Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 47

Selection of a class of orbits for a particular application is made based on the
requirements of that application. For example, in many high-bandwidth satellite
communications applications (e.g., direct broadcast video or high-rate data
trunking), it is desirable to have a nearly geostationary orbit to maintain a fixed line
of sight from the user to the satellite to avoid the need for the user to have an expen-
sive steerable antenna. On the other hand, for lower bandwidth mobile satellite ser-
vice applications, where lower data latency is desirable, it is preferable to use LEO
or MEO satellites to reduce range from the user to the satellite.
As a specific example of constellation design using this body of work ([16-18]),
consider the design of a constellation of MEO satellites providing worldwide con-
tinuous coverage above a minimum 10° elevation angle. The objective is to mini-
mize the number of satellites providing this level of coverage within the class of
Rider orbits. Specifically, consider the case with h = 10,385 km (corresponding to

an orbital period of 6 hours). With = 10°, the Earth central angle can be com-

puted from (2.13) to be 58.0°.
Rider's results in Table 4 of [17] then show that with two orbital planes, the
optimal inclination is 45°, and c = 45°. We now have enough information to solve

(2.14) for S . This solution is S 4.3, but since satellites come only in integer quanti-

ties, one must round up to 5 satellites per plane. Hence, Rider's work indicates that
with 2 orbital planes, one must have 5 satellites per plane to produce continuous
worldwide coverage with a minimum of 1 satellite above a minimum 10° elevation
angle. With 3 orbital planes of the same altitude and with the same coverage
requirement, Rider's work shows c

=

3.6, or 4 satellites per plane. In
this case, 12 total satellites would be required to provide the same level of coverage
if one were to use 3 planes. Clearly it is more cost effective (by 2 satellites) to use a 2
×

= 35.26°, and S =

4). As it turns
out, this example yielded exactly the constellation design envisioned by Inmarsat in
its original concept for the ICO satellite communications system (a 2

5 constellation ( P = 2, S = 5) versus a 3 × 4 constellation ( P = 3, S =

5 constella-
tion of 6-hour orbits inclined 45°). The ICO system added a spare satellite in each
plane for robustness, but the baseline operational constellation was the 2

×

× 5 Rider

constellation discussed here.

2.3.2.3 Walker Constellations
It turns out that the more generalized Walker constellations [16] can produce a
given level of coverage with fewer satellites in general than the Rider constellations
[17]. Walker constellations use circular inclined orbits of equal altitude and inclina-
tion, where the orbital planes are equally spaced around the equatorial plane and
satellites are equally spaced within orbital planes, as with Rider constellations.
However, Walker constellations allow more general relationships between the
number of satellites per plane and the phasing between planes. To that end, Walker
introduced the notation T / P / F , where T is the total number of satellites in the con-
stellation, P is the number of orbital planes, and F is the phase offset factor that
determines the phasing between adjacent orbital planes (see Figure 2.12 for an illus-
tration of the concept of phasing between orbital planes). With the number of satel-
lites per plane, S , it is obvious that T = S × P . F is an integer such that 0 < F < P − 1,