ellipse, as exemplified in Figure 2-2 in which both ellipses have the same
semi-major axis but different eccentricities.
The general equation for a conic section, of which an ellipse is just one
type, may be written in a form which reveals many useful relationships:

a(1 -e2)
r= (2 - 4)
1 + e(cos u)

a=3 b=l a=3 b=2
e = 0.94 e = 0.75

Rgure 2-2. Eccentricity defines the shape of an ellipse.