# Could JWST stay at L2 “forever”?

Using only reaction wheels powered by solar panel and the sunshield as a sail (in continuous active attitude control) to generate thrust from solar photon pressure in the desired direction, could JWST stay in its orbit around L2 "forever" (theoretically at least)?

In this case it couldn't fulfill it's main objective, which is to be a space telescope pointing at distant objects for long exposure time. But this is a hypothetical question asking about its orbital dynamics.

Anyway, could this be a practical way to set JWST on "pause" for say 2 years, without burning fuel/ejecting mass to keep its orbit around L2?

• Here are some different, but related questions whose answers may contain information that is also helpful here: How will JWST manage solar pressure effects to maintain attitude and station keep it's unstable orbit? and also What happens to JWST after it runs out of propellant?. – uhoh Apr 9 at 12:55
• Reaction wheels have to be desaturated occasionally. That takes fuel. Solar radiation pressure is a hindrance on JWST rather than something the vehicle can use to its advantage, more than doubling the stationkeeping costs compared to a vehicle in a similar unstable orbit but without such a huge sunshield. – David Hammen Apr 9 at 15:26
• @DavidHammen If considering an hypothetical very high sail surface/mass ratio probe, meant to solely keep orbit at one Lagrange point, could desaturation of reaction wheel be made by shifting centre of mass (reaction wheel) coplanar to sail, inducing a counter-torque allowing wheel to slow down, thereby using no fuel? – qq jkztd Apr 9 at 16:20
• Ok I found this about solar sail attitude control and propulsion, which goes into the direction of even getting rid of reaction wheel system, and desaturation related issues. – qq jkztd Apr 9 at 19:08
• @DavidHammen I suggested without proof that with enough acrobatics (pairings of maneuvers) the station-keeping could be angular momentum neutral over time. If the momentum wheels could be fairly well centered near zero to begin with, then maybe unloading could be managed with torque from photon pressure as well, since the center of mass is offset from the sunshade. Also, I am not sure the photon pressure is really a hindrance. I think you just ride several km in front of the halo orbit as if you were leaving it towards Earth along the unstable manifold, but always being pushed back. – uhoh Apr 10 at 1:57

According to Wikipedia, the delta-v requirements to stay at L1 or L2 are about 30-100 m/s per year. That seems quite high, however, more likely is around 5-16 m/s. The sun shield has an area of about 300 m^2. The thrust possible is about 0.00279664 N, assuming purely reflective. Mass of JWST is about 6200 kg. Putting all of that together, the possible acceleration is around 14 m/s per year, not quite enough to station keep. Also, this assumes fully reflective sun shields, and pointed straight at the sun. I'm not sure what the actual direction of thrust that would be required to keep it at L2, but it probably wouldn't be straight on, thus reducing this further.

Bottom line, it might work, but would require some very careful placement of the shield to maintain the proper orientation.

EDIT: Per some new information, it turns out that my source was VERY misleading about the size, those dimensions were more of a diamond type dimensions, and not a rectangle, which is very odd. This paper has some interesting information, showing the area is actually closer to 160 m^2, with a station keeping budget of at most 2.25 m/s per year, taking everything in to account. That means it would entirely be possible to achieve. One of the biggest sources of uncertainty is the movement of the solar shield itself, it is likely if this was controlled it could actually be reduced significantly. The actual ability to station keep is closer to 6.7 m/s. Given sources that say between 5-16 m/s is typical stationkeeping values, it seems likely that to a degree at least, JWST will be controlled by sunlight, although that is VERY difficult to tell without complex analysis.

• That value of 30 to 100 m/s per year is a bogus number. Perhaps that's for EML1/EML2? This paper claims that "In recent years, typical annual station-keeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO." This paper, which addresses JSWT directly, estimates stationkeeping costs for JWST to be 2.43 m/s per year. – David Hammen Apr 9 at 15:19
• Double checking, that "30 - 100 m/s per year" is completely bogus, even for EML1/EML2. Per this paper, the ARTEMIS satellites experienced stationkeeping costs in the range of 5 to 16 m/s per year. – David Hammen Apr 9 at 16:02
• Good feedback, have improved. Now we just need to fix Wikipedia... – PearsonArtPhoto Apr 9 at 17:10
• NASA says "Actual dimensions: 21.197 m x 14.162 m (69.5 ft x 46.5 ft)". I thought rectangle. Turns out that was a bad assumption. Huh. Interesting paper in any case, added quite a bit to my answer. – PearsonArtPhoto Apr 10 at 1:13
• @uhoh - My first comment says exactly that (JWST stationkeeping is 2.43 m/s/yr). Note that this is high for vehicles in pseudo-orbits about SEL1 or SEL2. In my second comment I was poking deeper at the dubious values in the wikipedia article referenced in the answer, addressing the question I raised in the first comment: Are those dubious wikipedia values for Earth-Moon L1/L2? The answer is no. I picked ARTEMIS specifically because for a while they were in pseudo-orbits about EML1/L2. The costs are considerably higher than for Sun-Earth L1/L2, but not in the 30-100 m/s/yr range. – David Hammen Apr 10 at 1:36

This paper by Heiligers et al. explores Earth-moon libration point orbits with the addition of solar sail thrusting. While it is of course not directly translateable to Sun-Earth L2 (JWST) the dynamics of libration point orbits in both systems are at least comparable. The study shows that an increase in stability can be acquired for some orbits (lunar L2 halo being one of them).

