Lunar-Flyby-Assisted Plane Change

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

Lunar-flyby-assisted plane change is a transfer strategy in which the out-of-plane component built up during a close lunar encounter is used as the equivalent of an explicit plane-change maneuver, eliminating a dedicated out-of-plane impulse. The spacecraft departs on a planar trans-lunar trajectory and uses the flyby (typically a powered lunar flyby, PLF) to generate a Δv\Delta v in the out-of-plane direction; after the encounter the orbital plane has been rotated onto the target orbit's plane, and the spacecraft can enter the stable manifold of a 3D halo orbit (or close an inclination gap to a DRO) with a single impulse.

Geometry and savings

The flyby rotates the v⃗∞\vec v_\infty vector by the turning angle δ\delta, which is large at low perilune altitudes (see lunar flyby). If the inbound v⃗∞\vec v_\infty lies in the Earth-Moon orbital plane and the chosen B-plane aim point produces a v⃗∞(tout)\vec v_\infty(t_{\rm out}) with a substantial zz-component, the flyby has effectively produced a plane change for free, paid for by the Moon's gravity rather than by an onboard impulse. The equivalent Δv\Delta v can be on the order of 10210^2 m/s (Zanzottera et al. 2011, §5.1; Peng et al. 2024 report ΔvΣ<5\Delta v_\Sigma < 5 m/s for the explicit plane-matching impulse at the post-flyby plane crossing, with the flyby itself providing more than 200 m/s of equivalent zz-velocity change).

For a planar transfer to a halo orbit stable manifold, this is the mechanism that enables the single-impulse transfer: the flyby bends the planar trans-lunar arc out of the Earth-Moon plane and onto the halo orbit's stable manifold, eliminating what would otherwise have been a separate plane-change maneuver.

Method: two-body screening, then BCR4BP correction

Because the BCR4BP is not integrable, the operational workflow is: (1) use a Moon-centered two-body model to screen candidate perilune states and obtain an initial guess for the required Δv⃗\Delta\vec v at perilune; (2) correct in the BCR4BP ROT frame so that the spacecraft reaches the Earth-Moon orbital plane with the desired in-plane state. The Moon-centered two-body formula tan⁡δ+=v^pz/r^pz\tan\delta^+ = \hat v_p^z/\hat r_p^z gives the turning angle that zeroes the zz-component of v⃗∞(tout)\vec v_\infty(t_{\rm out}) in the Moon-centered inertial frame (Peng et al. 2024, Eq. 11), and ∣Δv⃗per∣|\Delta\vec v_{\rm per}| follows from energy conservation across the two hyperbolic segments. Differential correction then removes the residual zz-velocity and locks the trajectory onto the target manifold.

Application notes

  • GTO-to-DRO low-energy transfers. Combined with a WSB arc and a second PLF, the plane-change-by-PLF is what lets low-energetic transfers from inclined GTOs reach a planar DRO for a total Δv\Delta v below about 1200 m/s (Peng et al. 2024).

  • Earth-to-halo transfers. Zanzottera et al. (2011) use the Sun-perturbed lunar flyby to bridge the planar Earth-departure arc and the spatial stable manifold of a halo orbit, which is the canonical single-impulse Earth-to-halo transfer.

  • Close lunar flyby. A closely related term appears as the "close lunar flyby plane-change transfer" in some DRO transfer-design literature: same mechanism, emphasis on the close perilune that maximizes the turning angle.

References

  • Zanzottera et al., 2011, Low-energy Earth-to-halo transfers in the Earth-Moon scenario with Sun-perturbation, Acta Astronautica, §5.1

  • Peng et al., 2024, Low-Energy Transfers to Lunar Distant Retrograde Orbits from Geostationary Transfer Orbits, J. Spacecraft and Rockets, doi:10.2514/1.A35623, Sec. III.A