# Was Queqiao in a halo or Lissajous orbit? Why do sources disagree?

Wikipedia's Lissajous orbit says that sources disagree on the nature of Queqiao relay satellite's orbit; if it was in a proper halo orbit or just a Lissajous orbit.

Proper halo orbits have the same period for their in-plane oscillations and out of plane oscillations, so they are closed orbits with roughy circular motion in the rotating frame, whereas Lissajous orbits are those where the two periods are unequal. They could be closed with a period ratio that is a rational number or be open, non-repeating orbits. Either way they will have "etch-a-sketch" or "squiggly" Lissajous-like motion.

Question: Was Queqiao in a halo or Lissajous orbit? Why do sources disagree? Considering that Queqiao's radio signals were regularly monitored by amateur radio astronomers and its doppler shift well documented, it should be relatively easy for those skilled in the art to determine its trajectory with great precision. From an orbital-mechanical perspective don't understand why this couldn't be nailed down.

Amateur radio astronomers regularly listening to Queqiao from this answer and tweet:

• Doesn't have the Sun a considerable influence because of the Moon's orbital inclination of > 5⁰ with the ecliptic, and doesn't this fact cause the problem to be a "Four Bodies " one ? Jul 28, 2021 at 15:36
• @Cornelis since gravity is $1/r^2$ all solar system bodies affect each other, but as long as the influence of some is much larger than others it's a good approximation to treat only the ones with the largest effects. The Sun and Moon definitely are a an important perturbation for Earth satellites when they are in high Earth orbit (HEO) and a tiny one when they are in LEO, because Earth holds them 500 times more weakly in HEO. Likewise at Earth-Moon Lagrange point orbits if it stays close to the Moon the Sun's effect is of course there but probably a pretty weak perturbation.
– uhoh
Jul 28, 2021 at 22:49
• I've calculated that at the lunar L2 point the gravitational pull from the Sun is 5 times greater than that of the Moon. I think one can't ignore that. Jul 29, 2021 at 13:34
• @Cornelis oh, it's possible you forgot to take into account that the Sun pulls on the Moon just as hard as it pull on the spacecraft at L2. They are both in a heliocentric orbit together. The Sun can perturb an object at L2 only when it pulls harder or less hard than it does on the Moon. The effect is pretty small.
– uhoh
Jul 29, 2021 at 15:09
• @Cornelis no need on my behalf, this is an interesting discussion!
– uhoh
Jul 29, 2021 at 15:47

Was Queqiao in a halo or Lissajous orbit?

It is hard to say which, or even yes or no, because there are so many kinds of Lagrange point orbits possible that can be maintained with a little help from propulsive station keeping, and a specific, definitive answer would require either plenty of orbital tracking data or more information from the spacecraft's owners.

Why do sources disagree?

What appears to be the issue is that several conflicting definitions of a "halo" orbit is in use, in order of increasing strictness:

1. Halo orbits are orbits around L-points.
2. Halo orbits are Lissajous with an equal in-plane and out-of-plane oscillation period. (also exists in a variation where halo orbits are not counted as a subset).
3. Halo orbits are planar Lissajous orbits.

The spacenews source linked by Wikipedia is reporting on press releases using (1), while itself defines halo orbits as (3), and Wikipedia uses (2).

And thus the confusion is complete.

Since the press releases at the base of it all use the widest possible definition, it's, not actually possible to use them to determine whether the orbit satisfies (2) or (3).

Actual spacecraft can't manage to stay for long in perfect but unstable halo orbits. They will eventually degrade back to some close Lissajous orbit.

• Thanks for the answer to the second part; "Why do sources disagree?" But to the first part "Was Queqiao in a halo or Lissajous orbit?" possible answers include "halo", "Lissajous", "both", "neither", "yes", "no", "it depends", "impossible to answer" and I'm sure others. Is it possible to address it in some definitive way?
– uhoh
Oct 3, 2020 at 2:03
• @uhoh Not from the sources I have available. Oct 3, 2020 at 6:19
• slightly related: 1) the answer to Are some Halo Orbits actually Stable? seems to be yes, and refers to this longer answer, but of course that's CR3BP halo orbits, and invoking the word "spacecraft" invokes solar system reality at which point "stable" looses a singular definition. 2) I don't know what a "planar Lissajous orbit" even is, so I'll have to read up on that. and...
– uhoh
Oct 3, 2020 at 23:59
• 3) Any further thoughts on Is a 2:1 “figure-eight” Lissajous orbit possible in the Circular Restricted Three Body Problem?
– uhoh
Oct 3, 2020 at 23:59
• Since the bounty was in "grace period" mode and I wanted to award it, I've added a preamble based on what you've expressed in comments. Feel free to roll back or edit further, but I think that this addition will be helpful to future readers who arrive at this page with an interest in finding out.
– uhoh
Oct 9, 2020 at 1:33