JWST is however not a typical solar sail spacecraft. These have much higher area/mass ratios and will produce more acceleration, together with a lower mass (I'm assuming also lower inertia) which means they can steer their sails much more effectively.

I would assume that the conclusions from the paper can be applied to the JWST as well, but the impact on the stability will probably be much smaller than in the case of a regular solar sail spacecraft.

• That's a really beautiful paper! – uhoh Apr 10 at 1:41

tl;dr: I think there could be room to do this. However, I don't think a conclusive answer can be had through analyses of magnitudes on envelope-backs. A real answer would only come from even more detailed Monte Carlo calculations than those already outlined in Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope. Sounds like a fun project!

Let's look at this systematically using well-sourced facts.

## Thrust from photon pressure on sunshield

A photon's momentum $$p$$ is just its energy divided by the speed of light $$E/c=h\nu/c$$, so the force resulting in the perfect absorption of photons would be

$$F=\frac{dp}{dt}=\frac{1}{c}\frac{dE}{dt} = \frac{P}{c}$$

where $$P$$ is the total power of the light hitting the absorber, in units of Watts for example, and $$A$$ is the area of the incoming light field intercepting the absorber.

Since the sail is reflective rather than absorbing, there's a second beam of reflected light and a second force, and this one has a direction based on the orientation of the mirror. Let's just look at the magnitudes for now though.

Wikipedia gives the shape of the diamond-shaped sunshield as about 21 by 14 meters (the diagonals). That will have an area equal to half the product of the diagonals, or 147 m^2, agreeing nicely with Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope.

As shown in Figure 6, the effective area of the Sunshield in the Sunward direction can vary between 105 and 163 m², the range of allowed spacecraft attitudes that prevent the telescope from being exposed to stray light.

The solar constant is about 1360 W/m^2 at 1 AU, but the L2 area is 1% farther, so let's use

$$P_{max}=A \times \text{1330 W/m^2} \approx 196 \text{kW}$$

to get

$$F_{max} = 2 \frac{P_{max}}{c} \approx 1.3 \text{mN}.$$

Acceleration is force/mass. Using 6500 kg from Wikipedia:

$$a_{max} = \frac{F_{max}}{m} \approx 2.7 \times 10^{-7} \text{m/s²}.$$

A year has about 31.6 million seconds, so that's 6.3 m/s per year of delta-v available in the +z direction if the shade points mostly back towards the Sun, and somewhat less if a bit of tilt is used if perpendicular acceleration is needed.

## JWST's known station-keeping budget

The results of the analysis show that the SK delta-V budget for a 10.5 year mission is 25.5 m/sec, or 2.43 m/sec per year. This SK budget is higher than the typical LPO SK budget of about 1 m/sec per year, but JWST presents challenges that other LPO missions do not face. The Endof-Box analysis was critical to the JWST mission, because it provided a realistic value for the SK delta-V budget when it was needed to establish a complete spacecraft mass budget.

So the sail provides more than double the magnitude of the station-keeping delta-v.

SOHO is an example of a spacecraft in a halo orbit (around L1) and per Roberts 2002 (from Is this what station keeping maneuvers look like, or just glitches in data? (SOHO via Horizons)) it uses a station-keeping strategy of only thrusting in the z direction (toward or away from the Sun). However, Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope tells us:

In LPO dynamics is known that the x-y plane contains the stable and unstable directions, while the z direction is neutrally stable. Because JWST does not need to remain near a reference orbit, during SK maneuvers there is no need to thrust in the z direction, and the thrust vector is chosen to lie in the x-y plane.

This doesn't mean that in our non-telescope-mode, survival holding pattern we would also need the station-keeping (SK) thrust vector in the perpendicular x-y plane though, and I propose that in survival mode one could use some combination of modulation of the z-component and adding the x-y component by tilting and angling the sunshield within its safe limits will provide enough delta-v and flexibility in its direction to perform the station-keeping.

## Conclusions

• JWST will experience a steady delta-v of about 6 m/s per year due to the constant photon pressure of sunlight reflecting back from its sunshield.
• While this is of course already figured into it's orbit, this will mostly result in a halo orbit just slightly in front of (sunward-of) the halo orbit about L1 calculated without the effects of photon pressure. Here "slightly in front of" is probably of the order of a few kilometers or tens of kilometers only.
• Aggressive tilting of the sunshield within safe limits can both modulate the +z acceleration, and add a component in the x-y plane
• Rotating the spacecraft about the +z axis of the orbit in the rotating frame with a tilted sunshield will direct the component of the thrust within the x-y plane, though probably not enough to make up the full 2.4 m/s per year currently obtained from propulsive maneuvers every 21 days.