Take TT - UT from the historical record before 1972, so the far dates the clock reaches turn every body by the right amount

The clock reaches AD 1, but TT - UT was held at today's 69.184 s. At AD 1000 it was 1 574 s and at
AD 1 about 10 570 (Espenak and Meeus, NASA's Five Millennium Canon; Horizons' TDB - UT gives 1 658
and 10 466 on JD 2086455 and 1721600). So every spin but Earth's was (ΔT - 69 s) times its rate
out, Jupiter 15.2 degrees at AD 1000 and 106 at AD 1, Mars 6 and 43, and every orbit that much
behind: the Moon about 0.2 and 1.4 degrees.

ttMinusUtSeconds gives TT - UT for a date on the clock: the Espenak-Meeus polynomials before 1972,
32.184 s plus UTC's leap seconds from 1972 to the last one, at the start of 2017, and 69.184 s
held after it, as Horizons holds it. Its pieces join within 0.1 s. tdbFromUtc, which positions
and spins already share, now adds it. Within 0.2 s of Horizons in 1950, 105 s at AD 1 and 86 s
at AD 1000, where the historical record itself is that uncertain.

Earth is the exception: its turning is what UT counts, so the clock's date already says how far it
has turned, and ΔT would turn it again, 44 degrees at AD 1. Its W, fitted to today, keeps today's
69.184 s (bodyOrientation's followsUt, set for Earth in the system view and on its page).

In the running app at 1000-01-01 00:00 UT, Jupiter's drawn prime meridian sits 0.000 degrees from
its IAU W at TT and 15.164 from where the held offset put it; Earth's sits on its W at UT + 69.184 s,
6.288 degrees short of what TT would have turned it to.

The renderer spec now hands its frozen Horizons vectors over as the UT dates that name them
through the same TT - UT, and checks Jupiter's and Earth's prime meridians at AD 1000.

Controls: the leap-second rule used before 1972 fails "follows the historical record before 1972";
TT - UT held at 69 s fails "turns Jupiter at AD 1000 by its W"; Earth turned at TDB, or the renderer
or the page not keeping it on UT, fails the Earth tests.

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

src/app/shared/astro/constants.ts

@@ -20,22 +20,86 @@ export const DEFAULT_EPOCH_JD = 2451545.0;
 export const GM_SUN_AU3_PER_DAY2 = 0.01720209895 * 0.01720209895;
 
 /**
- * TT - UTC, 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. Held constant, as Horizons
- * holds it for dates past the last announced leap second; before 2017 it was smaller, about 29 s
- * in 1950.
+ * 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],
+  [1982, 7], [1983, 7], [1985, 7], [1988, 1], [1990, 1], [1991, 1], [1992, 7], [1993, 7], [1994, 7], [1996, 1],
+  [1997, 7], [1999, 1], [2006, 1], [2009, 1], [2012, 7], [2015, 7], [2017, 1]
+].map(([year, month]) => Date.UTC(year, month - 1, 1) / 86400000 + 2440587.5);
+const JD_1972 = Date.UTC(1972, 0, 1) / 86400000 + 2440587.5;
+
+/**
+ * TT - UT, in seconds, at a date on the map's clock: how far Earth's turning, which UT counts,
+ * has fallen behind the uniform time the ephemerides run on.
+ *
+ * From 1972 the clock is UTC, held to within 0.9 s of UT by leap seconds, and TT - UTC is exact:
+ * 32.184 s plus the 10 to 37 of them. After the last, at the start of 2017, it is held at 69.184 s,
+ * as Horizons holds it: no one knows the leap seconds to come. Before 1972 it is ΔT from the
+ * Espenak-Meeus polynomials (NASA's Five Millennium Canon, 2006), which fit the historical record
+ * of eclipses and occultations: 10 570 s at AD 1, 1 574 at AD 1000, 29 in 1950. Held at 69 s there,
+ * as it was, every spin but Earth's was a turn of (ΔT - 69 s) times its rate out, 15 degrees for
+ * Jupiter at AD 1000 and 106 at AD 1, and the Moon 0.22 and 1.43 degrees along its orbit.
+ */
+export function ttMinusUtSeconds(jdUt: number): number {
+  if (jdUt >= JD_1972) {
+    return 32.184 + 10 + LEAP_SECONDS_FROM.filter((from) => jdUt >= from).length;
+  }
+  const y = 2000 + (jdUt - 2451544.5) / 365.2425;
+  if (y < 500) {
+    const u = y / 100;
+    return 10583.6 - 1014.41 * u + 33.78311 * u ** 2 - 5.952053 * u ** 3 - 0.1798452 * u ** 4 + 0.022174192 * u ** 5 + 0.0090316521 * u ** 6;
+  }
+  if (y < 1600) {
+    const u = (y - 1000) / 100;
+    return 1574.2 - 556.01 * u + 71.23472 * u ** 2 + 0.319781 * u ** 3 - 0.8503463 * u ** 4 - 0.005050998 * u ** 5 + 0.0083572073 * u ** 6;
+  }
+  if (y < 1700) {
+    const t = y - 1600;
+    return 120 - 0.9808 * t - 0.01532 * t ** 2 + t ** 3 / 7129;
+  }
+  if (y < 1800) {
+    const t = y - 1700;
+    return 8.83 + 0.1603 * t - 0.0059285 * t ** 2 + 0.00013336 * t ** 3 - t ** 4 / 1174000;
+  }
+  if (y < 1860) {
+    const t = y - 1800;
+    return 13.72 - 0.332447 * t + 0.0068612 * t ** 2 + 0.0041116 * t ** 3 - 0.00037436 * t ** 4 + 0.0000121272 * t ** 5 - 0.0000001699 * t ** 6 + 0.000000000875 * t ** 7;
+  }
+  if (y < 1900) {
+    const t = y - 1860;
+    return 7.62 + 0.5737 * t - 0.251754 * t ** 2 + 0.01680668 * t ** 3 - 0.0004473624 * t ** 4 + t ** 5 / 233174;
+  }
+  if (y < 1920) {
+    const t = y - 1900;
+    return -2.79 + 1.494119 * t - 0.0598939 * t ** 2 + 0.0061966 * t ** 3 - 0.000197 * t ** 4;
+  }
+  if (y < 1941) {
+    const t = y - 1920;
+    return 21.2 + 0.84493 * t - 0.0761 * t ** 2 + 0.0020936 * t ** 3;
+  }
+  if (y < 1961) {
+    const t = y - 1950;
+    return 29.07 + 0.407 * t - t ** 2 / 233 + t ** 3 / 2547;
+  }
+  const t = y - 1975;
+  return 45.45 + 1.067 * t - t ** 2 / 260 - t ** 3 / 718;
+}
+
 /**
  * The TDB date every element set here is evaluated at, for a date on the map's clock, which is
- * UTC: Standish's T_eph, the SSD satellite and SBDB epochs and the IAU's d and T all run on TDB.
+ * UT: Standish's T_eph, the SSD satellite and SBDB epochs and the IAU's d and T all run on TDB.
  * Positions and spins both go through this, so a locked moon's face and the orbit it is drawn on
  * are taken at the same instant; taken at the clock's date, the orbits ran 69 s behind the spins,
  * which is 0.9 degrees of Phobos's orbit and 0.16 of Io's.
  */
 export function tdbFromUtc(jdUtc: number): number {
-  return jdUtc + TT_MINUS_UTC_DAYS;
+  return jdUtc + ttMinusUtSeconds(jdUtc) / 86400;
 }
 
 /** Converts a JS `Date` into a Julian date (days), for driving the Kepler propagator "now". */