Draw four moons' nodes at JPL's current rates, which Horizons and the IAU's poles agree with

The archived satellite table the moons are read from gives older node
periods than JPL's current one for Miranda (17.727 years against URA182's
17.787), Ganymede (132.654 against 137.812), Callisto (338.82 against
577.264) and Titan (704.60 against 687.370), and 74ea1d6 turned the IAU's
poles after those older rates, taking them for the right ones. They were
not: fitted to Horizons' osculating elements on Uranus's equator over
1601-2399, Miranda's node turns 2023.97 degrees a century (rms 0.04),
against the current table's 2023.95, the IAU's U11 2024.22 and the row's
2030.80. That commit moved Miranda's axis from 0.38 to 2.36 degrees of
Horizons' orbit normal. Mimas's node, 0.986 years in both tables, now takes
the IAU's S3, 36505.5 degrees a century, 1.2 from a Horizons fit where
the row's is 4.5.

The ETL spec carries the node period (nodePeriodYears), and the periapsis
keeps the row's longitude rate: the row gives the longitude's rate (Callisto
68.7 degrees a century, the current table 67.2), so the argument takes up
the change. On the row's argument Callisto's periapsis moved 44 degrees by
2100 and it strayed 0.71 degrees from Horizons over 1950-2100.

Worst angle from Horizons' osculating orbit normal (ICRF), HEAD then now:
- Miranda, 1601-2399: drawn orbit 2.11 -> 0.12, axis 2.36 -> 0.34.
- Mimas, 1750-2249: orbit 0.33 -> 0.11, axis 0.65 -> 0.40.
- Ganymede, 1600-2199: orbit 0.17 -> 0.11, axis 0.13 -> 0.01.
- Callisto, 1600-2199: orbit 0.53 -> 0.20, axis 0.02 -> 0.03.
- Titan, 1750-2249: orbit 0.048 -> 0.052.
Against the 1950-2100 Horizons tracks the ETL checks: Callisto 0.19 -> 0.08,
Miranda 1.73 -> 1.62, Ganymede 0.30 -> 0.29, Mimas 7.43 -> 7.42, Titan 0.06.

lockedToOrbit now barely moves the IAU's node terms: Miranda's U11 to
-2023.95, Ganymede's J5 to 261.23 (262.1), Mimas's S3 not at all, and
Callisto's J6, 3.1 per cent from its new node rate, to 62.36 (64.3), which
takes Callisto's axis from 0.56 to 0.22 degrees of its drawn orbit.

With the drawn rates right, leaving every node term at the IAU's rate no
longer failed the ETL (Mimas used to), nor did a 1 per cent tolerance, the
node's angle without its harmonics, or the older node periods. The axis
ceiling is now 0.25 degrees for Europa (0.13 measured), Ganymede (0.16),
Callisto (0.22), Rhea (0.17), Miranda (0.23) and Triton (0.15), and
Callisto's track ceiling 0.15 (0.08). Guarded mutants, each through the
solar ETL on the real catalogue and then the suite on the bodies.json it
wrote:
- node terms left at the IAU's rates: ETL "europa's spin axis leans up to
  0.33"; suite fails only 'turns the poles of Europa, Ganymede, Callisto,
  Rhea, Miranda and Triton round with their drawn nodes'.
- tolerance 1 per cent: ETL, Callisto 0.33; the same test, alone.
- harmonics dropped: ETL, Triton 0.29 (the suite's three dates miss it).
- the archived node periods: ETL, Callisto's track 0.19; the suite fails
  that test and 'draws Miranda's orbit, and turns its axis, where Horizons
  has its orbit in 1601 and 2390' (orbit 2.02, axis 2.36 at 1601).
- the row's argument kept: ETL, Callisto's track 0.71.

The docs that called the IAU's rates the wrong ones are corrected
(lockedToOrbit, the axis ceiling in build.ts, whose Titan node now turns
in 687 years), and the README and BodyRecord doc no longer say every
locked moon's node terms are re-rated: only those within 5 per cent of a
multiple of the node's rate, never the Moon's or Phobos's, and not the
circles Ariel's, Umbriel's, Titania's and Oberon's poles go round on
(0.36 to 0.50 degrees off their orbits). The README also names the five
bodies the IAU's elements do not turn. Unit suite 866 passed.

