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Turn each locked moon at its orbit's rate and Iapetus's pole round its orbit, so they face their planets at every date the clock reaches

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The IAU gives a locked moon's W the mean motion of whichever orbit its authors had, and JPL's table
has another. Near the present the difference is nothing; over the clock's AD 1 to 3000 it turned
Proteus's far side to Neptune at AD 1 (146 degrees), Mimas 52 degrees from Saturn and Miranda 23.
Iapetus was worse for another reason: its IAU pole is a straight line, 3.9 degrees a century in
right ascension, through its orbit normal's 3 439-year circle round the Laplace pole, which by AD 1
has run past the celestial pole (Dec 97.9), 11 degrees off the orbit, with the face 87 degrees
from Saturn. Mimas and Iapetus carry mission maps, so a wrong hemisphere was drawn facing Saturn.
The ETL's lock check sampled only 1950-2100, so none of it failed.

tools/etl/lib/locked-spin.ts, lockedToOrbit, called for every locked moon:
- W's rate becomes the orbit's own mean motion, its constant moved so W is unchanged on
  2025-01-01; the pole and every periodic term stay the IAU's. A W with a quadratic is left
  (Phobos's orbit already takes it; the Moon's is its tidal slowing, 0.75 degrees at AD 1). The
  kernel's rate must be within 1e-5 of the orbit's first (at most 3.4e-6, Iapetus).
- Iapetus (poleFollowsOrbit): the pole follows its orbit normal, as a moon in a Cassini state does,
  in the IAU's own form: sines of the node's angle and four harmonics on right ascension, cosines
  on declination, fitted to the normal's circle and pinned to the IAU pole at the present; W takes
  sines of the same angles, fitted to hold the face where it is today.

build.ts samples the lock over AD 1 to 3000 (8 114 dates, every 135 days) instead of 1950-2100, and
subPlanetLongitudeDeg moved to the lib, shared by both. Measured on the real catalogue: at most
5.36 degrees (Titan) but the Moon 7.62 (its eccentricity, and W's quadratic at AD 1: a new named
ceiling of 8), Mimas 8.94 (ceiling 11 -> 9.5) and Iapetus 15.95 (19 -> 16.5, 9.4 of it its row's
lag); Proteus's own ceiling of 9 is gone, at 2.66. Iapetus's axis stays within 0.74 degrees of its
orbit normal (11.06 before) and its pole is the IAU's at the present to 1e-4 degrees.

Live on :4301, the longitude facing the planet at AD 1 / 1000 / 2025 / 2999: Proteus 2.6 / 2.6 /
2.6 / 2.6 (was -146.5 / -72.9 / 2.6 / 74.5), Iapetus -15.9 / -15.4 / -15.3 / -9.3 (-87.0 / -50.9 /
-15.3 / 22.8), Mimas 4.1 / 6.8 / 5.7 / 8.4 (48.6 / 29.3 / 5.7 / -13.0), Miranda -0.1 / 2.2 / 0.0 /
1.4 (-23.4 / -9.6 / 0.0 / 12.6); the present is unchanged.

