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/features/galaxy-system/system-orbits-renderer.ts

@@ -294,6 +294,11 @@ interface TrackedMoon {
   parentId: string;
   rotationPeriodHours?: number;
   obliquityDeg?: number;
+  /**
+   * Where the moon and its planet go round a barycentre outside the planet (Charon): the moon's
+   * mass over the planet's, and the planet's own small orbit round that point.
+   */
+  barycentre?: { massRatio: number; parentOrbitLine: THREE.Line };
 }
 
 /**
@@ -378,7 +383,7 @@ export class SystemOrbitsRenderer {
       if (!parentTracked) {
         continue; // orphaned moon reference; skip rather than crash.
       }
-      const moon = this.addMoon(body.id, body.orbit, body.rates, body.radiusKm, parentTracked, moonFrame(body), appearanceForBody(body, bodies, hostLuminositySolar), { periodHours: body.rotationPeriodHours, obliquityDeg: body.obliquityDeg });
+      const moon = this.addMoon(body.id, body.orbit, body.rates, body.radiusKm, parentTracked, moonFrame(body), appearanceForBody(body, bodies, hostLuminositySolar), { periodHours: body.rotationPeriodHours, obliquityDeg: body.obliquityDeg }, body.massRatio);
       members.push({ id: body.id, kind: 'moon', marker: moon.marker, parentId: parent.id });
     }
 
@@ -466,6 +471,14 @@ export class SystemOrbitsRenderer {
       const orbital = positionAtEpoch(current);
       moon.marker.position.set(orbital.x, orbital.y, orbital.z).applyQuaternion(moon.frame);
       orientOrbit(moon.orbitLine.quaternion, current, moon.frame);
+      if (moon.barycentre) {
+        // The planet's elements place the pair's barycentre, which is where the pivot is: the
+        // planet sits the moon's share of their separation back from it, the moon the rest out.
+        const { massRatio, parentOrbitLine } = moon.barycentre;
+        parent.marker.position.copy(parent.position).addScaledVector(moon.marker.position, -massRatio / (1 + massRatio));
+        moon.marker.position.multiplyScalar(1 / (1 + massRatio));
+        parentOrbitLine.quaternion.copy(moon.orbitLine.quaternion);
+      }
       if (moon.rotationPeriodHours) {
         moon.marker.quaternion.copy(spinFor(current, moon.frame, moon.rotationPeriodHours, moon.obliquityDeg, epochJd - moon.elements.epochJd));
       }
@@ -545,7 +558,8 @@ export class SystemOrbitsRenderer {
     parent: TrackedTopLevelBody,
     frame: THREE.Quaternion,
     appearance?: PlanetAppearance,
-    rotation?: { periodHours?: number; obliquityDeg?: number }
+    rotation?: { periodHours?: number; obliquityDeg?: number },
+    massRatio?: number
   ): TrackedMoon {
     const pivot = new THREE.Group();
     const orbitLine = buildOrbitLine(elements, 'moon', frame);
@@ -555,7 +569,20 @@ export class SystemOrbitsRenderer {
     this.trackDisposable(orbitLine.geometry, orbitLine.material as THREE.Material);
     this.trackDisposable(marker.geometry, marker.material as THREE.Material);
 
-    const moon: TrackedMoon = { id, elements, rates, marker, orbitLine, frame, pivot, parentId: parent.id, rotationPeriodHours: rotation?.periodHours, obliquityDeg: rotation?.obliquityDeg };
+    let barycentre: TrackedMoon['barycentre'];
+    if (massRatio !== undefined) {
+      // Both orbits are the relative one, scaled: the moon's by the planet's share of the mass,
+      // the planet's by the moon's share and turned half round, since it is always opposite.
+      // Charon's then spans 17 460 km of radius, Pluto's 2 131, and neither passes through Pluto.
+      orbitLine.scale.setScalar(1 / (1 + massRatio));
+      const parentOrbitLine = buildOrbitLine(elements, parent.kind, frame);
+      parentOrbitLine.scale.setScalar(-massRatio / (1 + massRatio));
+      pivot.add(parentOrbitLine);
+      this.trackDisposable(parentOrbitLine.geometry, parentOrbitLine.material as THREE.Material);
+      barycentre = { massRatio, parentOrbitLine };
+    }
+
+    const moon: TrackedMoon = { id, elements, rates, marker, orbitLine, frame, pivot, parentId: parent.id, rotationPeriodHours: rotation?.periodHours, obliquityDeg: rotation?.obliquityDeg, barycentre };
     this.moons.push(moon);
     return moon;
   }