SenrokaiandClaude Opus 5.5
7b65ab4812
Standish's "Pluto" is the Pluto-Charon barycentre, and Charon is an eighth of Pluto's mass, so that point lies 2 131 km from Pluto's centre, 943 km above its surface. Drawn the usual way, with Pluto at its row's position and Charon going round it, Pluto sits where nothing is and Charon's orbit is 2 131 km too wide on one side. A moon record can now carry massRatio, its mass over its planet's. For such a moon the renderer keeps the pivot at the planet's elements, which is the barycentre, and each tick puts the planet massRatio / (1 + massRatio) of the relative separation back from it and the moon the rest out. Both orbits are the relative ellipse scaled, the moon's by 1 / (1 + q) and the planet's by -q / (1 + q), turned with the moon's node every tick: Charon's spans 17 460 km of radius and Pluto's 2 131, round the same point, and neither passes through Pluto. Only Charon will carry it; every other moon's barycentre is inside its planet. Checked against Horizons in the unit suite, on JPL's records for the two: Pluto (999) from the Pluto-system barycentre (9) in 2100 is 2 131.24 km out, and the renderer puts it within 5 km of that length and 0.5 degrees of that direction, exactly opposite Charon at the inverse of their mass ratio; Charon from Pluto is within 0.5 degrees of Horizons in 2100 (measured 0.37). The same table adds Titania, against Uranus's equator 120 years from its 1980 epoch, within 0.75 (measured 0.62). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
90 lines
3.8 KiB
TypeScript
90 lines
3.8 KiB
TypeScript
/**
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* Keplerian orbital elements at a reference epoch. Positions are derived client-side by
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* propagating these elements forward/backward from `epochJd` (see `shared/astro/kepler.ts`),
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* rather than fetching per-frame positions.
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*/
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export interface OrbitalElements {
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semiMajorAxisAu: number;
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eccentricity: number;
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inclinationDeg: number;
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longitudeOfAscendingNodeDeg: number;
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argumentOfPeriapsisDeg: number;
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meanAnomalyAtEpochDeg: number;
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epochJd: number;
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}
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/**
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* How a body's mean elements move away from their epoch, per day.
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*
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* Mean elements rather than one osculating set, because the map's clock runs decades in minutes.
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* An osculating orbit is exact at its instant and drifts from then on: fed to Kepler with a mass
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* ratio, the Moon's went round in 27.70 days instead of 27.32 and was 66 degrees out after a year.
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* A mean set carries its own measured motion, and the slow turning of its node and periapsis, so
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* it holds for as long as its source was fit over.
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*/
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export interface MeanElementRates {
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/**
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* How fast the body goes round in space, in degrees per day: the rate of its mean longitude.
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* 360 over this is its sidereal period.
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*/
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meanMotionDegPerDay: number;
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longitudeOfAscendingNodeDegPerDay: number;
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argumentOfPeriapsisDegPerDay: number;
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semiMajorAxisAuPerDay?: number;
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eccentricityPerDay?: number;
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inclinationDegPerDay?: number;
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/**
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* Standish's extra terms in the mean anomaly of Jupiter and beyond, `b T² + c cos(f T) +
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* s sin(f T)` degrees, with T in Julian centuries from the epoch and f in degrees per century:
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* the great-inequality wobble his 3000 BC to AD 3000 fit needs on top of its linear rates.
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*/
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meanAnomalyTerms?: { b: number; c: number; s: number; f: number };
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}
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/**
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* A solar-system planet, moon, or dwarf planet: JPL mean orbital elements, and JPL Horizons
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* physical data. `systemStarId` links back to the HYG star index (the Sun, see `SUN_STAR_ID`).
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*/
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export interface BodyRecord {
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id: string;
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systemStarId: number;
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name: string;
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kind: 'planet' | 'moon' | 'dwarf';
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radiusKm: number;
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/** Mean elements at `orbit.epochJd`, moving at `rates`. */
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orbit: OrbitalElements;
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rates: MeanElementRates;
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/**
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* The pole of the plane a moon's elements are measured against, where that is its local
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* Laplace plane or, for Uranus's and Pluto's moons, the planet's equator: right ascension and
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* declination in the ICRF. The node is then counted from where that plane crosses the ICRF
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* equator. Absent means the J2000 ecliptic, as for the planets and the Moon.
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*/
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laplacePole?: { raDeg: number; decDeg: number };
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/** Where the elements come from and the span they hold over, as the card prints it. */
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orbitSource: string;
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/**
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* For `kind: 'moon'`, the `id` of the planet it orbits — its `orbit` is expressed
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* relative to that planet, not heliocentrically. Undefined for planets/dwarfs.
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*/
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parentBodyId?: string;
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/**
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* For a moon heavy enough that it and its planet go round a point outside the planet — Charon,
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* an eighth of Pluto's mass, puts it 2 100 km from Pluto's centre, 900 km above its surface —
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* the moon's mass over the planet's, from the GMs on their Horizons pages. The planet's own
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* elements then place that barycentre, as Standish's "Pluto" does, and both bodies are drawn
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* going round it. Absent for every other moon.
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*/
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massRatio?: number;
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/**
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* How the body turns on its own axis: the sidereal rotation period in hours, negative where
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* Horizons gives a negative rate (Venus, Uranus), and the tilt of that axis from its orbital
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* plane — which past 90 degrees already says the turn is retrograde.
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*
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* Absent where Horizons publishes neither — the view then leaves the body still rather than
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* spinning it at an invented rate.
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*/
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rotationPeriodHours?: number;
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obliquityDeg?: number;
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}
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