# How to use "patch points" to make a continuous halo orbit?

update: I've found "patch points" mentioned throughout the following papers; it is likely that an answer can be found from these sources.

The excellent AI Solutions video Near Rectilinear Halo Orbit Explained and Visualized illustrates what the orbit looks like, how it fits in to various families of halo orbits, and shows this interesting insight into how the orbit can be constructed mathematically.

GIF

Patch points from the circular restricted model are iteratively corrected into a continuous, quasi-periodic halo orbit in a high-fidelity force model.

The "circular restricted" model is that of the Earth and Moon's masses in circular orbits around their common center of mass, and the "high-fidelity force model" would be a realistic simulation taking into account the real motion of the Earth and Moon as well as their orbit around the Sun and probably several other effects.

But I don't understand this short explanation; "Patch points... are iteratively corrected into a continuous, quasi-periodic halo orbit..."

Question: How does one iteratively correct patch points in this case? What does this mean? Is it possible to explain the procedure a bit further?

For more on the Gateway's orbit, see

• Start with a basic question: what is a patch point? As can be seen visually in Figure 2 of the first paper you link to, a patch point is basically a point in the trajectory where we require continuity, and usually have the option of performing a small maneuver. Therefore, we require strict continuity in position, and can usually allow for some small differences in velocity. The trajectory itself is only valid if all the patch points are connected. Is this clear? A differential corrector, i.e. using the STM to map small deviations, can be used to plan delta-Vs that connect the patch points. Commented Jun 18, 2019 at 19:19
• And, the process of differential correction is iterative, since the STM is a linearization of the full dynamics. (Note to avoid confusion: the strict continuity in position (and sometimes velocity) is required at the state constraint point, which may or may not overlap with the patch point. Consider the differences between Fig. 2a and 2b. If the patch point is not at the state constraint point, we also require strict continuity in velocity.) Commented Jun 18, 2019 at 19:20
• For additional details, please see p. 52-55 (in the book, not pdf) of descanso.jpl.nasa.gov/monograph/series12/LunarTraj--Overall.pdf Commented Jun 18, 2019 at 19:28
• @yeemonic Any chance you'd consider writing this up as a short answer instead of a series of comments? Answers can be fairly short as long as they are well-sourced, Thanks! Also, does "in the book, not pdf" just mean that 52-55 are the numbered pages? e.g. "Section 2.6.5 Differential Correction"?
– uhoh
Commented Jun 19, 2019 at 1:32
• Ok, I can write up a more formal short answer tonight. And yes, that is what I meant. Past p.55 contains even more details if you are interested, but at least 52-55 should give you the gist of it Commented Jun 19, 2019 at 19:09