Turn Earth by the Earth Rotation Angle, so its lit face stays Horizons' at AD 1 as it is today

Earth was turned by its IAU W, taken at the clock's UT plus today's 69.184 s. That W is a straight
line fitted to the present: 360.9856235 degrees a day, which, once its pole's -0.641 degrees a
century in right ascension is counted, runs 6.3e-6 degrees a day slow of Earth's real turning. The
followsUt comment said the clock's date "already says how far it has turned"; it did not. Against
Horizons (observer quantity 14 from the Sun, TIME_TYPE=UT, Earth one light-time back) the drawn
sub-solar point was 2.3 degrees off at AD 1000 and 4.5 at AD 1.

Earth is now turned by the IERS Earth Rotation Angle (IERS Conventions 2010, eq. 5.15) at the
clock's date, counted from the node the IAU's W starts at, 90 degrees past the pole's right
ascension. The pole is unchanged. Drawn minus Horizons, in degrees:

  date                       before    after
  2025-06-01 12:00 (unit)     +0.06   -0.003
  AD 1000, JD 2086455 (unit)  -2.3    -0.001
  AD 1, JD 1721600 (unit)     -4.5    +0.051
  live app, :4301, same probe as the review's
    JD 2460900.25             +0.089   +0.005
    JD 2086300.5              -2.281   +0.010
    JD 1800000                -4.049   +0.056
    JD 1721450.75             -4.530   +0.072

At noon UTC on 1 June 2025 the Sun now stands over 0.52 W on the drawn sphere, where the equation
of time puts it at 0.53 W (0.43 W before).

TT_MINUS_UTC_DAYS had no other use and is removed; its comment also counted 37 leap seconds where
UTC has taken 27 on top of the 10 s it started from in 1972.

Tests: body-orientation.spec 'lights Earth's face where Horizons does at the far end of the clock
too: AD 1000 and AD 1' (within 0.15 degrees), and the renderer's AD 1000 Earth test now checks the
drawn face against Horizons instead of against the IAU W the old code used. Control: turning Earth
by its IAU W at UT + 69.184 s again fails both named tests (2 failed, 834 passed). The README says
which model turns Earth.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

README.md

@@ -55,7 +55,8 @@ in it is measured and what is not.
 **System view** — selecting a star flies the camera continuously into its system rather than
 cutting to a new scene. The Sun gets the real solar-system bodies, moving on JPL's mean orbital
 elements — Standish's for the planets, JPL SSD's satellite table for the moons, the Small-Body
-Database for Ceres, Eris, Haumea and Makemake — and turned by the IAU's rotational elements; other
+Database for Ceres, Eris, Haumea and Makemake — and turned by the IAU's rotational elements, Earth
+by the IERS Earth Rotation Angle; other
 stars get their confirmed exoplanets. Orbits are drawn as ellipses and bodies are propagated
 along them by a Kepler solver to the date on the map's clock. Under them, a dashed grid marks out
 round distances in AU — 5 AU rings for the solar system, 0.01 AU rings for TRAPPIST-1 — with a
@@ -329,7 +330,7 @@ plugin's own files are kept so it can be listed from a marketplace of its own la
 ## Data credits
 
 Star catalogue: [HYG database](https://github.com/astronexus/HYG-Database) (Hipparcos, Yale
-Bright Star, Gliese) — 68 388 stars within 250 pc. Solar-system orbits: JPL approximate planetary mean elements (Standish), JPL SSD satellite mean elements and the JPL Small-Body Database; rotation: the IAU WGCCRE 2015 report via NAIF's pck00011; physical data, and the positions the orbits are checked against: NASA/JPL Horizons. Exoplanets: NASA Exoplanet
+Bright Star, Gliese) — 68 388 stars within 250 pc. Solar-system orbits: JPL approximate planetary mean elements (Standish), JPL SSD satellite mean elements and the JPL Small-Body Database; rotation: the IAU WGCCRE 2015 report via NAIF's pck00011, and for Earth the IERS Conventions 2010; physical data, and the positions the orbits are checked against: NASA/JPL Horizons. Exoplanets: NASA Exoplanet
 Archive. Deep-sky objects: [OpenNGC](https://github.com/mattiaverga/OpenNGC). Body and skybox
 imagery: NASA/JPL/USGS public domain and Solar System Scope (CC BY 4.0) — per-file provenance
 is recorded in `src/assets/textures/README.md`.

