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The moon's periodic motion would appear to impose a perturbation to the otherwise equilibrium state of the solar/earth L2 point.

uhoh
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JEH
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  • Welcome to Space SE, it's a really interesting question! The Moon and Earth orbit around their center of mass and are relatively close to each other compared to the distance to Sun-Earth L2, so to first order in potential they look like a single object. But to higher order they do look like a wiggling object. Remember though that JWST is in a giant halo orbit about L2. It's not near the L2 point but instead moves around a big tilted oval roughly 400,000 to 800,000 km from L2 as shown in the plots at the bottom of this answer – uhoh Dec 30 '21 at 01:45
  • Also remember that the Earth-Moon system are in a slightly elliptical orbit around the Sun, so that's a second perturbation that might even be larger than the Earth-Moon effect. – uhoh Dec 30 '21 at 01:47
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    The moon orbits Earth 6 times for each time the JWST orbits around L2, so it is really a very short-term cyclic perturbation, and will tend to cancel out its own effects. The harmonic with the bi-yearly cycle of the Halo orbit is exactly what makes that halo orbit more stable than loafing around at the L2 point itself. – CuteKItty_pleaseStopBArking Dec 30 '21 at 06:48

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