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Special Issues
Mathematical Problems in Engineering
/
2012
/
Article
/
Tab 5
/
Research Article
Semianalytic Integration of High-Altitude Orbits under Lunisolar Effects
Table 5
Averaged moon direction coefficients
𝑑
𝑗
,
𝑘
. Here,
𝑐
=
c
o
s
𝐽
,
𝑠
=
s
i
n
𝐽
, and
𝑒
≡
𝑒
☾
.
𝑗
𝑘
𝑑
𝑗
,
𝑘
2
0
0
±
1
𝑘
3
1
−
2
𝑒
2
1
2
1
𝜅
𝑐
𝑠
s
i
n
𝑁
−
4
𝜎
𝑠
2
s
i
n
2
𝑁
±
2
𝑘
3
1
−
2
𝑒
2
1
2
1
𝜎
𝑐
𝑠
s
i
n
𝑁
+
4
𝜅
𝑠
2
s
i
n
2
𝑁
3
0
𝑒
3
2
(
2
−
5
𝜎
2
)
𝜅
𝑠
s
i
n
𝜔
☾
+
3
4
(
4
−
5
𝜎
2
)
𝜎
s
i
n
(
𝑁
+
𝜔
☾
)
−
1
5
4
𝜎
2
𝜅
𝑠
s
i
n
(
2
𝑁
+
𝜔
☾
)
±
1
−
3
𝑘
𝑒
2
(
4
−
5
𝜎
2
)
𝜎
𝑠
s
i
n
𝜔
☾
+
1
4
(
4
−
1
5
𝜎
2
)
𝜅
s
i
n
(
𝑁
+
𝜔
☾
5
)
−
4
(
2
−
3
𝜎
2
)
𝜎
𝑠
s
i
n
(
2
𝑁
+
𝜔
☾
)
±
2
3
𝑘
𝑒
2
𝜎
2
𝜅
𝑠
s
i
n
𝜔
☾
−
1
4
(
2
−
3
𝜎
2
)
𝜎
s
i
n
(
𝑁
+
𝜔
☾
1
)
−
4
(
2
−
3
𝜎
2
)
𝜅
𝑠
s
i
n
(
2
𝑁
+
𝜔
☾
)
±
3
−
3
𝑘
𝑒
2
𝜎
3
𝑠
s
i
n
𝜔
☾
+
3
4
𝜎
2
𝜅
s
i
n
(
𝑁
+
𝜔
☾
3
)
+
4
(
2
−
𝜎
2
)
𝜎
𝑠
s
i
n
(
2
𝑁
+
𝜔
☾
)
4
0
0
±
1
𝑘
3
8
(
4
−
7
𝜎
2
)
𝜅
𝑠
s
i
n
𝑁
±
2
𝑘
3
8
(
6
−
7
𝜎
2
)
𝜎
𝑠
s
i
n
𝑁
±
3
𝑘
9
8
𝜎
2
𝜅
𝑠
s
i
n
𝑁
±
4
𝑘
3
8
𝜎
3
𝑠
s
i
n
𝑁