# Station-keeping delta-v per year for an Earth-Moon vanilla halo orbit?

This answer reminds us that an Earth-Moon L1 or L2 vanilla1 halo orbit remaining always visible to some patch on the Moon's surface requires station-keeping.

Queqiao uses such an orbit having continuous visibility with both Chang'e 4 on the Moon's far side and with Earth.

Question: Roughly how much station-keeping delta-v per year would be required for such an Earth-Moon halo orbit? This must have been worked out long ago, perhaps in "DoKaRoMo?"

note: For comparison, JWST will be in a vanilla halo orbit about the Sun-Earth L2 position and require only about 2.4 m/s per year for station-keeping! This is due to some clever balancing of solar radiation pressure and bi-weekly calculations and station-keeping maneuvers.

It's likely that an Earth-Moon halo orbit will require much more due to the Moon's eccentric and inclined orbit with respect to both Earth's equator and its orbital plane.

1vanilla meaning those proposed by Bob Farquhar (1, 2, 3, 4) and demonstrated numerically by Kathleen Connor Howell and not a near-rectilinear halo orbit (1, 2) or a butterfly orbit (3).

See also Farquhar, R. W.: "The Control and Use of Libration-Point Satellites", Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, California, 1968

## 1 Answer

I was going to leave this is a comment because I don't have a great answer, but I ran into a character limit with hyperlinks.

Sadly I can't give a specific answer for non-NRHO halos. But I did find this source, which mentions that ISEE-3 (the first mission to go to a Halo orbit) used about 8 m/s per year of delta-V for stationkeeping. This mission was in a Sun-Earth Halo, though.

I can tell you that stationkeeping costs increase as stability index increases (higher stab index means more unstable). See Section 5.1.1 and Figures 5.2-5.3 here for more context on stability index in the Halos. Dan Grebow has published some DV numbers for stationkeeping, shown in table 5.8 here. I'm sure there are more sources out there but these are what I could find quickly.

• This is an excellent start, thanks! From time to time "too long for a comment" yet very helpful answers are well received here, and I think this counts as one. I've never heard of stability index but I will go ahead and read about it now.
– uhoh
Jan 28, 2021 at 21:50