SYSTEM CONFIGURATION |
Satellites function as "orbiting control stations". There are
three issues concerning their use:
the issue of visibility from ground tracking stations,
As a consequence of their motion satellites "rise" and "set"
in a manner similar to stars. There are a number of orbit concepts that
are useful for understanding how satellite motion
is related to ground station visibility:
This is the time taken( T ) for a satellite to complete one revolution . It is related to the semi-major axis of orbital ellipse (a) according to Kepler's third law:
 |
(1.2-1) |
|---|
Hence the higher the satellite the longer the period, as illustrated in the Table below.
| Semi-major axis a ( km ) |
Altitude ( km ) |
Period ( min ) |
Comment |
|---|---|---|---|
6700 |
300 |
90 |
remote sensing satellites GPS satellites geostationary satellites |
* Length of a sidereal day |
The trace of the sub-satellite point across the surface of the earth. The angle of the equatorial crossing is a function of the period of the satellite and the rotation rate of the earth. In the case of GPS satellites the groundtracks are very nearly running north-south. The satellite inclination defines the maximum and minimum latitude of the groundtrack. If the inclination is less than 90 the orbit is said to be prograde, and if it is greater than 90 the orbit is said to be retrograde. A plot of the groundtrack of a satellite on a polar plot centred at a tracking station's zenith is known as a "skyplot". Figure 1 shows the groundtracks for two GPS satellites over one day.
Figure 1. Groundtracks of two GPS satellites for one day.
The station horizon, or visibility circle, is the locus of all points around the tracking station which define the sub-satellite points observable at the local horizon. In practice satellites are not tracked down to the horizon, but to some minimum elevation angle (say 15 or 20). The size of the visibility circles varies with the altitude of the satellite.
The number of revolutions in a sidereal day:
 |
(1.2-2) |
|---|
where T is in minutes. If the number of daily revolutions is not an integer,
the groundtrack repeat period is the number of days needed to complete an
integer number of revolutions. For example, 14 
revs/day implies a 3
day repeat period. After 3 days the groundtrack is along the same path as
previously. In the case of GPS, the groundtrack repeats each day to
within a few kilometres.
This can be computed from the coordinates of the ground station and the satellite. The unit vector pointing from the ground station to the satellite is first computed:
 |
(1.2-3) |
|---|
where r is the station-satellite range, xs
is the satellite position vector (in the earth-fixed reference system),
and x is the station position vector. 
and 
are
the ellipsoidal latitude and longitude of the station, and i, j,
k are the unit vectors of the local coordinate frame given by:
 |
(1.2-4) |
The zenith angle 
and the azimuth
follow from the solution to the
scalar products (HOFMANN-WELLENHOF
et al, 1998):
 |
(1.2-5) |
|---|
The following conclusions can therefore be drawn:
The higher the satellite, the longer they are visible above
the horizon (the extreme case is that of the geostationary satellites).
The higher the satellite, the better the coverage due to
a combination of long flyover times and extended visibility of the satellite
over large areas.
No satellite can be seen simultaneously from all locations
on the earth.
Depending on the measurement type and positioning principles
being employed there may be a requirement for observations to be made to
several satellites simultaneously from one or more ground stations.
The orbital characteristics of GPS satellites are described in further detail
in section 2.2.1.
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© Chris Rizos, SNAP-UNSW, 1999