Page 63 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 43

In addition to the equatorial bulge, the earth is not perfectly circular
−5
in the equatorial plane; it has a small eccentricity of the order of 10 .
This is referred to as the equatorial ellipticity. The effect of the equato-
rial ellipticity is to set up a gravity gradient, which has a pronounced
effect on satellites in geostationary orbit (Sec. 7.4). Very briefly, a satel-
lite in geostationary orbit ideally should remain fixed relative to the
earth. The gravity gradient resulting from the equatorial ellipticity
causes the satellites in geostationary orbit to drift to one of two stable
points, which coincide with the minor axis of the equatorial ellipse.
These two points are separated by 180° on the equator and are at approx-
imately 75° E longitude and 105° W longitude. Satellites in service are
prevented from drifting to these points through station-keeping maneu-
vers, described in Sec. 7.4. Because old, out-of-service satellites even-
tually do drift to these points, they are referred to as “satellite
graveyards.” It may be noted that the effect of equatorial ellipticity is
negligible on most other satellite orbits.

2.8.2 Atmospheric drag
For near-earth satellites, below about 1000 km, the effects of atmos-
pheric drag are significant. Because the drag is greatest at the
perigee, the drag acts to reduce the velocity at this point, with the
result that the satellite does not reach the same apogee height on succes-
sive revolutions.
The result is that the semimajor axis and the eccentricity are both
reduced. Drag does not noticeably change the other orbital parameters,
including perigee height. In the program used for generating the
orbital elements given in the NASA bulletins, a pseudo-drag term is
generated, which is equal to one-half the rate of change of mean motion
(ADC USAF, 1980). An approximate expression for the change of major
axis is

n 0 2/3
a > a c d (2.16)
0
n nr (t t )
0
0
0

where the “0” subscripts denote values at the reference time t , and n 0
0
is the first derivative of the mean motion. The mean anomaly is also
changed, an approximate value for the change being:
nr

M 0 (t t 0 ) 2 (2.17)
2
From Table 2.1 it is seen that the first time derivative of the mean
motion is listed in columns 34–43 of line 1 of the NASA bulletin. For the