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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
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tools/etl/fetchSolarSystem.ts
+10 -6
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@@ -9,6 +9,7 @@ import { MeanOrbit, parsePlanetMeanElements, parseSatelliteMeanElements, parseSm
import { fetchPlanetMeanElementsText, fetchSatelliteMeanElementsHtml, fetchSmallBodyAnswer } from './lib/mean-elements';
import { MIN_PERIODIC_TERM_DEG, orbitalTermsOfPrimeMeridian, parsePckRotationalElements, SUN_ROTATIONAL_ELEMENTS } from '../../src/app/shared/astro/rotational-elements';
import { fetchPckText } from './lib/pck';
import { lockedToOrbit } from './lib/locked-spin';
import { dataPath, ensureDataDir } from './lib/paths';
const HOURS_PER_DAY = 24;
@@ -54,6 +55,8 @@ interface BodySpec {
* given. See `orbitalTermsOfPrimeMeridian`.
*/
orbitFromW?: { angleRateDegPerCentury?: number };
/** A locked moon whose pole is carried round with its orbit's, as Iapetus's; see `lockedToOrbit`. */
poleFollowsOrbit?: boolean;
/**
* Days between the Horizons positions the orbit is checked against from 1950 to 2100; 2 unless
* the error changes faster than that. Nereid, at an eccentricity of 0.75, sweeps through its
@@ -131,7 +134,7 @@ const BODY_SPECS: BodySpec[] = [
// Hyperion tumbles ("Rotational period = Chaotic") and Phoebe, captured, turns in 9.27 hours.
// Hyperion's eccentricity is 0.105 in JPL's current table (ssd.jpl.nasa.gov/sats/elem, SAT441).
{ id: 'hyperion', name: 'Hyperion', kind: 'moon', horizonsCommand: '607', center: '500@699', parentBodyId: 'saturn', spinsFreely: true, measuredEccentricity: 0.105, trackStepDays: 1 },
{ id: 'iapetus', name: 'Iapetus', kind: 'moon', horizonsCommand: '608', center: '500@699', parentBodyId: 'saturn' },
{ id: 'iapetus', name: 'Iapetus', kind: 'moon', horizonsCommand: '608', center: '500@699', parentBodyId: 'saturn', poleFollowsOrbit: true },
// Phoebe's row gives a mean motion of 0.6569114 degrees a day, a 548.02-day year, where its
// Horizons page and JPL's current table (SAT441) give 550.30: the table's own note warns that
// its source misstated the mean motions of retrograde moons. On the row's figure Phoebe was
@@ -245,10 +248,11 @@ export async function fetchSolarSystem(): Promise<{ bodies: BodyRecord[]; horizo
// A moon listed here is tidally locked unless its spec says otherwise, so its day is its
// orbit: the sidereal period from the same mean motion that carries it round. Not every page
// says so — the Moon's gives a rate, Titan's and Proteus's nothing. Every locked moon here is
// turned by its IAU W rather than by this day, and `build.ts` checks that W and the orbit keep
// its face to its planet from 1950 to 2100; this day is what the renderer would turn a moon
// without W by.
const rotationPeriodHours = result.tidallyLocked || (spec.kind === 'moon' && !spec.spinsFreely)
// turned by its IAU W, at this same rate (see `lockedToOrbit`), and `build.ts` checks that W and
// the orbit keep its face to its planet from AD 1 to 3000; this day is what the renderer would
// turn a moon without W by.
const locked = spec.kind === 'moon' && !spec.spinsFreely;
const rotationPeriodHours = result.tidallyLocked || locked
? (360 / mean.rates.meanMotionDegPerDay) * HOURS_PER_DAY
: (spec.rotationPeriodHours ?? (smallBody ? smallBody.rotationPeriodHours : result.rotationPeriodHours));
const parentGm = spec.barycentric && spec.parentBodyId ? gmById.get(spec.parentBodyId) : undefined;
@@ -274,7 +278,7 @@ export async function fetchSolarSystem(): Promise<{ bodies: BodyRecord[]; horizo
...(parentGm !== undefined ? { massRatio: result.gmKm3PerS2! / parentGm } : {}),
...(rotationPeriodHours !== undefined ? { rotationPeriodHours } : {}),
...((result.obliquityDeg ?? spec.obliquityDeg) !== undefined ? { obliquityDeg: result.obliquityDeg ?? spec.obliquityDeg } : {}),
...(rotation ? { rotationalElements: rotation.elements } : {})
...(rotation ? { rotationalElements: locked ? lockedToOrbit(rotation.elements, mean, spec.name, spec.poleFollowsOrbit) : rotation.elements } : {})
});
}