Derive a surface for every body that was never photographed

Fifteen bodies here have a real photograph. Every exoplanet does not, and
never will on current instruments — none has ever been imaged — and nor do
several of the solar system's own moons. Those all shared one crude
stand-in: a few noisy bands tinted by category, cached per colour, so
every exoplanet in the app was literally the same picture.

They now get a surface reasoned from what has actually been measured.

The chain is standard at every link. A host star's luminosity comes from
its catalogued apparent magnitude and its parallax distance — that pair is
exactly an absolute magnitude — plus a bolometric correction for its
spectral class. The correction is not optional: an M dwarf radiates most
of its light in the infrared, so its visual magnitude understates it more
than tenfold, and M dwarfs are what most nearby planet hosts are.
Luminosity and the semi-major axis then give an equilibrium temperature,
mass and radius give a bulk density, and size, temperature and density
together give a class of world.

Checked against the solar system the temperatures land on Earth 255 K,
Jupiter 112 K, Neptune 46 K, all within a kelvin or two of published
values, and 51 Pegasi b comes out at 1227 K against a published 1200.

Each class carries a palette reasoned from its chemistry — methane absorbs
red light, which is why the ice giants are blue — and a structure: zonal
bands for a body with a fluid envelope, because a rapidly rotating
atmosphere organises into them, and fractal terrain for one with a solid
surface. Polar caps grow and shrink with the derived temperature, which is
the clearest visible consequence of the whole chain.

The generator samples three-dimensional noise along the sphere rather than
a flat field, so there is no seam to stitch at the antimeridian and no
pinching at the poles, and it writes into a byte array rather than a
canvas — a pure function, testable, with no 2D context to be unavailable.

Two things the derivation cannot do, both stated on screen next to the
measurements it rests on. Equilibrium temperature ignores greenhouse
warming and internal heat, so Venus comes out at 300 K against a real
surface of 737 K and Io, kept molten by tides, classifies as ice. And
these are illustrations: reasoned, but not observations.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WaySiNst4HhDXBHnMy8p5G

