Hill Problem Analytical Theory to the Order Four: Application to the Computation of Frozen Orbits around Planetary Satellites

Table 1

Initial orbital elements of an elliptic frozen orbit for 𝜀=0.0470573, 𝜎=0.422618.

Theory	𝑎 (Hill units)	𝑒	𝐼 (deg)	𝑔 (deg)	ℎ	ℓ
Classical	0.130342	0.674094	55.0995	−90	0	0
2nd order	0.130342	0.648065	55.6915	−90	0	0
3rd order	0.130515	0.637316	56.1798	−90	0	0
4th order	0.130538	0.634803	56.2813	−90	0	0