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

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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>
This commit is contained in:
Senrokai
2026-09-29 18:37:58 +02:00
co-authored by Claude Opus 5.5
parent db3af1a820
commit f8ee3ac3ab
6 changed files with 238 additions and 43 deletions
Download Patch File Download Diff File Expand all files Collapse all files
tools/etl/fetchSolarSystem.ts
+39 -18
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@@ -5,7 +5,7 @@ import { SUN_STAR_ID } from '../../src/app/shared/models/star.model';
import { fetchHorizonsBody } from './lib/horizons';
import { MeanOrbit, parsePlanetMeanElements, parseSatelliteMeanElements, parseSmallBodyElements } from '../../src/app/shared/astro/mean-elements';
import { fetchPlanetMeanElementsText, fetchSatelliteMeanElementsHtml, fetchSmallBodyAnswer } from './lib/mean-elements';
import { MIN_PERIODIC_TERM_DEG, parsePckRotationalElements } from '../../src/app/shared/astro/rotational-elements';
import { MIN_PERIODIC_TERM_DEG, orbitalTermsOfPrimeMeridian, parsePckRotationalElements } from '../../src/app/shared/astro/rotational-elements';
import { fetchPckText } from './lib/pck';
import { dataPath, ensureDataDir } from './lib/paths';
@@ -42,8 +42,17 @@ interface BodySpec {
nodeOffsetDeg?: number;
epochJd?: number;
periodDays?: number;
/**
* The terms of the IAU's W that are this locked moon's motion along its orbit, which its row has
* no column for: W's quadratic, and the term whose angle turns at `angleRateDegPerCentury`, if
* given. See `orbitalTermsOfPrimeMeridian`.
*/
orbitFromW?: { angleRateDegPerCentury?: number };
}
/** S5 in pck00011.tpc, 316.45 + 506.2 T: the libration of Mimas and Tethys in their 4:2 resonance. */
const MIMAS_TETHYS_LIBRATION = { angleRateDegPerCentury: 506.2 };
/**
* The poles of the equators JPL refers Uranus's and Pluto's moons to, from the IAU WGCCRE 2015
* report, each taken at the end the table's inclinations are measured from (Titania 0.079
@@ -82,15 +91,15 @@ const BODY_SPECS: BodySpec[] = [
{ id: 'haumea', name: 'Haumea', kind: 'dwarf', horizonsCommand: '136108;', center: '500@10', sbdb: 'Haumea', radiusKm: 797.6 },
{ id: 'makemake', name: 'Makemake', kind: 'dwarf', horizonsCommand: '136472;', center: '500@10', sbdb: 'Makemake', radiusKm: 715 },
{ id: 'moon', name: 'Moon', kind: 'moon', horizonsCommand: '301', center: '500@399', parentBodyId: 'earth' },
{ id: 'phobos', name: 'Phobos', kind: 'moon', horizonsCommand: '401', center: '500@499', parentBodyId: 'mars' },
{ id: 'phobos', name: 'Phobos', kind: 'moon', horizonsCommand: '401', center: '500@499', parentBodyId: 'mars', orbitFromW: {} },
{ id: 'deimos', name: 'Deimos', kind: 'moon', horizonsCommand: '402', center: '500@499', parentBodyId: 'mars' },
{ id: 'io', name: 'Io', kind: 'moon', horizonsCommand: '501', center: '500@599', parentBodyId: 'jupiter', apsidesRegress: true },
{ id: 'europa', name: 'Europa', kind: 'moon', horizonsCommand: '502', center: '500@599', parentBodyId: 'jupiter', apsidesRegress: true },
{ id: 'ganymede', name: 'Ganymede', kind: 'moon', horizonsCommand: '503', center: '500@599', parentBodyId: 'jupiter' },
{ id: 'callisto', name: 'Callisto', kind: 'moon', horizonsCommand: '504', center: '500@599', parentBodyId: 'jupiter' },
{ id: 'mimas', name: 'Mimas', kind: 'moon', horizonsCommand: '601', center: '500@699', parentBodyId: 'saturn' },
{ id: 'mimas', name: 'Mimas', kind: 'moon', horizonsCommand: '601', center: '500@699', parentBodyId: 'saturn', orbitFromW: MIMAS_TETHYS_LIBRATION },
{ id: 'enceladus', name: 'Enceladus', kind: 'moon', horizonsCommand: '602', center: '500@699', parentBodyId: 'saturn' },
{ id: 'tethys', name: 'Tethys', kind: 'moon', horizonsCommand: '603', center: '500@699', parentBodyId: 'saturn' },
{ id: 'tethys', name: 'Tethys', kind: 'moon', horizonsCommand: '603', center: '500@699', parentBodyId: 'saturn', orbitFromW: MIMAS_TETHYS_LIBRATION },
{ id: 'dione', name: 'Dione', kind: 'moon', horizonsCommand: '604', center: '500@699', parentBodyId: 'saturn' },
{ id: 'rhea', name: 'Rhea', kind: 'moon', horizonsCommand: '605', center: '500@699', parentBodyId: 'saturn' },
{ id: 'titan', name: 'Titan', kind: 'moon', horizonsCommand: '606', center: '500@699', parentBodyId: 'saturn' },
@@ -148,6 +157,15 @@ export async function fetchSolarSystem(): Promise<{ bodies: BodyRecord[]; horizo
horizonsOrbits.set(spec.id, result.orbit);
gmById.set(spec.id, result.gmKm3PerS2);
// NAIF numbers a small body 2 000 000 past its catalogue number: Ceres, "1;" to Horizons, is 2000001.