src/app/shared/astro/body-appearance.spec.ts

@@ -0,0 +1,94 @@
+import { describe, expect, it } from 'vitest';
+
+import { BodyRecord } from '../models/body.model';
+import { ExoplanetRecord } from '../models/exoplanet.model';
+import { appearanceForBody, appearanceForExoplanet, heliocentricDistanceAu } from './body-appearance';
+import { DEFAULT_EPOCH_JD } from './constants';
+
+const ORBIT = { eccentricity: 0, inclinationDeg: 0, longitudeOfAscendingNodeDeg: 0, argumentOfPeriapsisDeg: 0, meanAnomalyAtEpochDeg: 0, epochJd: DEFAULT_EPOCH_JD };
+
+const JUPITER: BodyRecord = { id: 'jupiter', systemStarId: 0, name: 'Jupiter', kind: 'planet', radiusKm: 69911, orbit: { ...ORBIT, semiMajorAxisAu: 5.204 } };
+/** Europa's own orbit is around Jupiter: 671,000 km, which is 0.00449 AU. */
+const EUROPA: BodyRecord = { id: 'europa', systemStarId: 0, name: 'Europa', kind: 'moon', radiusKm: 1560, parentBodyId: 'jupiter', orbit: { ...ORBIT, semiMajorAxisAu: 0.00449 } };
+const EARTH: BodyRecord = { id: 'earth', systemStarId: 0, name: 'Earth', kind: 'planet', radiusKm: 6371, orbit: { ...ORBIT, semiMajorAxisAu: 1 } };
+const ORPHAN: BodyRecord = { ...EUROPA, id: 'orphan', parentBodyId: 'nowhere' };
+
+const BODIES = [JUPITER, EUROPA, EARTH, ORPHAN];
+
+describe('heliocentricDistanceAu', () => {
+  it('uses a planet own orbit', () => {
+    expect(heliocentricDistanceAu(JUPITER, BODIES)).toBeCloseTo(5.204, 6);
+  });
+
+  it('uses a moon parent orbit, not the moon own', () => {
+    // The load-bearing case: Europa's own semi-major axis is 0.0045 AU. Fed to an equilibrium
+    // temperature it would put Europa closer to the Sun than Mercury and boil it.
+    expect(heliocentricDistanceAu(EUROPA, BODIES)).toBeCloseTo(5.204, 6);
+  });
+
+  it('has no answer for a moon whose parent is missing', () => {
+    expect(heliocentricDistanceAu(ORPHAN, BODIES)).toBeUndefined();
+  });
+});
+
+describe('appearanceForBody', () => {
+  it('derives an ice world for a moon of Jupiter, at Jupiter distance', () => {
+    const europa = appearanceForBody(EUROPA, BODIES, 1);
+
+    expect(europa.equilibriumTemperatureK).toBeCloseTo(112, -0.5);
+    expect(europa.planetClass).toBe('icy');
+  });
+
+  it('would have melted that same moon if it used the moon own orbit', () => {
+    // Pinning the bug the parent lookup exists to avoid, so it cannot come back silently.
+    const wrong = appearanceForBody({ ...EUROPA, parentBodyId: undefined }, BODIES, 1);
+    expect(wrong.equilibriumTemperatureK!).toBeGreaterThan(2000);
+    expect(wrong.planetClass).not.toBe('icy');
+  });
+
+  it('derives Earth as temperate with a polar cap', () => {
+    const earth = appearanceForBody(EARTH, BODIES, 1);
+
+    expect(earth.planetClass).toBe('temperate');
+    expect(earth.equilibriumTemperatureK).toBeCloseTo(255, -0.5);
+    expect(earth.polarCapExtentDeg).toBeGreaterThan(0);
+  });
+
+  it('has no density for a solar-system body, since Horizons publishes no masses', () => {
+    expect(appearanceForBody(EARTH, BODIES, 1).bulkDensityGramsPerCm3).toBeNull();
+  });
+
+  it('still classifies a body when the host luminosity is unknown', () => {
+    const earth = appearanceForBody(EARTH, BODIES, null);
+    expect(earth.equilibriumTemperatureK).toBeNull();
+    expect(earth.planetClass).toBe('rocky');
+  });
+});
+
+describe('appearanceForExoplanet', () => {
+  const KEPLER_186F: ExoplanetRecord = { id: 'Kepler-186 f', hostStarId: 1, hostStarName: 'Kepler-186', name: 'Kepler-186 f', radiusEarth: 1.17, orbit: { semiMajorAxisAu: 0.432 } };
+
+  it('derives a temperature from the host star output and the published orbit', () => {
+    // A quarter of a solar luminosity at 0.432 AU: cool, but not frozen.
+    const derived = appearanceForExoplanet(KEPLER_186F, 0.04);
+    expect(derived.equilibriumTemperatureK).toBeGreaterThan(150);
+    expect(derived.equilibriumTemperatureK).toBeLessThan(250);
+  });
+
+  it('derives a density where both a radius and a mass are published', () => {
+    const withMass = appearanceForExoplanet({ ...KEPLER_186F, massEarth: 1.4 }, 0.04);
+    expect(withMass.bulkDensityGramsPerCm3).toBeCloseTo((5.51 * 1.4) / Math.pow(1.17, 3), 4);
+  });
+
+  it('falls back to size alone for a host that never cross-referenced to the catalogue', () => {
+    // 5685 of the 6319 archive records have no matching HYG star. None of them is rendered in a
+    // system, but any of them can still be opened from search.
+    const derived = appearanceForExoplanet({ ...KEPLER_186F, hostStarId: null }, null);
+    expect(derived.equilibriumTemperatureK).toBeNull();
+    expect(derived.planetClass).toBe('rocky');
+  });
+
+  it('is stable per planet, so a world keeps its face between visits', () => {
+    expect(appearanceForExoplanet(KEPLER_186F, 0.04).seed).toBe(appearanceForExoplanet(KEPLER_186F, 0.04).seed);
+  });
+});