Draw a planet and a heavy moon going round their barycentre, as Pluto and Charon do

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>

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

@@ -56,9 +56,9 @@ export interface BodyRecord {
   rates: MeanElementRates;
   /**
    * The pole of the plane a moon's elements are measured against, where that is its local
-   * Laplace plane: right ascension and declination in the ICRF. The node is then counted from
-   * where that plane crosses the ICRF equator. Absent means the J2000 ecliptic, as for the
-   * planets and the Moon.
+   * Laplace plane or, for Uranus's and Pluto's moons, the planet's equator: right ascension and
+   * declination in the ICRF. The node is then counted from where that plane crosses the ICRF
+   * equator. Absent means the J2000 ecliptic, as for the planets and the Moon.
    */
   laplacePole?: { raDeg: number; decDeg: number };
   /** Where the elements come from and the span they hold over, as the card prints it. */
@@ -68,6 +68,14 @@ export interface BodyRecord {
    * relative to that planet, not heliocentrically. Undefined for planets/dwarfs.
    */
   parentBodyId?: string;
+  /**
+   * For a moon heavy enough that it and its planet go round a point outside the planet — Charon,
+   * an eighth of Pluto's mass, puts it 2 100 km from Pluto's centre, 900 km above its surface —
+   * the moon's mass over the planet's, from the GMs on their Horizons pages. The planet's own
+   * elements then place that barycentre, as Standish's "Pluto" does, and both bodies are drawn
+   * going round it. Absent for every other moon.
+   */
+  massRatio?: number;
   /**
    * How the body turns on its own axis: the sidereal rotation period in hours, negative where
    * Horizons gives a negative rate (Venus, Uranus), and the tilt of that axis from its orbital