src/app/features/galaxy-system/system-orbits-renderer.spec.ts

@@ -1,7 +1,7 @@
 import * as THREE from 'three/webgpu';
 import { describe, expect, it, vi } from 'vitest';
 
-import { DEFAULT_EPOCH_JD, GM_SUN_AU3_PER_DAY2, TT_MINUS_UTC_DAYS, ttMinusUtSeconds } from '../../shared/astro/constants';
+import { DEFAULT_EPOCH_JD, GM_SUN_AU3_PER_DAY2, ttMinusUtSeconds } from '../../shared/astro/constants';
 import { keplerRates } from '../../shared/astro/kepler';
 import { eclipticToEquatorial, laplacePlaneToEquatorial, OBLIQUITY_J2000_DEG } from '../../shared/astro/coordinates';
 import { orientationAt } from '../../shared/astro/rotational-elements';
@@ -734,15 +734,17 @@ describe('solar-system bodies against Horizons', () => {
     expect((drawnPrimeMeridian('jupiter').angleTo(iauPrimeMeridian('jupiter', jdUt + 1574.1 / 86400)) * 180) / Math.PI).toBeLessThan(0.01);
   });
 
-  it('turns Earth by the UT the clock names, which is its turning: at AD 1000 its W is not moved on by ΔT', () => {
+  it('turns Earth by the UT the clock names, which is its turning: at AD 1000 the Sun stands over Horizons’ point', () => {
-    const jdUt = 2086307.5;
+    // Horizons' sub-solar longitude from the Sun (observer quantity 14, TIME_TYPE=UT) on JD 2086455,
-    renderer.update(jdUt);
+    // 1.0510 E, is Earth as it was 8.454 minutes before. Turned by the IAU's W at UT the drawn face
-    expect((drawnPrimeMeridian('earth').angleTo(iauPrimeMeridian('earth', jdUt + TT_MINUS_UTC_DAYS)) * 180) / Math.PI).toBeLessThan(0.01);
+    // was 2.3 degrees off; taken at TDB, 6.6.
+    renderer.update(2086455 - 8.45437443 / 1440);
+    expect(apart(facing('earth', new THREE.Vector3()).eastDeg, 1.05101)).toBeLessThan(0.15);
   });
 
   it('lights Earth where the Sun really stands: within 4 degrees of Greenwich at noon UTC', () => {
     // The equation of time is all that separates them: on 1 June 2025 it puts the Sun over 0.53 W,
-    // and the drawn sphere has it over 0.43 W.
+    // and the drawn sphere has it over 0.52 W.
     renderer.update(JUNE_1_2025_NOON_UTC);
     expect(Math.abs(facing('earth', new THREE.Vector3()).eastDeg)).toBeLessThan(4);
   });

src/app/shared/astro/constants.ts

@@ -19,13 +19,6 @@ export const DEFAULT_EPOCH_JD = 2451545.0;
  */
 export const GM_SUN_AU3_PER_DAY2 = 0.01720209895 * 0.01720209895;
 
-/**
- * TT - UTC today, in days: 32.184 s plus the 37 leap seconds UTC has taken since 1972, the last at
- * the end of 2016. TDB, which ephemerides run on, stays within 2 ms of TT. See {@link ttMinusUtSeconds}
- * for other dates.
- */
-export const TT_MINUS_UTC_DAYS = 69.184 / 86400;
-
 /** The first day of each month UTC took a leap second at the start of, from its 10 s of 1972. */
 const LEAP_SECONDS_FROM = [
   [1972, 7], [1973, 1], [1974, 1], [1975, 1], [1976, 1], [1977, 1], [1978, 1], [1979, 1], [1980, 1], [1981, 7],

src/app/shared/rendering/body-orientation.spec.ts

@@ -47,6 +47,15 @@ describe('bodyPageView', () => {
     expect(Math.abs(geodetic - 22.260426)).toBeLessThan(0.05);
   });
 
