Page 64 - Satellite Communications, Fourth Edition

44 Chapter Two

2
example shown in Fig. 2.6, this is 0.00000307 rev/day . Thus the changes
resulting from the drag term will be significant only for long time inter-
vals, and for present purposes will be ignored. For a more accurate
analysis, suitable for long-term predictions, the reader is referred to ADC
USAF (1980).

2.9 Inclined Orbits
A study of the general situation of a satellite in an inclined elliptical
orbit is complicated by the fact that different parameters relate to dif-
ferent reference frames. The orbital elements are known with refer-
ence to the plane of the orbit, the position of which is fixed (or slowly
varying) in space, while the location of the earth station is usually
given in terms of the local geographic coordinates which rotate with
the earth. Rectangular coordinate systems are generally used in cal-
culations of satellite position and velocity in space, while the earth sta-
tion quantities of interest may be the azimuth and elevation angles and
range. Transformations between coordinate systems are therefore
required.
Here, in order to illustrate the method of calculation for elliptical
inclined orbits, the problem of finding the earth station look angles and
range will be considered. It should be kept in mind that with inclined
orbits the satellites are not geostationary, and therefore, the required look
angles and range will change with time. Detailed and very readable
treatments of orbital properties in general will be found, for example, in
Bate et al. (1971) and Wertz (1984). Much of the explanation and the
notation in this section is based on these two references.
Determination of the look angles and range involves the following
quantities and concepts:

1. The orbital elements, as published in the NASA bulletins and
described in Sec. 2.6
2. Various measures of time
3. The perifocal coordinate system, which is based on the orbital plane
4. The geocentric-equatorial coordinate system, which is based on the
earth’s equatorial plane
5. The topocentric-horizon coordinate system, which is based on the
observer’s horizon plane.

The two major coordinate transformations needed are:
■ The satellite position measured in the perifocal system is trans-
formed to the geocentric-horizon system in which the earth’s rotation