The renderer spec now takes the rotational elements from bodies.json too, so no hand copy is left,
and a new test turns Proteus, Miranda, Mimas and Iapetus to their planets at AD 1 and AD 3000.
Guarded mutants, each run through the solar ETL and then the full suite on what it wrote:
lockedToOrbit bypassed (validator: Mimas 52.30, ceiling 9.5; the new test fails), Iapetus on the
IAU's straight pole (98.48), and its pole round the orbit without W's terms (73.13); each fails the
new test and only it.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
This commit is contained in:
Senrokai
2026-09-30 15:58:04 +02:00
co-authored by Claude Opus 5.5
parent 09eaf9532f
commit 3b4fd1af6c
6 changed files with 312 additions and 107 deletions
Download Patch File Download Diff File Expand all files Collapse all files
tools/etl/build.ts
+23 -30
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@@ -11,6 +11,7 @@ import { fetchDeepSky } from './fetchDeepSky';
import { fetchExoplanets } from './fetchExoplanets';
import { fetchSolarSystem, FREELY_SPINNING_MOONS, offsetFromTrackDeg } from './fetchSolarSystem';
import { TrackPoint } from './lib/horizons';
import { subPlanetLongitudeDeg } from './lib/locked-spin';
import { BYTES_PER_STAR_META, BYTES_PER_STAR_POSITION, decodeStarCatalog, encodeStarCatalog } from '../../src/app/shared/models/star-catalog';
import { fetchStars } from './fetchStars';
import { describeSources } from './sources/registry';
@@ -223,37 +224,29 @@ const MAX_OBLIQUITY_OFFSET_DEG = 0.1;
/**
* How far from its planet a locked moon's drawn face may turn: the east longitude, on the IAU's
* body-fixed frame, of the direction to the planet from where the mean elements put the moon,
* sampled every 135 days from 1950 to 2100, where both the tables and the IAU's elements hold.
* sampled every 135 days over the clock's AD 1 to 3000. Every locked moon's W turns at its orbit's
* own rate (see `lockedToOrbit`); at the IAU's own rates, and sampled only from 1950 to 2100, this
* let Proteus turn its far side to Neptune at AD 1 (146 degrees), Iapetus 87 degrees, Mimas 52 and
* Miranda 23, on dates the clock offers.
*
* Measured on this catalogue: at most 6.70 degrees (the Moon, whose longitude swings 6.3 either
* way with its eccentricity; Horizons has the same). Three need their own. Mimas 10.15: its drawn
* face runs from 2.5 to 10.15 degrees, about 6.3 off on average because the IAU's W and JPL's mean
* longitude disagree, drifting 3.3 over the span because W turns 6.0e-5 degrees a day faster than
* the row's n, and swung 2.3 either way (2e) by its eccentricity. None of that is Mimas: its
* measured physical libration is 0.84 degrees (Tajeddine et al. 2014, Science 346, 322), and W
* carries none; Horizons, on the same W against its integrated orbit, runs from -2.7 to 12.7
* degrees over 1950-2100 with the 71-year S5 term the orbit here cancels. Iapetus
* 18.33, whose row sits 9.4 degrees behind Horizons; and Proteus 8.18, whose W turns 6.3e-7 of
* its rate slower than its orbit, a drift of 74 degrees by AD 3000. What this catches is an orbit
* and a W that go round at different rates: the tidal acceleration W carried and the orbit did not
* turned Phobos 13.8 degrees from Mars by 2100, and the Mimas-Tethys libration Mimas 54.5.
* Measured on this catalogue: at most 5.36 degrees (Titan) but for three. The Moon 7.62, at AD 1:
* its longitude swings 6.3 either way with its eccentricity, Horizons' too, and W's quadratic, the
* tidal slowing its orbit here does not carry, adds 0.75 by then. Mimas 8.94: about 6.3 off on
* average because the IAU's W and JPL's mean longitude disagree, and swung 2.3 either way (2e) by
* its eccentricity. None of that is Mimas: its measured physical libration is 0.84 degrees
* (Tajeddine et al. 2014, Science 346, 322), and W carries none; Horizons, on the same W against its
* integrated orbit, runs from -2.7 to 12.7 degrees over 1950-2100 with the 71-year S5 term the
* orbit here cancels. Iapetus 15.95, whose row sits 9.4 degrees behind Horizons. What this catches
* is an orbit and a W that go round at different rates: the tidal acceleration W carried and the
* orbit did not turned Phobos 13.8 degrees from Mars by 2100, and the Mimas-Tethys libration Mimas
* 54.5.
*/
const MAX_SUB_PLANET_LONGITUDE_DEG = 7;
const SUB_PLANET_CEILINGS_DEG: Record<string, number> = { mimas: 11, iapetus: 19, proteus: 9 };
const LOCK_DATES_JD = Array.from({ length: 407 }, (_, index) => 2433282.5 + index * 135);
/** The planet's east longitude on a moon's IAU body-fixed frame, from the moon's mean place, at a TDB date. */
function subPlanetLongitudeDeg(body: BodyRecord, jd: number): number {
const own = positionAtEpoch(meanElementsAt(body.orbit, body.rates, jd));
const place = body.laplacePole ? laplacePlaneToEquatorial(own, body.laplacePole) : eclipticToEquatorial(own);
const { poleRaDeg, poleDecDeg, primeMeridianDeg } = orientationAt(body.rotationalElements!, jd);
const pole = { raDeg: poleRaDeg, decDeg: poleDecDeg };
const w = primeMeridianDeg * DEG_TO_RAD;
const meridian = laplacePlaneToEquatorial({ x: Math.cos(w), y: Math.sin(w), z: 0 }, pole);
const east = laplacePlaneToEquatorial({ x: -Math.sin(w), y: Math.cos(w), z: 0 }, pole);
const along = (axis: { x: number; y: number; z: number }) => -(place.x * axis.x + place.y * axis.y + place.z * axis.z);
return Math.atan2(along(east), along(meridian)) / DEG_TO_RAD;
}
const SUB_PLANET_CEILINGS_DEG: Record<string, number> = { moon: 8, mimas: 9.5, iapetus: 16.5 };
/** The clock's window, AD 1 to 3000 (`CLOCK_WINDOW` in `time.store.ts`), as Julian dates. */
const CLOCK_START_JD = Date.parse('0001-01-01T00:00Z') / 86400000 + 2440587.5;
const CLOCK_END_JD = Date.parse('3000-01-01T00:00Z') / 86400000 + 2440587.5;
const LOCK_DATES_JD = Array.from({ length: Math.floor((CLOCK_END_JD - CLOCK_START_JD) / 135) + 1 }, (_, index) => CLOCK_START_JD + index * 135);
function angleBetweenDeg(a: { x: number; y: number; z: number }, b: { x: number; y: number; z: number }): number {
const cosine = (a.x * b.x + a.y * b.y + a.z * b.z) / (Math.hypot(a.x, a.y, a.z) * Math.hypot(b.x, b.y, b.z));
@@ -368,10 +361,10 @@ function validateBodies(bodies: BodyRecord[], horizonsOrbits: Map<string, Orbita
// have to agree, or its face turns away from its planet.
assertCondition(rotation !== undefined, `Moon ${body.id} is locked but has no W to keep its face to its planet by.`);
const ceiling = SUB_PLANET_CEILINGS_DEG[body.id] ?? MAX_SUB_PLANET_LONGITUDE_DEG;
const worst = Math.max(...LOCK_DATES_JD.map((jd) => Math.abs(subPlanetLongitudeDeg(body, jd))));
const worst = Math.max(...LOCK_DATES_JD.map((jd) => Math.abs(subPlanetLongitudeDeg(body, rotation!, jd))));
assertCondition(
worst <= ceiling,
`Moon ${body.id} turns its face up to ${worst.toFixed(2)} degrees from its planet between 1950 and 2100 (at most ${ceiling} expected) — its orbit and its W disagree.`
`Moon ${body.id} turns its face up to ${worst.toFixed(2)} degrees from its planet between AD 1 and 3000 (at most ${ceiling} expected) — its orbit and its W disagree.`
);
spins.push(`${body.id} faces ${worst.toFixed(2)}`);
}