Page 48 - Intro to Space Sciences Spacecraft Applications

Orbital Principles

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orbit

Figure 2-5. Constant angular momentum. This property of an orbit results in
an inertially-fixed orbital plane.

earth in the figure.) The figure shows that in half a year, as the earth has
moved from one side of the sun to the other, the angular momentum (and
thus the plane) of the satellite’s orbit has remained pointing toward the
same inertial direction in space.
During this time, the earth has also been rotating daily beneath the
satellite’s fixed orbital plane. This affects the satellite’s ground track (the
path which the satellite appears to etch across the earth’s surface), a point
which we will discuss shortly.

Total Energy. Another important result of Newton’s laws states that the
total energy of an orbiting body is also a constant. The expression for the
specific total energy E of an orbiting body is:

E=- v2 -- CL
2 r

The first term on the right-hand side of the equation can be seen to
relate to the kinetic energy of the orbiting body and the second term rep-
resents the body’s potential energy. For the total energy of an orbiting
body to remain constant, the kinetic energy term must decrease as the
potential energy term increases. (Since the potential energy term is a neg-
ative value in the equation above, this term will increase [become less
negative] as the orbital radius r increases.) This corresponds to what was
stated earlier in Kepler’s second law and demonstrated in Figure 2-3.