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James Webb is in a Halo orbit around Earth's L2 point. It is in a gravitational saddle: two directions are stable ("up-down" and "front-back"). The "in-out" direction is unstable: Earth's tidal forces add to the Sun's and the combined gradient is too much for the Coriolis effect to stabilize.

Webb only has thrusters on it's sunward side (the exhaust must not get to the instruments) and so stays just inside the balance point (which is in turn just inside the L2 point due to solar radiation pressure). It periodically fires it's thrusters to keep from falling toward Earth.

Suppose a burn was an overcorrection (highly unlikely!) and Webb ended up just beyond the L2 point. Would it be forced to turn and expose it's delicate instruments to sunlight? Would we still be able to control and use it if it ends up "drifting away" (in some sort of horseshoe orbit)?

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  • $\begingroup$ "It periodically fires it's thrusters to keep from falling toward Earth" SOHO does that. I don'k know for sure, but I thought that since JWST can observe the same target at different rotations around its axis, the average thrust due to solar pressure can be increased or decreased already (different orientations of the sunshield and the momentum flap wrt sunshine), and that it does not actually require regular impulses from the thrusters on order to stay the right "in-out" distance. I could be wrong. $\endgroup$
    – uhoh
    Oct 12, 2022 at 11:15
  • $\begingroup$ @uhoh Isn't the fuel for the "out" burns actually the main limiting factor of the lifetime of JWST? The other directions are stable, so if this could just be balanced by radiation pressure, JWST would be able to keep station indefinitely. I suspect the sunshield isn't nowhere near big enough to exert enough thrust (that would probably require JWST staying uncomfortably close to the L2 point of no return). $\endgroup$
    – TooTea
    Oct 12, 2022 at 17:33
  • $\begingroup$ @TooTea fuel for stationkeeping (of order ~2 km/s per year only) is certainly a lifetime limiting factor, and while the OP's description of a theoretical halo orbit for Earth in a perfectly circular orbit around the Sun and no moon holds, real world orbits denoted as "halo orbits" (this one is denoted a more general Lissajous, not halo) are always unstable because no situation is a proper three-body problem. This means you always need constant small corrections. So there's no a priori assumption that the stationkeeping is predominantly radial and not needed in the other two directions. $\endgroup$
    – uhoh
    Oct 12, 2022 at 20:30
  • $\begingroup$ @TooTea I seem to remember that solar pressure is used to completely balance forces in the radial ("in-out") direction to first order and there is some degree of flexibility to vary it via orientation without significant impact to the observing plan, but like I say "I don'k know for sure". $\endgroup$
    – uhoh
    Oct 12, 2022 at 20:35
  • $\begingroup$ @TooTea If I ever find my round tuit I will read Dichmann, Alberding and Yu (2014) Stationkeeping Monte Carlo Simulation For The James Webb Space Telescope (discussed here and here) which likely has the answer; but hopefully someone will beat me tuit since this is a great question and in need of a quantitative answer. $\endgroup$
    – uhoh
    Oct 12, 2022 at 20:39

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Answer: If JWST goes “over the hill” past SEL2, it will enter a horseshoe orbit. But it will be non-operational in this orbit. A “rescue burn” of its thruster might restore its halo orbit.

As you said in the OP, JWST is currently in an unstable halo orbit around SEL2. If allowed to free-fall, it would likely “fall” past the Earth and follow a horseshoe orbit around the sun, alternating between being inside and outside the earth’s orbit. If JWST was mistakenly allowed to drift antisunward past SEL2, it would enter the same horseshoe orbit, but would start its first revolution around the sun beyond Earth’s orbit, instead of inside it.

I know that sounds weird. How can JWST end up in the same orbit if it goes in the opposite direction? Let’s look at horseshoe orbits.

enter image description here

This diagram is from Invariant Manifolds, the Three-body Problem and Space Mission Design G Gomez et al 2001.

