A proposed option for the lunar orbit of a Lunar Orbital Platform-Gateway (formerly known as Deep Space Gateway) is a near rectilinear halo orbit, or NRHO.

This excellent answer discusses the various tradeoffs between different lunar orbit options and explains why the NRHO appears to be such a good candidate.

But what is a near rectilinear halo orbit to begin with? Is it different than a "normal" halo orbit or just a subclass? Is there such a thing as a "true" rectilinear halo orbit as well? What makes it so special?

There are some visual clues in the video, especially here and here but the captions are minimal. These might be good places to start.

For convenience I've managed to find some links to some of the papers listed at the end of the video.


1 Answer 1


Halo orbit families exist near the L1, L2, and L3 librations points. This video focuses on the L1 and L2 halo families. There are northern and southern families at each of the libration points. The northern family is identical to the southern family but mirrored across the x-y plane.

At each point, the family bifurcates from the planar Lyapunov family of orbits. That is, the first halo in the family is planar, and it is also a member of the kidney-bean-shaped Lyapunov family. You can step up in the z direction and find another member of the halo family. And step up again to find the next. The family thus evolves out of plane, as you see in the video, and it keeps growing and approaches the smaller primary (the Moon if we're working in the Earth-Moon system). The Near Rectilinear Halo Orbits are the tall, nearly-polar ones that get really close to the Moon. How are they defined?

We've defined the NRHOs as those members of the halo families whose stability indices are bounded. That is, they're marginally stable, or nearly so, in a linear analysis. You can see a plot of the stability indices of the L1 and L2 halo families, a zoom of the NRHO portions of the two families, and the butterflies as a bonus, in Figure 2 of this paper: https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Conferences/2017_AAS_DavPhiHow.pdf

Check out the top plot in Figure 2b. See how the stability indices are bounded (with a value of 3 or less) until you hit a perilune radius (rp) of 16,000 or 18,000 km, and then the stability indices begin to grow quickly? We've defined "NRHO" to lie to the left of that bifurcation- those halos with bounded stability properties. There's another bifurcation on the far left of those plots, where the stability index is equal to 1. You can see it for the red L2 line; for the blue L1 line that point is below the lunar surface and isn't included in the plot. That bifurcation marks the lower limit of the NRHO portion of the halo families.

Why are they special? As discussed in Ryan Whitley's paper you linked to, they're favorable for transferring into and out of, which is nice when your spacecraft is meant to be a staging ground for exploration, with other ships coming and going. They also provide really great lunar south pole coverage, since they whip quickly around the north pole and spend almost all of their time in the southern hemisphere. See: https://engineering.purdue.edu/people/kathleen.howell.1/Publications/Journals/2008_JSR_GreOziHowFol.pdf

In addition, they're close to stable. In a flatter, less stable halo, if you miss a stationkeeping maneuver or have an unexpected perturbation, you might escape from the halo in just a few weeks or less. In an NRHO, the lower stability index means that a missed maneuver or a perturbation affects your orbit less, and there's more time to recover before the spacecraft escapes the orbit. So- orbit maintenance (or stationkeeping) is required, but there's more recovery time than in a flatter Earth-Moon halo like Artemis flew.

Illustration for clarity:

enter image description here

Figure 2b from this paper:

enter image description here

  • $\begingroup$ Thank you for the thorough answer! It will take a day or two for me to read through it carefully, this is really extremely helpful! Also, welcome to Space Exploration Stackexchange! $\endgroup$
    – uhoh
    Dec 13, 2017 at 22:00
  • $\begingroup$ I've added a screenshot of Figure 2b. You're welcome to remove it either by editing again or if you click the word "edited" to the left of your icon, you can select roll-back. $\endgroup$
    – uhoh
    Dec 13, 2017 at 22:08
  • 2
    $\begingroup$ You may want to merge this account with your registered one so the reputation is pooled appropriately and you can freely edit all your posts. $\endgroup$ Dec 14, 2017 at 4:20
  • $\begingroup$ Thanks for pointing that out, Nathan. I've sent the merge request. $\endgroup$
    – Diane
    Dec 14, 2017 at 14:19
  • $\begingroup$ Nice answer!. Are that particular "stability" properties of NRHOs related to some sort of almost-linear propagation of the states in that orbit or there is not a relation at all? $\endgroup$
    – Julio
    Dec 14, 2017 at 14:52

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