What does the BackFlip lunar cycler do in its pass by Earth?

Question

This paper describes an Earth-moon cycler orbit. In this concept, a 180 degree "BackFlip" is used to modify a more simple cycler orbit. However, I can't figure out what cycler orbit it modifies, and correspondingly, what this thing is doing on the Earth-return leg.

I think I understand the backflip itself, with the patched conic approximations. The highly elliptical orbit is aimed at the moon such that the hyperbolic pass redirects the velocity to that angle above the plane. So in terms of order, let's assume we start from "Translunar Trajectory" in the image:

• Do a precisely timed burn from LEO to hit the moon with the right angle and extra velocity
• The (un-powered) pass by the moon redirects it into the 14-day backflip half-orbit
• The previous pass is repeated in reverse (or very close to reverse), putting it on the Earth Return Trajectory
• Then what?

By the time you reach apogee again, the moon will have moved on. And that's a really high apogee. It seems to defeat the point. This orbit should be repeatable indefinitely, and I don't see how it is.

The source of the idea is credited to Uphoff 1989. I tried to figure it out from that paper, but it doesn't really add much information which isn't in the other paper.

Answer 1

Page 10 of the article: "Earth-return trajectory that has a period of 1/2 month (or 1/3 month is some cases) in order to ensure return to the Moon after 2 (or 3) revolutions of the Cycler in its Earth-return orbit".

Those revolutions are not shown in the diagram; "Earth Return Trajectory" and "Translunar Trajectory" only show half of their respective orbits. After perigee with Earth, the Cycler makes 1 (or 2) highly elliptical orbits whose apogee is at lunar orbit, but with the Moon 180° (or 120°) out of phase. Then on the 2nd (or 3rd) apogee, the Cycler is in sync with the Moon again and may perform another BackFlip.