Could JWST stay at L2 "forever"?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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!

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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

Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope tells us:

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.

Momentum unloading

I haven't through too much about how to do momentum unloading of JWST's momentum wheels using only solar photon pressure. The wheels will be needed to not only maintain attitude but also to execute regular tilts and rotations needed to direct the photon pressure for station-keeping.

As soon as the spacecraft tilts a bit, the center of the resulting photon pressure will not include the spacecraft's center of mass, so there will be at least some torque to work with.

It is possible that these attitude maneuvers can be designed in pairs to be angular momentum-neutral such that they naturally cancel each other in terms of rotations of the wheels over time.

Opinion

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!

Answer 4

The short answer is no. Lagrange points are saddle points, in topological terms. They are only quasi-stable, but not actually stable. Solar radiation pressure is enough to cause a nutation and precession of the Wind spacecraft's spin axis over the course of a year (forms an ellipse on a polar graph with a diameter of about 1 degree). That force alone would nudge any spacecraft out place eventually, so no, it could not stay indefinitely.

There are also perturbations in gravitational fields, that, over long time periods would also nudge a spacecraft off of any quasi-stable saddle point.

There is also dust from interplanetary and interstellar space that impacts spacecraft at hypersonic speeds causing small plasma plumes. The dust from interstellar space has a preferred direction, thus would slowly kick any spacecraft off of a quasi-stable saddle point.

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?

Even with a spinning spacecraft, the orbit starts to exponentially decay after about a month. Wind performs only four station keeping maneuvers per year and each only costs ~4-10 cm/s of fuel (equivalent to something like 0.1 kg or less). The ACE, by comparison, performs maneuvers every other week or so. The difference is that ACE is a sun-pointed spinner and Wind is an ecliptic spinner. ACE needs to point in a specific direction for communication with Earth and because one of its plasma instruments is failing (so they canted the spin axis a little to rely more heavily on the less damaged anodes).

One could, in princple, just wait 9 months and re-insert Wind about the Earth-Sun L1 point, but the longer you wait, the more expensive (fuel-wise) it becomes. If we waited 2 years, Wind (or any other Lagrange-point-orbiting spacecraft) would be in a heliocentric orbit about the Sun just like Earth. If the spacecraft was at L1(L2), the spacecraft would orbit the Sun faster(slower) than Earth. This is actually what the STEREO do.

So no, if JWST didn't use fuel for 2 years, it would be in a heliocentric orbit about the Sun.

Fun Side Note: The JWST flight operations team came up with a new set of thrusting options to try and preserve fuel and in early 2014 they presented their idea to me and the Wind team. They want to use Wind as a test run to see if the thruster maneuvers would not only work, but would save fuel.

The old way was to only thrust when the spacecraft was on the Earth-Sun line and the thrusts would be aligned with the Earth-Sun line (well, as close as possible). The reason being, you do not want to apply a torque to either your orbit about the Lagrange point or your orbit around the Sun. The JWST teams idea was to thrust off the Earth-Sun line at angles to the Earth-Sun line. So I pointed out this would insert torques to the system and I was concerned. They went and published a paper on, found at doi:10.2514/6.2014-4304. Turns out, because the maneuvers only use a few to a few 10s of cm/s, the torques would be minimal and not critical so we went forward with it. It reduced our typical fuel cost per maneuver by ~5-10%.

I still find this a little funny because at the time Wind had over 120 years worth of fuel left...