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Commits
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  SenrokaiandClaude Opus 5.5
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b0d7989c6f |
Read moons given against their planet's equator, and dwarf planets from the Small-Body Database
Two sources the missing bodies need, read and tested before any body uses them.
JPL's satellite table gives Uranus's and Pluto's moons against the planet's equator ("Mean
equatorial orbital elements") rather than a Laplace plane, and does not print that equator's
pole. parseSatelliteMeanElements now takes the pole from its caller for such a section and reads
the row against it exactly as against a Laplace plane's; it throws if a section is equatorial and
no pole was given, or a pole was given for a section that is not. Read as ecliptic elements, which
is what the old code would have done, Titania is 88 degrees from Horizons on 2025-01-01. The
section's plane is now the nearest heading above the row, with the ecliptic as before where there
is none.
Ceres, Eris, Haumea and Makemake are in none of Standish's tables. parseSmallBodyElements reads a
JPL SBDB answer (sbdb.api?sstr=...&phys-par=1&full-prec=1): the osculating heliocentric elements
against the J2000 ecliptic, carried round at their own n with nothing turning, and half the
published diameter and the rotation period where the answer has them. full-prec matters: without
it SBDB rounds to three figures, Ceres's n to 0.214 degrees a day for 0.2143045, 1.1 degrees out
within a decade. The fetcher, tools/etl/lib/mean-elements.ts, caches the answer like the others.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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SenrokaiandClaude Opus 5.5
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48319c3fe2 |
Move the solar system on JPL's mean elements, so it stays right as the clock runs
Every body carried one set of osculating elements from Horizons at 2025-01-01, run forward by
Kepler with a GM from a table of mass ratios. That set is exact at its instant and drifts from
then on, and the clock now runs a month a second: the Moon, with Earth's mass ratio lacking its
own and the osculating axis, went round in 27.70 days instead of 27.32, 66 degrees out after a
year, and its locked face was spun at the same wrong rate.
Planets and Pluto now take Standish's Table 2a/2b ("Keplerian Elements for Approximate
Positions of the Major Planets"): elements against the J2000 ecliptic, their rates per century,
and the b, c, s, f terms of Jupiter to Pluto, fit for 3000 BC to AD 3000. Table 1 is closer near
the present (Saturn 0.23 degrees at worst 1950-2100, against 0.32 here) but is only fit for
1800-2050, and by AD 3000 has Saturn 4.3 degrees out where Table 2 holds every planet within 0.3.
The moons take JPL SSD's satellite mean elements: sidereal mean motion n to ten figures, the
periods of their node and periapsis, and each one's local Laplace plane by its pole. They
propagate with n itself, never a GM: gmForParent and its mass table are gone. Horizons still
gives size, spin and obliquity.
Both tables are read from the Internet Archive's copy of JPL's pages, pinned to one capture: the
live approx_pos page has dropped Pluto, and the live sats/elem page has dropped n and rounds the
period to four or five figures (Phobos 0.3187 d, a revolution out within a decade).
What the tables leave implicit, measured against Horizons before it was accepted:
- The precession periods are magnitudes. A node regresses on a prograde orbit and advances on a
retrograde one; a periapsis advances except where a resonance forces the eccentricity. Io's
and Europa's follow their conjunction line backwards at 2 n(Europa) - n(Io) = 0.74 degrees a
day, which is exactly the 1.625- and 1.394-year periods in the table. Read as advancing, Io
was 0.9 degrees out and Europa 2.1.
- On a retrograde orbit the node's turning is added back to the mean anomaly. Taken off, Triton
drifted a degree a year, 105 degrees by 2100.
- The Laplace frame's x axis is where the plane rises through the ICRF equator, RA of the pole
plus 90. Read against the ecliptic, Io was 2.8 degrees out, Phobos 54 and Titan 127.
Orbit lines are now drawn in their own plane and turned by a quaternion each tick, so a turning
node carries the line with the body: fixed at one date, the Moon's line would be up to 69 000 km
off it nine years on. The Earth row is the Earth-Moon barycentre, 4 700 km from Earth, 0.002
degrees from the Sun. A tidally locked moon's day is now 360 / n, its sidereal period (the Moon
27.321662 d), so it stays locked to the orbit it is drawn on.