const naifId = spec.horizonsCommand.endsWith(';') ? 2_000_000 + Number.parseInt(spec.horizonsCommand, 10) : Number(spec.horizonsCommand);
const rotation = parsePckRotationalElements(pck, naifId);
if (!rotation) {
console.warn(` no IAU rotational elements for ${spec.name}; its pole and meridian are not known.`);
} else if (rotation.skippedDeg.length > 0) {
console.log(` ${spec.name}: ${rotation.skippedDeg.length} periodic terms under ${MIN_PERIODIC_TERM_DEG} degrees left out, the largest ${Math.max(...rotation.skippedDeg)}.`);
}
const parentName = BODY_SPECS.find((candidate) => candidate.id === spec.parentBodyId)?.name;
const smallBody = spec.sbdb ? parseSmallBodyElements(await fetchSmallBodyAnswer(spec.sbdb, `sbdb-${spec.id}.json`)) : undefined;
const read: MeanOrbit =
@@ -155,7 +173,7 @@ export async function fetchSolarSystem(): Promise<{ bodies: BodyRecord[]; horizo
(parentName
? parseSatelliteMeanElements(satelliteElements, parentName, spec.name, spec.apsidesRegress ?? false, spec.equatorPole)
: parsePlanetMeanElements(planetElements, spec.id));
const mean: MeanOrbit = {
const corrected: MeanOrbit = {
...read,
orbit: {
...read.orbit,
@@ -164,17 +182,28 @@ export async function fetchSolarSystem(): Promise<{ bodies: BodyRecord[]; horizo
},
rates: spec.periodDays ? { ...read.rates, meanMotionDegPerDay: 360 / spec.periodDays } : read.rates
};
if (spec.orbitFromW && !rotation) {
throw new Error(`${spec.name}'s orbit takes terms from a W the kernel does not give.`);
}
const fromW = spec.orbitFromW && orbitalTermsOfPrimeMeridian(rotation!.elements, corrected.orbit.epochJd, spec.orbitFromW.angleRateDegPerCentury);
const mean: MeanOrbit = fromW
? {
...corrected,
orbit: { ...corrected.orbit, meanAnomalyAtEpochDeg: corrected.orbit.meanAnomalyAtEpochDeg + fromW.meanAnomalyDeg },
rates: { ...corrected.rates, meanMotionDegPerDay: corrected.rates.meanMotionDegPerDay + fromW.meanMotionDegPerDay, meanAnomalyTerms: fromW.meanAnomalyTerms }
}
: corrected;
const radiusKm = smallBody?.radiusKm ?? spec.radiusKm ?? result.radiusKm;
if (radiusKm === undefined) {
console.warn(` no physical radius found for ${spec.name}; defaulting to 0.`);
}
// 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, which keeps one
// face towards the parent however long the clock runs. Not every page says so — the Moon's
// gives a rate, Titan's and Proteus's nothing. The Kepler period of the osculating orbit this
// used to take, 27.70 days for the Moon, would now turn its face five degrees an orbit away
// from the orbit it is drawn on.
// 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)
? (360 / mean.rates.meanMotionDegPerDay) * HOURS_PER_DAY
: smallBody
@@ -187,14 +216,6 @@ export async function fetchSolarSystem(): Promise<{ bodies: BodyRecord[]; horizo
if (rotationPeriodHours === undefined) {
console.warn(` no rotation period found for ${spec.name}; it will not turn.`);
}
// NAIF numbers a small body 2 000 000 past its catalogue number: Ceres, "1;" to Horizons, is 2000001.
const naifId = spec.horizonsCommand.endsWith(';') ? 2_000_000 + Number.parseInt(spec.horizonsCommand, 10) : Number(spec.horizonsCommand);
const rotation = parsePckRotationalElements(pck, naifId);
if (!rotation) {
console.warn(` no IAU rotational elements for ${spec.name}; its pole and meridian are not known.`);
} else if (rotation.skippedDeg.length > 0) {
console.log(` ${spec.name}: ${rotation.skippedDeg.length} periodic terms under ${MIN_PERIODIC_TERM_DEG} degrees left out, the largest ${Math.max(...rotation.skippedDeg)}.`);
}
bodies.push({
id: spec.id,