Page 58 - Satellite Communications, Fourth Edition

38 Chapter Two

7200.607 km

r p 7192.335(1 0.0011501)
7184.063 km
The corresponding heights are:
h a r a R
829.6 km

h p r p R
813.1 km

2.8 Orbit Perturbations

The keplerian orbit described so far is ideal in the sense that it assumes
that the earth is a uniform spherical mass and that the only force acting
is the centrifugal force resulting from satellite motion balancing the
gravitational pull of the earth. In practice, other forces which can be sig-
nificant are the gravitational forces of the sun and the moon and atmos-
pheric drag. The gravitational pulls of sun and moon have negligible
effect on low-orbiting satellites, but they do affect satellites in the geo-
stationary orbit as described in Sec. 3.5. Atmospheric drag, on the other
hand, has negligible effect on geostationary satellites but does affect low-
orbiting earth satellites below about 1000 km.

2.8.1 Effects of a nonspherical earth
For a spherical earth of uniform mass, Kepler’s third law (Eq. 2.2) gives
the nominal mean motion n as
0

(2.7)
n 0
Å a 3
The 0 subscript is included as a reminder that this result applies for
a perfectly spherical earth of uniform mass. However, it is known that
the earth is not perfectly spherical, there being an equatorial bulge and
a flattening at the poles, a shape described as an oblate spheroid. When
the earth’s oblateness is taken into account, the mean motion, denoted
in this case by symbol n, is modified to (Wertz, 1984).

2
K (1 1.5 sin i)
1
n n c1 d (2.8)
0
2 1.5
2
a (1 e )