The IAU gives a locked moon's W the mean motion of whichever orbit its authors had, and JPL's table
has another. Near the present the difference is nothing; over the clock's AD 1 to 3000 it turned
Proteus's far side to Neptune at AD 1 (146 degrees), Mimas 52 degrees from Saturn and Miranda 23.
Iapetus was worse for another reason: its IAU pole is a straight line, 3.9 degrees a century in
right ascension, through its orbit normal's 3 439-year circle round the Laplace pole, which by AD 1
has run past the celestial pole (Dec 97.9), 11 degrees off the orbit, with the face 87 degrees
from Saturn. Mimas and Iapetus carry mission maps, so a wrong hemisphere was drawn facing Saturn.
The ETL's lock check sampled only 1950-2100, so none of it failed.
tools/etl/lib/locked-spin.ts, lockedToOrbit, called for every locked moon:
- W's rate becomes the orbit's own mean motion, its constant moved so W is unchanged on
2025-01-01; the pole and every periodic term stay the IAU's. A W with a quadratic is left
(Phobos's orbit already takes it; the Moon's is its tidal slowing, 0.75 degrees at AD 1). The
kernel's rate must be within 1e-5 of the orbit's first (at most 3.4e-6, Iapetus).
- Iapetus (poleFollowsOrbit): the pole follows its orbit normal, as a moon in a Cassini state does,
in the IAU's own form: sines of the node's angle and four harmonics on right ascension, cosines
on declination, fitted to the normal's circle and pinned to the IAU pole at the present; W takes
sines of the same angles, fitted to hold the face where it is today.
build.ts samples the lock over AD 1 to 3000 (8 114 dates, every 135 days) instead of 1950-2100, and
subPlanetLongitudeDeg moved to the lib, shared by both. Measured on the real catalogue: at most
5.36 degrees (Titan) but the Moon 7.62 (its eccentricity, and W's quadratic at AD 1: a new named
ceiling of 8), Mimas 8.94 (ceiling 11 -> 9.5) and Iapetus 15.95 (19 -> 16.5, 9.4 of it its row's
lag); Proteus's own ceiling of 9 is gone, at 2.66. Iapetus's axis stays within 0.74 degrees of its
orbit normal (11.06 before) and its pole is the IAU's at the present to 1e-4 degrees.
Live on :4301, the longitude facing the planet at AD 1 / 1000 / 2025 / 2999: Proteus 2.6 / 2.6 /
2.6 / 2.6 (was -146.5 / -72.9 / 2.6 / 74.5), Iapetus -15.9 / -15.4 / -15.3 / -9.3 (-87.0 / -50.9 /
-15.3 / 22.8), Mimas 4.1 / 6.8 / 5.7 / 8.4 (48.6 / 29.3 / 5.7 / -13.0), Miranda -0.1 / 2.2 / 0.0 /
1.4 (-23.4 / -9.6 / 0.0 / 12.6); the present is unchanged.
The renderer spec now takes the rotational elements from bodies.json too, so no hand copy is left,
and a new test turns Proteus, Miranda, Mimas and Iapetus to their planets at AD 1 and AD 3000.
Guarded mutants, each run through the solar ETL and then the full suite on what it wrote:
lockedToOrbit bypassed (validator: Mimas 52.30, ceiling 9.5; the new test fails), Iapetus on the
IAU's straight pole (98.48), and its pole round the orbit without W's terms (73.13); each fails the
new test and only it.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
SenrokaiandClaude Opus 5.5
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