Move Mimas, Tethys and Phobos along their orbits by the terms their IAU W already carried

The IAU W of a locked moon follows its mean longitude, so a term of W that is the moon running
ahead of and behind its mean motion is its orbit's too. Two were in bodies.json's W and in no
orbit: the 71-year libration of the Mimas-Tethys 4:2 resonance, -44.85 degrees on Mimas and
+2.23 on Tethys on the angle S5 = 316.45 + 506.2 T of pck00011.tpc, and Phobos's tidal
quadratic, 9.536e-9 degrees a day squared about J2000. JPL's satellite table has a column for
neither. orbitalTermsOfPrimeMeridian now turns each into the row's meanAnomalyTerms about the
row's own epoch (Phobos's 1950 row gets the quadratic re-centred, which adds to its mean motion
and mean anomaly at the epoch), and the ETL takes them for the three moons named in their specs.

Against Horizons: Mimas on 2026 May 27, near the libration's extreme, 2.24 degrees instead of
43.3; Tethys the same day 0.18 instead of 2.05; Phobos in 2100 1.25 instead of 11.1. On the
ETL's 2025-01-01 check Mimas is 1.56 degrees, so its named 46-degree ceiling is gone. The renderer
spec freezes the Mimas and Phobos vectors.

The day-equals-orbit check checked a number that turns no locked moon: since cdf474b every one is
turned by its IAU W. build.ts now checks what is drawn instead: the east longitude of the planet
on the moon's IAU body-fixed frame, from where the mean elements put it, every 135 days from 1950
to 2100. Measured: at most 6.70 degrees (the Moon's own eccentricity swing), with Mimas 10.15
(its physical libration, which Horizons shows too), Iapetus 18.33 (its row sits 9.4 degrees
behind Horizons) and Proteus 8.18 under their own ceilings. The lock holds only over that span:
Proteus's W turns 6.3e-7 of its rate slower than its orbit, which drifts its face 74 degrees by
AD 3000, and Mimas's W runs 6e-5 degrees a day ahead of the table's mean motion. Without the new
terms the check fails: Phobos's face turned 13.78 degrees from Mars by 2100, and Mimas's 54.5.

The comments that promised the lock "however long the clock runs" now say what the check covers.
The ceilings comment in build.ts gives Hyperion's and Nereid's worst offsets sampled daily (22.2
and 11.2 degrees, where twelve New Year's Days gave 20.2 and 2.6).

Controls: dropping the libration's cosine term, the quadratic, the quadratic's re-centring or
swapping sine and cosine each fails its named test; the ETL without Mimas's term fails at 44.68
degrees and without Phobos's at 13.78.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