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

tools/etl/lib/locked-spin.ts

@@ -23,8 +23,8 @@ const POLE_HARMONICS = 5;
 
 /**
  * How far a periodic term's angle may turn from a multiple of the node's rate, as a fraction of it,
- * and still be taken for the node's angle as the IAU's source had it. Measured: at most 3.4e-2
- * (Ganymede's J5), then Rhea's R4 1.2e-2 and Miranda's U11 3.2e-3; the nearest that is not a node is
+ * and still be taken for the node's angle as the IAU's source had it. Measured: at most 3.1e-2
+ * (Callisto's J6), then Rhea's R4 1.2e-2 and Ganymede's J5 3.3e-3; the nearest that is not a node is
  * a term of Miranda's W alone, 6.0e-2 from three times it. Multiples go up to the ninth, the most the
  * report takes (Triton's N7); past that, Umbriel's W has a term 1.0e-2 from ten times its node's.
  */
@@ -58,14 +58,20 @@ export function subPlanetLongitudeDeg(body: Pick<BodyRecord, 'orbit' | 'rates' |
  *
  * The node's angle goes the same way. A moon in a Cassini state keeps its axis on its orbit normal,
  * which goes round the Laplace pole with the node, and the IAU's pole goes round with it on a term
- * of the node's angle, at the node's rate as its source had it: Miranda's U11 at -2024.22 degrees a
- * century, where the table the orbit is drawn from has -2030.80. On a 4.3-degree circle that parted
- * the axis from the drawn orbit by 7.9 degrees at AD 1, and Mimas's by 2.6. Every term whose angle
- * turns within {@link MAX_NODE_RATE_OFFSET} of a multiple of the node's rate is set to that multiple,
- * its constant moved so the angle is unchanged at the present, and the pole with it: over AD 1-3000
- * Miranda's axis stays within 0.42 degrees of its orbit normal and Mimas's within 0.47, and the
- * Io's, Europa's, Ganymede's, Rhea's and Triton's within 0.17. The rest of the pole and its terms
- * are the IAU's: Callisto's J6 turns 40 per cent slower than its node, and is left.
+ * of the node's angle, at the node's rate as its source had it, not quite JPL's current one the
+ * orbit is drawn at (see `nodePeriodYears` in `fetchSolarSystem.ts`): Rhea's R4 turns 1.2 per cent
+ * faster than its node, Callisto's J6 3.1 per cent, and Miranda's U11 0.013 per cent, which on a
+ * 4.4-degree circle over twenty centuries still adds up. On the IAU's rates the axes part from the
+ * drawn orbits by AD 1 or 3000: Rhea's by 0.77 degrees, Miranda's 0.59, Triton's 0.51, Europa's and
+ * Callisto's 0.33. Every term whose angle turns within {@link MAX_NODE_RATE_OFFSET} of a multiple of
+ * the node's rate is set to that multiple, its constant moved so the angle is unchanged at the
+ * present, and the pole with it: over AD 1-3000 the axes of Io, Europa, Ganymede, Callisto, Rhea,
+ * Miranda and Triton stay within 0.23 degrees of their orbit normals, and Mimas's, whose drawn node
+ * takes the IAU's S3 itself, within 0.44. The rest of the pole and its terms are the IAU's, and so
+ * are all of the Moon's and Phobos's, left whole with their W: Ariel's, Umbriel's, Titania's and
+ * Oberon's poles go round on angles of their own at none of their nodes' multiples (Oberon's, the
+ * nearest, 8.7 per cent from three times its node's rate), and their axes stay within 0.50 degrees
+ * of their orbit normals without.
  *
  * `poleFollowsOrbit` is for Iapetus, whose IAU pole moves 3.9 degrees a century in right ascension
  * and 1.1 in declination: a straight line through its orbit normal's 3 439-year circle round the