Global Positioning System Reference
In-Depth Information
ellites in planes (i.e., for a given orbital altitude, how many satellites are required in
what set of orbital planes to provide a given level of coverage with the fewest satel-
lites). The level of coverage is usually characterized by the minimum number of sat-
ellites required to be visible in some region of the world above a minimum elevation
angle.
2.3.2.2 Inclined Circular Orbits
As an example of how to use one of these constellation design studies, consider
Rider's work [17] on inclined circular orbits. Rider studied the class of orbits that
are circular and of equal altitude and inclination. This specific study further limited
its analysis to constellations of P orbital planes with S satellites per plane and equal
phasing between planes (i.e., satellite 1 in plane 1 passes through its ascending node
at the same time as satellite 1 in plane 2). Figure 2.12 illustrates equal versus
unequal phasing between planes in the case of two orbital planes with three equally
spaced satellites per plane ( P
3). The orbital planes are equally spaced
around the equatorial plane so that the difference in right ascension of ascending
node between planes equals 360°/ P , and satellites are equally spaced within each
orbital plane.
Rider [17] made the following definitions:
=
2, S
=
elevation angle
R e =
=
spherical radius of the Earth (these studies all assume a spherical Earth)
h
orbital altitude of the constellation being studied
Then the Earth central angle,
, as shown in Figure 2.13, is related to these
parameters as follows:
cos
α
(
)
cos
θα
+=
+
(2.13)
h Re
1
Orbital
plane 1
Orbital
plane 1
Orbital
plane 2
Orbital
plane 2
2
2
1
2
Equatorial
plane
Equatorial
plane
1
1
1
2
3
3
3
3
Equal phasing
(satellite 1 in plane 1 is at its ascending
node at the same time that satellite 1
is in plane 2)
Unequal phasing
(satellite 1 in plane 1 is at its ascending
node after satellite 1
is in plane 2)
Figure 2.12
Equal versus unequal phasing between orbital planes.
Search WWH ::




Custom Search