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

Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits
Eq.(5-15) starts with ξ 0
Rewrite Eq.(5-2) as follows
= 1 and η0 = 0 .
N
��
45
n
ae
n+
m+
1
∂U
∂U
∂U
GM
( m)
grad(
U ) = ( , , ) = grad(
) + GM grad{
Pn
(sin ϕ)(
Cnmξ
m + S nmηm
)}
∂x
∂y
∂z
r
n=
2 m=
0 r
where
n
n
∂ a
a
{
e
} = −(
n + m + 1)
e
x
∂x
r
n + m + 1
r
n + m + 3
∂ a
{
∂y
n+
r
n
e
m+
1
n
a
} = −(
n + m + 1)
n+
r
n
e
m+
3
∂ ae
ae
{ } = −(
n + m + 1)
z
∂z
n+
m+
1
n+
m+
3
r
r
∂ ( m)
zx ( m+
1)
[ Pn
(sin ϕ)]
= − P (sin ϕ)
∂
3 n
x
r
∂ ( m)
zy ( m+
1)
[ Pn
(sin ϕ)]
= − P (sin ϕ)
∂
3 n
y
r
∂ ( m)
1 z ( m+
[ Pn
(sin ϕ)]
= − P
∂
3 n
z
r r
2
n
1)
y
(sin ϕ)
n
(5-16)
(5-17)
(5-18)
(5-19)
(5-20)
(5-21)
(5-22)
According to Eq.(5-13) and Eq.(5-14), the derivatives of ξm, ηm
to coordinate components x, y, z are expressed
by
∂ξ m
∂x
m x
= [ ξ m + tanϕ
cos λ sin ϕξ m + ηm
r r
sin λ
] = mξ
m−1
cosϕ
(5-23)
∂ξ m
∂y
m y
= [ ξ m + tanϕ
sin λ sin ϕξ m −η
m
r r
cos λ
] = −mη
m−1
cosϕ
(5-24)
∂ξ m
∂z
m z
= [ ξ m − tanϕ
cosϕξ
m ] = 0
r r
(5-25)
∂ηm
∂x
m x
= [ ηm
+ tanϕ
cos λ sin ϕηm
−ξ
m
r r
sin λ
] = mηm−1
cosϕ
(5-26)
∂ηm
∂y
m y
= [ ηm
+ tan ϕ sin λ sin ϕη m + ξ m
r r
cos λ
] = mξ
m−1
cosϕ
(5-27)
∂ηm
∂z
m z
= [ ηm
− tanϕ
cosϕη
m ] = 0
r r
(5-28)
From Eq.(5-12) to Eq.(5-28), the geopotential perturbation can be computed.
5.1.3 The Effect of Geopotential Perturbation
The effects of geopotential perturbation on IGSO and GEO satellite orbits were computed according to
discussion above. In the computation, GEM-T2 Earth model is used. The results are listed in Table 5-1 to Table
5-2 for IGSO satellite and in Table 5-3 to Table 5-4 for GEO satellite.