Semianalytic Integration of High-Altitude Orbits under Lunisolar Effects

Table 1

Direction coefficients 𝑡_𝑗,𝑘 and 𝑑_𝑗,𝑘 and eccentricity coefficients 𝐸_𝑗,𝑘. The unit vector (𝑥,𝑦,𝑧) defines the direction of the center of mass of the third body.

𝑗	𝑘	𝑡𝑗,𝑘	𝑑𝑗,𝑘	𝐸𝑗,|𝑘|
2	0	1−3𝑧^2	0	2+3𝑒^2
	±1	𝑦𝑧	−𝑘𝑥𝑧
	±2	𝑥^2−𝑦^2	𝑘𝑥𝑦	𝑒^2
3	0	0	𝑧(3−5𝑧^2)
	±1	𝑥(1−5𝑧^2)	𝑘𝑦(1−5𝑧^2)	(4+3𝑒^2)𝑒
	±2	4𝑥𝑦𝑧	−𝑘(𝑥^2−𝑦^2)𝑧
	±3	3𝑥(𝑥^2−3𝑦^2)	𝑘𝑦(3𝑥^2−𝑦^2)	𝑒^3
4	0	3−30𝑧^2+35𝑧^4	0	8+40𝑒^2+15𝑒^4
	±1	𝑦𝑧(3−7𝑧^2)	−𝑘𝑥𝑧(3−7𝑧^2)
	±2	(𝑥^2−𝑦^2)(1−7𝑧^2)	𝑘𝑥𝑦(1−7𝑧^2)	(2+𝑒^2)𝑒^2
	±3	3𝑦(3𝑥^2−𝑦^2)𝑧	−𝑘𝑥(𝑥^2−3𝑦^2)𝑧
	±4	𝑥^4−6𝑥^2𝑦^2+𝑦^4	𝑘𝑥𝑦(𝑥^2−𝑦^2)	𝑒^4
5	0	0	𝑧(15−70𝑧^2+63𝑧^4)
	±1	𝑥(1−14𝑧^2+21𝑧^4)	𝑘𝑦(1−14𝑧^2+21𝑧^4)	(8+68𝑒^2+29𝑒^4)𝑒
	±2	4𝑥𝑦𝑧(1−3𝑧^2)	−𝑘(𝑥^2−𝑦^2)𝑧(1−3𝑧^2)
	±3	3𝑥(𝑥^2−3𝑦^2)(1−9𝑧^2)	𝑘𝑦(3𝑥^2−𝑦^2)(1−9𝑧^2)	(8+7𝑒^2)𝑒^3
	±4	16𝑥𝑦(𝑥^2−𝑦^2)𝑧	−𝑘(𝑥^4−6𝑥^2𝑦^2+𝑦^4)𝑧
	±5	5𝑥(𝑥^4−10𝑥^2𝑦^2+5𝑦^4)	𝑘𝑦(5𝑥^4−10𝑥^2𝑦^2+𝑦^4)	𝑒^5