Precise Orbit Determination of Global Navigation Satellite System of ...

Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits
Difference (meter)
Difference (meter)
40
30
20
10
0
-10
-20
-30
-40
dx
dy
dz
0 24 48 72 96 120 144 168 192 216 240
T im e ( h o u r )
Figure 5-22 The Effect of Geopotential Perturbation Sectorial and Tesseral Terms, 5≤ n ≤10, 1≤ m ≤n
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
dx
dy
dz
0 24 48 72 96 120
Tim e (hour)
144 168 192 216 240
Figure 5-23 The Effect of Geopotential Perturbation Sectorial and Tesseral Terms, 6≤ n ≤10, 1≤ m ≤n
From figures above it is clear that the influence of geopotential perturbation on GEO satellites is much larger
than that on IGSO satellites. Also very interesting is that for zonal terms, the effects from the odd terms are
almost zero, for example, from Eq.(5-1) geopoptential J3 can be written by
2
U GM ae
5 2 1
3 = J
3 3 sin ϕ( sin ϕ − )
(5-22)
r 2 6
for GEO satellite ϕ = 0 , the effect of J3 becomes zero. Other odd terms of the zonal part show the same
property. Due to this reason, the effects of total geopotential perturbation are mainly from the even terms.
Actually ϕ will not be zero for GEO satellites, therefore the effects of odd zonal terms are not totally zero, but
very small like J3 in Fgure 5-16.
5.1.3.3 Geopotential Influence on MEO (GPS)
Influence of geopotential perturbation on MEO(GPS) satellite is listed in Table 5-5 (Landau,1988).
Table 5-5 The Effect of Geopotential Perturbation on MEO(GPS) Satellite
Perturbation Force Acceleration Orbit Errors (m)
(m/sec 2 ) One Day 7 Days
J2 5×10 -5 10(km) 100(km)
Cnm, Snm(n,m8)