To confuse you, the Sun is labeled “J” and the Earth is labeled “M”. To further confuse you, “Stable” and “Unstable” are not used in the usual sense. “Stable” trajectories are those which are heading towards a libration point, like L2. “Unstable” means trajectories which are heading away from a libration point. “Stable” orbits are drawn in green and “Unstable” orbits in red. After an object has been on an “Unstable” trajectory (away from a libration point) it will make a transition to head towards a libration point (the same or perhaps a different libration point from the one it just left). Its orbit now becomes “Stable”. These transitions from red to green and back are shown in the diagram with black transition lines labeled U1 –U4.

An object in a horseshoe orbit follows the invariant manifold. On one leg of the orbit, it is Sunward of Earth’s orbit, catching up to Earth. On the next leg, it is outside Earth’s orbit, falling behind.

An “invariant manifold” is a surface comprising all possible green/red orbits with a given energy level. So an object on any of the orbits which make up an invariant manifold does not need any delta-v during its orbit.

There are an infinite number of similar invariant manifolds nested inside each other, like telescope tubes.

Although it is difficult to appreciate from the diagram, “Stable” orbits become closer to their previous pass as they approach L2, forming a halo orbit.

enter image description here

Representations of Invariant Manifolds for Applications in Three-Body Systems / The Journal of the Astronautical Sciences, Vol. 54, No. 1,

These “Stable” halo orbits are almost identical trajectories to the halo orbits of the corresponding “Unstable” orbits.

JWST was launched on a “Stable” orbit towards SEL2. At insertion into its permanent orbit, it was left just shy of the L2 “Stable” halo in an “Unstable” halo which would return it towards Earth without occasional corrections.

The OP rightly pointed out JWST only has thrusters on the sunshield side. Since JWST is usually oriented with the sunshield side towards the sun (duh!), the thrusters are appropriately oriented to counter the Earthward drift of JWST’s “Unstable” halo orbit.

However, if a mishap pushed JWST beyond L2, there is no reason JWST could not change attitude for a corrective burn in the antisunward direction. The science instruments need deep cryo to function, but they were not damaged by years at room temperature before launch. As long as the image of the Sun, Earth dayside or Lunar dayside are not focused on the secondary mirror during attitude changes, instruments would not warm above room temperature and should operate normally once cooled back down.

This “rescue burn” would have risks, but the alternative would be functional loss of JWST.

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    $\begingroup$ Thanks for the detailed explanation of the stable/unstable mess! $\endgroup$
    – asdfex
    Oct 22, 2022 at 12:31
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    $\begingroup$ Do you have a source for the statement in the last paragraphs? Exposing the sensitive parts to the direct light of the sun would likely heat them up a lot more than room temperature. Remember that they even did a complicated roll maneuver during launch to keep specific parts in the shade. $\endgroup$
    – asdfex
    Oct 22, 2022 at 12:33
  • $\begingroup$ @asdfex .... Brylle Reyes in academia.edu/934756/Thermal_Control_Handbook has an interesting concept: a standard 1 m Black Body sphere with absorptivity = 1.0, at thermal equilibrium with space. If the sphere is 1 AU from the sun, equilibrium temperature is +6 °C. Not surprisingly, this is close to the average surface temperature of Earth. JWST has absorptivity <1.0, so it would take “a while” to reach this equilibrium temperature. “A while”=longer than the seconds needed for a station keeping burn. $\endgroup$
    – Woody
    Oct 22, 2022 at 16:12
  • $\begingroup$ @asdfex ... according to stsci.edu/files/live/sites/www/files/home/jwst/documentation/… JWST station keeping burns are "tens of seconds". This is less than "a while" by an order of magnitude (in Imperial Units). $\endgroup$
    – Woody
    Oct 22, 2022 at 16:37
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    $\begingroup$ They would for sure try a rescue burn. The worst that could happen is that they lose the telescope during the try (because the antennas and solar panels are on the bus, when the telescope turns around we would not have any communication and the telescope would have to rely on battery power). So it would be a high risk maneuver where tons of stuff could go wrong and where there is a high probsability of stuff breaking. But still better than a certain loss. $\endgroup$
    – TrySCE2AUX
    Oct 27, 2022 at 5:04

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