Angular error against Horizons VECTORS (ICRF, TDB; heliocentric for planets, planet-centred for
moons), degrees, read from the live renderer's markers in the running app:
body 1950-01-01 1975-01-01 1987-07-23 2000-01-01 2025-01-01 2037-03-06 2050-01-01 2075-01-01 2100-01-01 max
mercury 0.004 0.002 0.003 0.002 0.002 0.001 0.000 0.002 0.000 0.004
venus 0.003 0.007 0.003 0.004 0.004 0.004 0.003 0.004 0.004 0.007
earth 0.003 0.008 0.002 0.005 0.004 0.009 0.003 0.002 0.003 0.009
mars 0.009 0.010 0.008 0.024 0.009 0.012 0.009 0.011 0.028 0.028
jupiter 0.063 0.030 0.171 0.135 0.013 0.020 0.056 0.041 0.075 0.171
saturn 0.080 0.064 0.018 0.320 0.066 0.114 0.044 0.164 0.177 0.320
uranus 0.018 0.169 0.068 0.050 0.101 0.015 0.141 0.017 0.114 0.169
neptune 0.070 0.028 0.004 0.021 0.036 0.037 0.013 0.029 0.072 0.072
pluto 0.045 0.054 0.041 0.033 0.019 0.020 0.023 0.027 0.026 0.054
moon 0.486 1.928 0.127 0.631 1.407 1.086 0.720 0.339 1.180 1.928
phobos 2.068 0.294 0.881 1.113 0.313 0.636 2.089 5.862 11.099 11.099
deimos 0.077 0.043 0.310 0.066 0.164 0.068 0.034 0.468 0.044 0.468
io 0.021 0.015 0.010 0.019 0.009 0.035 0.006 0.011 0.022 0.035
europa 0.036 0.039 0.053 0.064 0.078 0.032 0.006 0.034 0.044 0.078
ganymede 0.132 0.103 0.018 0.007 0.023 0.054 0.091 0.118 0.044 0.132
callisto 0.040 0.019 0.023 0.019 0.038 0.008 0.060 0.119 0.056 0.119
titan 0.003 0.019 0.023 0.023 0.027 0.028 0.048 0.008 0.014 0.048
triton 0.051 0.029 0.009 0.021 0.052 0.048 0.063 0.089 0.137 0.137
Three miss what was hoped for, and why:
- Jupiter 0.17, Saturn 0.32, Uranus 0.17 against the 0.1 hoped for: short-period perturbations
of the giants by one another, which no Keplerian fit carries. Standish states his own Table 2
errors as 600, 1 000 and 2 000 arcseconds (0.17, 0.28, 0.56 degrees). Out to AD 3000, measured
at 1800, 2200, 2400, 2600 and 3000, every planet stays within 0.3.
- The Moon, 1.9: evection (1.27) and variation (0.66), which a mean ellipse leaves out.
- Phobos, 2.1 until 2050, then 5.9 in 2075 and 11.1 in 2100, growing as the square of the time:
its tidal acceleration, which the table has no column for. Its elements are MAR080's, epoch
1950. The map's dates are also UTC where the elements are TDB, 69 s today,
which is 0.9 degrees of Phobos and nothing for anything else.
Held in place by:
- build.ts: each body's mean elements against Horizons' own osculating elements on the ETL's
2025-01-01, at most 0.25 degrees for a planet and 2.5 for a moon (measured: Uranus 0.101, the
Moon 1.407; a regressing Triton node reads 10.24 and fails), and every moon's day equal to its
sidereal period (a 1% error fails).
- Unit tests freezing nine Horizons vectors (Earth 2100, Jupiter 1950, Saturn 2075, Pluto 1975,
the Moon 2050, Io and Europa 1950, Titan and Triton 2100) through SystemOrbitsRenderer, the
Moon kept on its own turning line, the retrograde rule, the Standish terms, the Laplace frame,
and both table parsers. Nine mutants each fail the test named for them, and the two
validators each refuse a mutated build of the real catalogue.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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