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

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.

• Yes, when you look at the drawing, it seems to imply two trajectory legs both equaling 14 days, but that can't be right. When you try to read the paper, the authors complain that making it periodic is a problem, but my sleepy head cannot tease out if they solved it. And if it is not periodic, how is it a cycler? I'll look again over morning coffee. Mar 5, 2014 at 5:39
• Wow. If the comments from 2016 about 2 or 3 out of phase ellipses are correct than you should consider the non-zero but low delta-V, planar solutions in the paper below. Roughly 50m/s dV per cycle. ntrs.nasa.gov/citations/20160004674 Oct 10, 2021 at 2:32