On equatorial inclination of parking orbits in transfers to lunar halo orbits

• A set of equations have been derived for the computation of the equatorial LEO inclination in the preliminary design of a LEO–LPO transfer.
• Equatorial inclination of the departure LEO is time-related.
• The ranges of the equatorial inclination variation with the departure time are distinct for different transfer orbits.
• In general, for a halo orbit with greater amplitude, the boundary values of the range of the equatorial inclination variation are also larger.
• The value of the equatorial LEO inclination can be affected by as much as 57° through varying the departure time, regardless of the types of transfer trajectories.

This paper presents a detailed analysis on the equatorial inclination of Earth parking orbits associated with transfer trajectories to lunar libration point orbits. Orbital inclination in this work is defined with respect to the Earth’s equator other than the lunar orbital plane as commonly adopted in previous works. This definition connects to the convention widely adopted in current aerospace industry, and therefore has practical meanings. By introducing a number of intermediate reference frames, an algorithm to compute the parking orbit’s equatorial inclination is presented. Numerical results show that, for the same transfer trajectory designed in the autonomous framework of CR3BP (circular restricted three-body problem), the value of the equatorial inclination of the departure LEO largely depends on the choice of departure time at which the spacecraft is injected into the transfer trajectory. Two types of major periodicity, both due to the natural motion of the Moon and the Earth, are discovered to play a role in this time dependency. It is concluded that the equatorial inclination of the departure LEO can be varied by as much as 57° through changing the departure times within half a month. Extensive results obtained in this work should provide good reference for the selections of both launch sites and launch windows in all missions involving Earth–Moon libration point orbits.