src/app/features/galaxy-system/system-orbits-renderer.spec.ts

@@ -506,6 +506,10 @@ describe('solar-system bodies against Horizons', () => {
     charon: {kind: 'moon', orbit: {semiMajorAxisAu: 0.00013095774631236113, eccentricity: 0.0002, inclinationDeg: 0.08, longitudeOfAscendingNodeDeg: 26.928, argumentOfPeriapsisDeg: 146.106, meanAnomalyAtEpochDeg: 131.07, epochJd: 2451545}, rates: {meanMotionDegPerDay: 56.362521, longitudeOfAscendingNodeDegPerDay: -0.00010926638529337138, argumentOfPeriapsisDegPerDay: 0.00009683851540842405}, laplacePole: {raDeg: 132.993, decDeg: -6.163}, parentBodyId: 'pluto', massRatio: 0.1220485755631374},
     venus: {kind: 'planet', orbit: {semiMajorAxisAu: 0.72332102, eccentricity: 0.00676399, inclinationDeg: 3.39777545, longitudeOfAscendingNodeDeg: 76.67261496, argumentOfPeriapsisDeg: 55.094942169999996, meanAnomalyAtEpochDeg: 50.21215136999999, epochJd: 2451545}, rates: {meanMotionDegPerDay: 1.6021304750882956, longitudeOfAscendingNodeDegPerDay: -0.000007467261875427789, argumentOfPeriapsisDegPerDay: 0.000009022264750171116, semiMajorAxisAuPerDay: -7.118412046543463e-12, eccentricityPerDay: -1.398220396988364e-9, inclinationDegPerDay: 1.1908008213552361e-8}},
     mars: {kind: 'planet', orbit: {semiMajorAxisAu: 1.52371243, eccentricity: 0.09336511, inclinationDeg: 1.85181869, longitudeOfAscendingNodeDeg: 49.71320984, argumentOfPeriapsisDeg: -73.63065768, meanAnomalyAtEpochDeg: 19.3493162, epochJd: 2451545}, rates: {meanMotionDegPerDay: 0.5240328362061601, longitudeOfAscendingNodeDegPerDay: -0.000007351794934976044, argumentOfPeriapsisDegPerDay: 0.00001973334866529774, semiMajorAxisAuPerDay: 2.6557152635181385e-11, eccentricityPerDay: 2.5048596851471597e-9, inclinationDegPerDay: -1.9842765229295004e-7}},
+    // Mimas and Phobos carry the terms of their IAU W that are motion along the orbit: the Mimas-Tethys
+    // libration and Phobos's tidal acceleration (see `orbitalTermsOfPrimeMeridian`).
+    mimas: {kind: 'moon', orbit: {semiMajorAxisAu: 0.0012402516100785653, eccentricity: 0.0196, inclinationDeg: 1.574, longitudeOfAscendingNodeDeg: 173.027, argumentOfPeriapsisDeg: 332.499, meanAnomalyAtEpochDeg: 14.848, epochJd: 2451545}, rates: {meanMotionDegPerDay: 381.9944948, longitudeOfAscendingNodeDegPerDay: -0.9996209770462032, argumentOfPeriapsisDegPerDay: 1.9992419540924065, meanAnomalyTerms: {b: 0, c: 30.901081394463684, s: -32.50608664008527, f: 506.2}}, laplacePole: {raDeg: 40.589, decDeg: 83.536}, parentBodyId: 'saturn'},
+    phobos: {kind: 'moon', orbit: {semiMajorAxisAu: 0.00006267468885838895, eccentricity: 0.0151, inclinationDeg: 1.075, longitudeOfAscendingNodeDeg: 207.784, argumentOfPeriapsisDeg: 150.057, meanAnomalyAtEpochDeg: 94.2394819925, epochJd: 2433282.5}, rates: {meanMotionDegPerDay: 1128.8444085925948, longitudeOfAscendingNodeDegPerDay: -0.43579001784832494, argumentOfPeriapsisDegPerDay: 0.871002371303956, meanAnomalyTerms: {b: 12.721927969999998, c: 0, s: 0, f: 0}}, laplacePole: {raDeg: 317.671, decDeg: 52.893}, parentBodyId: 'mars'},
   };
   // The IAU WGCCRE 2015 rotational elements bodies.json carries for them, from pck00011.tpc.
   const ROTATION: Record<string, RotationalElements> = {
@@ -521,7 +525,9 @@ describe('solar-system bodies against Horizons', () => {
   // Each ceiling sits just above what these elements measure on that date: Earth 0.003 degrees,
   // Jupiter 0.063, Saturn 0.164, Pluto 0.054, the Moon 0.72 (no mean ellipse has its evection or
   // variation), Io 0.021, Europa 0.036, Titan 0.014, Triton 0.137, Titania 0.62 (against Uranus's
-  // equator, 120 years from its 1980 epoch), Charon 0.37.
+  // equator, 120 years from its 1980 epoch), Charon 0.37, Mimas 2.24 on 2026 May 27, when its libration has it
+  // 44 degrees ahead of its mean motion (43.3 without the term), and Phobos 1.25 in 2100 (11.1 without its
+  // tidal acceleration).
   const HORIZONS: Array<[id: string, jd: number, x: number, y: number, z: number, maxDeg: number]> = [
     ['earth', 2488069.5, -0.1574071329883954, 0.890666220858489, 0.3859132211165683, 0.02],
     ['jupiter', 2433282.5, 3.406605247558555, -3.425997624196318, -1.551719750032203, 0.1],
@@ -534,6 +540,8 @@ describe('solar-system bodies against Horizons', () => {
     ['triton', 2488069.5, -0.001421151845853369, -0.0001894510477241482, 0.001888790702926415, 0.2],
     ['titania', 2488069.5, -0.00151919968294745, -0.0003387914082135071, 0.002465657830788125, 0.75],
     ['charon', 2488069.5, -0.00003046411046017432, -0.000009404114448552256, 0.0001270457155789907, 0.5],
+    ['mimas', 2461187.5, -3.840685116962088e-4, 1.182766232573268e-3, -2.006928678577268e-5, 3],
+    ['phobos', 2488069.5, 4.269855297288105e-5, -2.759158950396543e-5, -3.816269137755616e-5, 1.5],
   ];
 
   function record(id: string): BodyRecord {