+  it('lights Earth’s face where Horizons does at the far end of the clock too: AD 1000 and AD 1', () => {
+    // Horizons' sub-solar longitude from the Sun (observer quantity 14, TIME_TYPE=UT), Earth taken
+    // one light-time back: 1.0510 E on JD 2086455 and 1.5606 E on JD 1721600. The IAU's W, taken at
+    // UT, drew them 2.3 and 4.5 degrees west of that.
+    for (const [jdUt, lightMinutes, eastDeg] of [[2086455, 8.45437443, 1.05101], [1721600, 8.45020842, 1.560644]]) {
+      expect(Math.abs(subSolarPoint(EARTH, jdUt - lightMinutes / 1440).eastDeg - eastDeg)).toBeLessThan(0.15);
+    }
+  });
+
   it('takes a moon’s Sun from where it and its planet are: the Moon’s sub-solar point is Horizons’', () => {
     const moon = subSolarPoint(MOON, JUNE_1_2025_NOON_UTC);
     // 116.2859 E and 1.5030 N, seen from Earth's centre.

src/app/shared/rendering/body-orientation.ts

@@ -1,6 +1,6 @@
 import * as THREE from 'three/webgpu';
 
-import { tdbFromUtc, TT_MINUS_UTC_DAYS } from '../astro/constants';
+import { tdbFromUtc } from '../astro/constants';
 import { CartesianCoordinates, eclipticToEquatorial, laplacePlaneToEquatorial } from '../astro/coordinates';
 import { meanElementsAt, positionAtEpoch } from '../astro/kepler';
 import { orientationAt } from '../astro/rotational-elements';
@@ -54,14 +54,18 @@ export function poleFrame(pole: { raDeg: number; decDeg: number }, target = new
  *
  * The clock is UT and the IAU's elements run on TDB, 69.184 s ahead today and 1 574 s at AD 1000;
  * in 69 s Earth turns 0.29 degrees, Jupiter 0.70 and Phobos 0.90, so the date is taken to TDB here
- * (see `tdbFromUtc`). Earth, `followsUt`, is the one exception: its turning is what UT counts,
+ * (see `tdbFromUtc`). Earth, `followsUt`, is the one exception: its turning is what UT counts, so
- * so the clock's date already says how far it has turned, and its W, fitted to today, is taken at
+ * it is turned by the IERS Earth Rotation Angle at the clock's date (IERS Conventions 2010, eq.
- * that date plus today's TT - UTC. Taken at TDB, it would turn ΔT further: 44 degrees at AD 1.
+ * 5.15), counted from the node its W starts at, 90 degrees past its pole's right ascension. The
+ * IAU's W for Earth, fitted to today, runs 6.3e-6 degrees a day slow of that once its pole's drift
+ * is counted: taken at UT, it left Earth's lit face 2.3 degrees off Horizons at AD 1000 and 4.5 at
+ * AD 1. Taken at TDB, it would have turned ΔT further, 44 degrees at AD 1.
  */
 export function bodyOrientation(elements: RotationalElements, jdUtc: number, target = new THREE.Quaternion(), followsUt = false): THREE.Quaternion {
-  const { poleRaDeg, poleDecDeg, primeMeridianDeg } = orientationAt(elements, followsUt ? jdUtc + TT_MINUS_UTC_DAYS : tdbFromUtc(jdUtc));
+  const { poleRaDeg, poleDecDeg, primeMeridianDeg } = orientationAt(elements, tdbFromUtc(jdUtc));
+  const turnDeg = followsUt ? 360 * (0.779057273264 + 1.00273781191135448 * (jdUtc - 2451545)) - 90 - poleRaDeg : primeMeridianDeg;
   return poleFrame({ raDeg: poleRaDeg, decDeg: poleDecDeg }, target)
-    .multiply(scratchTurn.setFromAxisAngle(Z_AXIS, primeMeridianDeg * DEG_TO_RAD))
+    .multiply(scratchTurn.setFromAxisAngle(Z_AXIS, turnDeg * DEG_TO_RAD))
     .multiply(MAP_TO_BODY);
 }