Research Article

Semianalytic Integration of High-Altitude Orbits under Lunisolar Effects

Table 3

Inclination coefficients 𝑝 4 , 𝑗 , 𝑘 and 𝑝 5 , 𝑗 , 𝑘 ; for brevity, we use the notation 𝛾 ( 1 ± 𝑐 ) .

𝑗 𝑘 𝑝 4 , 𝑗 , 𝑘 𝑝 5 , 𝑗 + 1 , 𝑘

0 0 ( 3 / 2 0 4 8 ) ( 3 3 0 𝑐 2 + 3 5 𝑐 4 ) ( 1 5 / 4 0 9 6 ) 𝑠 ( 1 1 4 𝑐 2 + 2 1 𝑐 4 )
± 1 ( 1 5 / 5 1 2 ) 𝑠 𝑐 ( 3 7 𝑐 2 ) ( 1 5 / 8 1 9 2 ) 𝛾 ( 1 ± 2 8 𝑐 4 2 𝑐 2 8 4 𝑐 3 + 1 0 5 𝑐 4 )
± 2 ( 1 5 / 1 0 2 4 ) 𝑠 2 ( 1 7 𝑐 2 ) ( 1 0 5 / 4 0 9 6 ) 𝑠 𝛾 ( 1 3 𝑐 9 𝑐 2 ± 1 5 𝑐 3 )
± 3 ( 3 5 / 5 1 2 ) 𝑠 3 𝑐 ( 3 5 / 1 6 3 8 4 ) 𝑠 2 𝛾 ( 1 ± 6 𝑐 1 5 𝑐 2 )
± 4 ( 1 0 5 / 4 0 9 6 ) 𝑠 4 ± ( 3 1 5 / 3 2 7 6 8 ) 𝑠 3 𝛾 ( 1 5 𝑐 )
± 5 ( 6 3 / 1 6 3 8 4 ) 𝑠 4 𝛾

2 0 ( 1 0 5 / 5 1 2 ) 𝑠 2 ( 1 7 𝑐 2 ) ( 2 4 5 / 8 1 9 2 ) 𝑠 3 ( 1 9 𝑐 2 )
± 1 ± ( 1 0 5 / 2 5 6 ) 𝑠 𝛾 ( 1 ± 7 𝑐 1 4 𝑐 2 ) ( 7 3 5 / 1 6 3 8 4 ) 𝑠 2 𝛾 ( 1 ± 6 𝑐 1 5 𝑐 2 )
± 2 ( 1 0 5 / 2 5 6 ) 𝛾 2 ( 1 7 𝑐 + 7 𝑐 2 ) ± ( 7 3 5 / 8 1 9 2 ) 𝑠 𝛾 2 ( 1 1 2 𝑐 + 1 5 𝑐 2 )
± 3 ( 2 4 5 / 2 5 6 ) 𝑠 𝛾 2 ( 1 2 𝑐 ) ( 2 4 5 / 9 8 3 0 4 ) 𝛾 3 ( 1 3 5 4 𝑐 + 4 5 𝑐 2 )
± 4 ( 7 3 5 / 1 0 2 4 ) 𝑠 2 𝛾 2 ± ( 2 2 0 5 / 6 5 5 3 6 ) 𝑠 𝛾 3 ( 3 5 𝑐 )
± 5 ( 4 4 1 / 3 2 7 6 8 ) 𝑠 2 𝛾 3

4 0 ( 2 2 0 5 / 2 0 4 8 ) 𝑠 4 ( 6 6 1 5 / 8 1 9 2 ) 𝑠 5
± 1 ( 2 2 0 5 / 5 1 2 ) 𝑠 3 𝛾 ( 3 3 0 7 5 / 1 6 3 8 4 ) 𝑠 4 𝛾
± 2 ( 2 2 0 5 / 1 0 2 4 ) 𝑠 2 𝛾 2 ± ( 3 3 0 7 5 / 8 1 9 2 ) 𝑠 3 𝛾 2
± 3 ( 7 3 5 / 5 1 2 ) 𝑠 𝛾 3 ( 1 1 0 2 5 / 3 2 7 6 8 ) 𝑠 2 𝛾 3
± 4 ( 2 2 0 5 / 4 0 9 6 ) 𝛾 4 ± ( 3 3 0 7 5 / 6 5 5 3 6 ) 𝑠 𝛾 4
± 5 ( 1 3 2 3 / 3 2 7 6 8 ) 𝛾 5