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How much fuel did JWST save due to an accurate Arianne 5 launch, and how much fuel will be remaining after JWST L2 orbital insertion? And how many years is that fuel expected to last?

According to https://en.wikipedia.org/wiki/James_Webb_Space_Telescope "Eight smaller thrusters are used for attitude control—the correct pointing of the spacecraft.[74] The engines use hydrazine fuel (159 liters or 42 U.S. gallons at launch) and dinitrogen tetroxide as oxidizer (79.5 litres or 21.0 US gallons at launch).[75]"

"It was designed to carry enough fuel for ten years,[172] but the precision of the Ariane 5 launch and the first midcourse correction were credited with saving enough onboard fuel, that the observatory should be able to maintain its orbit for "significantly more" than this."

But it doesn't say how much of this fuel was expected to remain after L2 orbital insertion assuming the expected less than perfect Arianne5 launch which was planned for; lets call this number e for expected fuel and lets call the number a for actual remaining fuel with the much better launch than expected. And it doesn't say much fuel is expected to be used annually for JWST orbital maintenance and momentum dumping; call this number y for expected yearly orbital maintenance. These numbers could be used to compute how many years the more efficient Arianne 5 launch increased the JWST lifetime. $$\text{years_gained} \approx \frac{a-e}{y}$$

I think I've read that the expected planned mission of 10 years was gated by the annual orbital maintenance which would imply: $$\text{planned_lifetime} \approx \frac{e}{y}\approx 10\;\text{years}$$ The actual fuel limited lifetime would be: $$\text{actual_limited_lifetime} \approx \frac{a}{y}\;\text{years}$$

https://arstechnica.com/science/2022/01/all-hail-the-ariane-5-rocket-which-doubled-the-webb-telescopes-lifetime/

Mike Menzel, said the agency had completed its analysis of how much "extra" fuel remained on board the telescope. Roughly speaking, Menzel said, Webb has enough propellant on board for 20 years of life.

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    $\begingroup$ I clarified the numbers I'm interested in. $\endgroup$
    – Sheldon
    Jan 9, 2022 at 6:55
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    $\begingroup$ It won't run out of fuel after 10 years. 10 year design lifetime means "there is no chance of running out of fuel, no matter how bad things go (within reasonable assumptions)". I.e. worst possible injection, many missed correction maneuvers, more momentum unloading etc. Under nominal conditions that should last at least 15 - 20 years. (no citation, so not an answer). $\endgroup$
    – asdfex
    Jan 9, 2022 at 10:00
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    $\begingroup$ @asdfex: Mike Menzel (Lead Mission Systems Engineer for James Webb Space Telescope) is quoted by numerous sources as confirming that thanks to the precise insertion by Ariane 5 and the two correction burns, Webb has enough fuel for its maximum design life of 20 years. I have not found a first-party source, unfortunately, but Arianespace has re-tweeted several of those third-party sources, which indicates they agree with the assessment. Here's just one example: twitter.com/ariane5/status/1479923663881256966 $\endgroup$
    – Jörg W Mittag
    Jan 9, 2022 at 10:24
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    $\begingroup$ Yes... 20 years correspond to roughly 6 m/s per year (at 120m/s remaining after 30 m/s for the MCCs). If we assume momentum unloading at 2 m/s/year and take the public 2-4 m/s/year for station keeping there's still a huge range of possible lifetimes. $\endgroup$
    – asdfex
    Jan 9, 2022 at 10:35
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    $\begingroup$ @NgPh Stacking up worst case upon worst case ... upon worst case, and doing so in the worst possible way easily results in a launch vehicle that cannot launch or a spacecraft that cannot reach its objectives. What we do instead is lots (and lots and lots) of statistical analyses (e.g., Monte Carlo, Markov Chain Monte Carlo, bootstrap, jackknife, ...) to determine behaviors at, for example, the three sigma level. Non-space industry has gone far beyond this and is moving toward six sigma processes. Space exploration is nowhere near six sigma. $\endgroup$
    – David Hammen
    Jan 9, 2022 at 17:05

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The three MCC course correction burns, which are listed In this NASA blog and and this NASA blog have totaled 24.4$\frac{m}{s}$ fuel used so far, in burns totaling 79.5 minutes.

  • Dec 25th, 20$\frac{m}{s}$, 65 minutes
  • Dec 27th, 2.8$\frac{m}{s}$, 9.5 minutes
  • Jan 24th, 1.6$\frac{m}{s}$, 5 minutes

JWST started out with 150$\frac{m}{s}$ worth of thruster fuel James Webb telescope; limits to propellant lifetime?, of which 2-4$\frac{m}{s}$ are expected to be used annually for station keeping. A Monte Carlo simulation estimate was: 2.43$\frac{m}{s}$ annual station keeping usage; James Webb telescope; limits to propellant lifetime?, and Stationkeeping ... James Webb Space Telescope

By my math, this leaves JWST about 125$\frac{m}{s}$ worth of fuel remaining for both station keeping and momentum dumping, which is good enough for 20 years of fuel limited lifetime given a reasonable upper bound annual fuel usage of 6$\frac{m}{s}$.

Finally, there is this quote, "The first, MCC-1a, is expected to be a long, continuous burn (potentially up to 3 hours) performed approximately twelve hours after launch"; JWST Mid-Course Correction. If the total of the three MCC burns had turned out to be 190 minutes instead of 80 minutes, then by my math the accurate Arianne launch saved 110 minutes worth of MCC burn, which equates to 34$\frac{m}{s}$, which increased the JWST lifetime by at least six years, and maybe as much as ten years. Of course, a 3 hour burn would probably be worst case, but given the unpredictability of launch vehicles, such a scenario had to be considered realistically possible...

One final NASA link I found also states that JWST has 20 years of fuel instead of 10 years worth of fuel. NASA: Webb arrives in orbit of L2. JWST's lifetime is probably not going to be fuel limited...

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  • $\begingroup$ I concur. My answer to your linked question is "Bottom line: My best guess is currently 150 - 67 = 83, and 83 / (2 to 4) = 41 to 21 years." $\endgroup$
    – uhoh
    Jan 24, 2022 at 21:59
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    $\begingroup$ what blows my mind is how small the station keeping maneuvers really are. Today's burn amounts to only 1.6$\frac{m}{s}$, or 3.4 mph, and the total annual station keeping might only be 2.5$\frac{m}{s}$, which is only 5.6mph. These are tiny tiny numbers compared to the $\Delta_V$ from the Guiana spaceport to L2 which might be 12.5$\frac{km}{s}$ or 28000mph when including the atmospheric drag. $\endgroup$
    – Sheldon
    Jan 24, 2022 at 23:12
  • $\begingroup$ Yes, every two weeks for ~six months means twelve nudges per orbit, but they are certainly relatively small nudges. I wonder how much lower it could be if they forgot about it being an astronomical observatory and went for the absolute minimum delta-v plan. Perhaps with the sunshield more active as an additional propulsive, it could get really low. $\endgroup$
    – uhoh
    Jan 25, 2022 at 0:14

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