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>
Every element set here runs on TDB: Standish's T_eph, the SSD satellite and SBDB epochs, the
IAU's d and T. bodyOrientation already took the clock's UTC to TDB, but SystemOrbitsRenderer.update
and the body page's heliocentricPosition fed the UTC date straight to meanElementsAt, so in one
frame each body's place was 69.184 s behind its spin. That is n x 69 s of orbit: Phobos 0.90
degrees, Mimas 0.31, Deimos 0.23, Enceladus 0.21, Miranda 0.20, Io 0.16, Tethys 0.15, Europa
0.08, the Moon 0.011. 48319c3's table measured the app at a UTC date against Horizons at the same
number read as TDB, which hid it, and its "nothing for anything else" was wrong: Io's 0.16 is four
to five times Io's worst model error there (0.035).
tdbFromUtc, in constants.ts, is now the one conversion, and positions and spins both go through
it. In the running app, clock pinned to 2025-06-01 12:00 UTC, Io's face towards Jupiter is at
0.024 E, latitude -0.009, where Horizons (observer quantity 14 from Jupiter's centre) has 0.036 E
and -0.003: 0.012 degrees apart, where it was 0.175. The renderer spec checks that point, and now
hands its frozen Horizons vectors, which are TDB, to update() as the UTC dates that name them,
69.184 s earlier; the same frozen rows fed at the UTC date fail for Io and Europa. A body-page test
checks that the Sun lights the point it stands over at the same TDB instant the body is turned for.
Controls: taking the renderer's orbits at the clock's UTC fails "faces jupiter and the Sun with the
points Horizons gives on io"; taking the page's Sun there fails "takes the Sun where it stands at
the same TDB instant".
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
The body page used to spin every body about its pole at 0.08 radians a second, under a light at
(4, 3, 5) whatever the date. A body with IAU elements is now drawn as it is at the map's clock,
using the same pole, prime meridian and map convention as the system view. It is shown pole up
under a Sun held at the light's old azimuth, so the camera still opens on the day side. The Sun's
height above the equator is the real one, and so is the face it lights. The clock's rate now
turns the page too: at 1 h/s Earth's sub-solar point moved 15.17 degrees in the 1.012 h of sky
one wall second carried. What the page gives up is the stars, which do not turn with the body.
bodyPageView in src/app/shared/rendering/body-orientation.ts takes the Sun's direction from where
the body is: a planet's own mean elements, a moon's planet's place plus its own offset. It sets
the sphere's rotation and the light's direction. Exoplanets, Eris, Haumea and Makemake keep the
old slow turn and light.
Saturn's rings now lie flat in its equator, the page's horizontal. They used to lean 17 degrees,
which put them out of the plane they orbit in.
Measured:
- Live app, clock pinned to 2025-06-01 12:00 UTC: the Sun stands over 0.433 W, 22.125 N on
Earth's page, the same point as on its sphere in the system view.
- Unit test, raycast on the page's own sphere: Earth one light-time earlier is 0.09 degrees from
Horizons' sub-solar longitude. Its latitude, put on the flattened Earth, is within 0.03.
- The Moon's sub-solar point is within 0.004 of Horizons'.
Three mutants each fail their named test: a moon lit as if it had no planet; the Sun not held at
the page's azimuth; the body left in the ICRF instead of the page's frame.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
SenrokaiandClaude Opus 5.5