Turn a locked moon's pole round with its drawn node, so its axis stays on its orbit at every date the clock reaches

The IAU carries a locked moon's pole round its orbit normal on a term of the node's angle, as a
moon in a Cassini state keeps it, but at the node rate the IAU's source had: Miranda's U11 at
-2024.22 degrees a century where the JPL table its orbit is drawn from has -2030.80, Mimas's S3 at
-36505.5 against -36511.16. Over AD 1-3000 that parted Miranda's drawn axis from its drawn orbit
normal by up to 7.89 degrees (AD 9), so Uranus swung 7.6 degrees north and south on its sky every
1.41 days, and Mimas's by 2.63. Only Iapetus's pole had been put on its orbit.

lockedToOrbit now sets every periodic term whose angle turns within 5 per cent of k times the
drawn node rate (k from 1 to 9, the most the report takes, Triton's) to exactly that multiple, and
moves its constant so the angle, and the pole and W with it, are unchanged on 2025-01-01 (the
2025 pole and W of every changed moon are identical to the 1e-14 degree). Measured: the largest
offset taken is Ganymede's J5, 3.4e-2, then Rhea's 1.2e-2; the nearest term that is not a node is
6.0e-2 out (a W-only term of Miranda's), and Umbriel's W has one 1.0e-2 from ten times its node,
which the k limit leaves. Ten moons change: Deimos, Io, Europa, Ganymede, Mimas, Tethys, Rhea,
Miranda, Triton and Proteus. The Moon and Phobos, whose W carries a quadratic, are left as before,
and so is Callisto's J6, 40 per cent from its node rate.

Worst angle between the spin axis and the drawn orbit normal over AD 1-3000, every 135 days,
before and after: Miranda 7.89 -> 0.42, Mimas 2.63 -> 0.47, Rhea 0.77 -> 0.17, Triton 0.51 ->
0.15, Europa 0.33 -> 0.13, Ganymede 0.50 -> 0.16. Faces: Miranda 2.75 -> 2.39, Mimas 8.94 ->
8.89, Deimos 2.14 -> 2.08, Triton 2.88 -> 2.81; none got worse.

build.ts now checks that angle for every locked moon over the same 8114 dates as the face check,
at most 1 degree (Tethys 0.97, whose IAU pole sits 0.69 from its orbit today; Titan 0.94, whose
IAU pole is still while its node turns in 705 years), with four named ceilings: the Moon 7.1 (its
real 6.7-degree tilt, 6.98 at worst), Phobos 2 and Deimos 2 (1.81 and 1.74) and Proteus 1.2
(1.09), whose IAU poles nod with Mars's and Neptune's precessing poles while the Laplace poles
their orbits are drawn round are fixed. The obliquity check at Horizons' epoch shares the new
axisFromOrbitDeg with it. Nothing checked the axis against the orbit before: an Iapetus pole left
on its Laplace pole, 8.30 degrees off at every date, passed the ETL and the suite.

Guarded mutants, each through the solar ETL and then the suite on the data it wrote:
- node terms left at the IAU rates: the ETL fails with "Moon mimas's spin axis leans up to 2.63
  degrees ... (at most 1 expected)", and the suite with only the new test failing;
- Iapetus's pole put on its Laplace pole, W re-phased so its face today is unchanged (worst face
  16.41, under its 16.5 ceiling): the ETL fails with "Moon iapetus's spin axis leans up to 8.30
  degrees", and the suite with only the new test failing.

Also: lockedToOrbit called the Iapetus normal's circle "8.3 degrees across"; 8.3 is its radius (the
row's i = 8.298 to the Laplace plane) and it is 16.6 across. The README credited every rotation to
pck00011 without saying that a locked moon's W and node terms are re-rated to its JPL mean elements
and Iapetus's pole carried round its orbit normal; both of its lines now say so, as the body
model's doc does.

Unit suite 858/858, etl:typecheck and tsc -p tsconfig.app.json clean, solar ETL passes on the
real data.

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

src/app/shared/models/body.model.ts

@@ -105,8 +105,9 @@ export interface BodyRecord {
   /**
    * Where the body's pole points and which way its prime meridian faces at any date, from the IAU
    * WGCCRE 2015 report (Archinal et al. 2018) as NAIF's `pck00011.tpc` carries it, but that a locked
-   * moon's W turns at its drawn orbit's rate and Iapetus's pole goes round with its orbit's, so they
-   * keep their faces to their planets over the clock's AD 1 to 3000 (see `lockedToOrbit` in the
+   * moon's W, and its pole's terms on its node, turn at its drawn orbit's rates and Iapetus's pole
+   * goes round with its orbit's, so they keep their faces to their planets, and their poles round
+   * their orbits', over the clock's AD 1 to 3000 (see `lockedToOrbit` in the
    * ETL). Where present it alone sets how the body is drawn, and the ETL checks the period and
    * obliquity above against it. Absent where the report gives none: Hyperion tumbles, and Nereid,
    * Eris, Haumea and Makemake have no model.