DE441 error spectrum — v0.5.0 (38-body roster) vs v0.3.1 (26-body roster)¶
Re-run of the per-body FFT residual analysis on the v0.5.0 encoder (38 bodies: original 26 + Jupiter inner regulars + classical Saturnian moons + Saturn co-orbitals + 3 new Saturnian/Jovian resonances). User's instruction: "don't ship before we sweep against DE441 and look for signals to FFT."
Headline finding: the planet FFT signature is unchanged¶
For the 10 bodies that JPL DE441 has ephemeris truth for — earth, jupiter, mars, mercury, moon, neptune, pluto, saturn, uranus, venus — every FFT residual peak amplitude in v0.5.0 is byte-for-byte identical to the v0.3.1 baseline.
| Body | Top peak (period yr, amplitude °) | v0.3.1 | v0.5.0 | Δ |
|---|---|---|---|---|
| earth | 5.31 yr, 0.93° | 0.93° | 0.93° | 0.00 |
| jupiter | 9.56 yr, 44.6° | 44.63° | 44.63° | 0.00 |
| mars | 7.96 yr, 3.45° | 3.45° | 3.45° | 0.00 |
| mercury | 10.69 yr, 9.19° | 9.19° | 9.19° | 0.00 |
| moon | 7.29 yr, 2.44° | 2.44° | 2.44° | 0.00 |
| saturn | 9.56 yr, 45.0° | 45.02° | 45.02° | 0.00 |
| neptune | 168 yr, 0.43° | 0.43° | 0.43° | 0.00 |
| pluto | 252 yr, 13.1° | 13.12° | 13.12° | 0.00 |
| uranus | 84 yr, 2.69° | 2.69° | 2.69° | 0.00 |
| venus | 505 yr, 0.27° | 0.27° | 0.27° | 0.00 |
The full per-body table at results/de441_error_spectrum.md is
identical to the v0.3.1 baseline aside from two metadata fields
(native-encoder flag flipped from False → True; total encode time
dropped from 314.9 s → 14.6 s, a 21× speedup thanks to the
C native path).
Why the signal is unchanged¶
v0.5.0's structural changes are:
- +12 moons in
BODIES. Each gets a new omega_diag entry and a new moon–planet static coupling. - +3 resonance entries in
RESONANCES: Mimas–Tethys 4:2, Enceladus–Dione 2:1, Titan–Hyperion 4:3.
For the 10 DE441-coverable bodies, here's why the spectrum doesn't move:
- omega_diag for the 10 bodies is unchanged. Their orbital periods didn't change between releases.
- Planet–planet
L_staticcouplings are unchanged. The new couplings are moon–planet, but the FFT'd bodies aren't moons (except Earth's Moon, whose moon–earth coupling is unchanged). - The new RESONANCES act between moons, not between moons and planets. Mimas, Tethys, Enceladus, Dione, Titan, Hyperion all participate in the new entries, but Saturn itself is in NONE of them. Saturn's encoded phase therefore receives no breathing modulation from the new physics — its 9.56-yr Jupiter-coupling signature stays exactly as v0.3.1 recorded it.
This is mathematically expected: the resonances we wired model moon-internal physics (Mimas-Tethys libration shapes the Cassini Division; Enceladus-Dione 2:1 forces Enceladus's tidal heating; Titan-Hyperion 4:3 chaos is in Hyperion's rotation). None of these back-react on Saturn's mean motion in our coupling topology — they'd need a Saturn–moon entry, but Saturn doesn't participate in those resonances physically.
What this means for shipping v0.5.0¶
The v0.5.0 expansion is strictly additive on the FFT validation surface:
- ✅ No regressions on any of the 10 reportable bodies.
- ✅ No new smoking-gun peaks to author patches against (for these 10 bodies). The v0.4.0 catalog patches (Mars 7.96 yr, Mercury 10.69 yr, Jupiter–Saturn 9.56 yr) remain the right targets.
- ✅ 21× faster sweep thanks to the v0.4.1 C native + the v0.5.0 SPICE-free initial-phases path keeping the encoder running natively without runtime calibration overhead.
- ⏳ The new moons themselves are unvalidated. DE441 only
contains the planet barycenters + Sun + Earth + Moon. Galilean
moons, Saturnian moons, Mars's moons, asteroids — all use a
period-based fallback initial phase at codegen time (not
ephemeris truth). To FFT-validate them we need supplementary
kernels (
jup365.bsp,sat441.bsp,mar097.bsp); see roadmap.
Roadmap — supplementary-kernel moon validation (v0.5.x)¶
Pull supplementary moon ephemerides into the codegen + sweep:
| Kernel | Bodies | Size |
|---|---|---|
mar097.bsp |
Phobos, Deimos | ~10 MB |
jup340.bsp |
Galileans + Amalthea / Thebe / Metis | ~6 MB |
sat441.bsp |
All major Saturnians (Mimas → Phoebe) | ~70 MB |
With those staged at codegen time:
- Initial phases for the moons get baked from real ephemeris truth (not the period-based fallback).
- The DE441 sweep can FFT-compare each moon's encoded longitude against ephemeris truth.
- If the v0.5.0 resonance entries have authored the right physics, we should see Mimas/Tethys/Enceladus/Dione/Titan/Hyperion FFT peaks at the resonance periods. Authoring catalog patches against any residuals is then v0.5.x phase-by-phase.
The wheel does NOT need to ship these kernels — they're codegen-time
inputs, used to bake _data/initial_phases.json and the C-side
es_initial_phases[]. Runtime stays SPICE-free.
Verdict¶
Ship v0.5.0. The user-visible promise — "all of Jupiter and Saturn moons join us" — is delivered: the encoder now integrates 38 bodies including Metis through Phoebe, with all three famous Saturnian resonances (Cassini Division, Enceladus–Dione, Titan–Hyperion) modeled. The structural commitment is also delivered: byte-exact backwards compatibility on the FFT validation surface, the C native path running 21× faster on the sweep, and a clear roadmap for moon-validation work in v0.5.x.