Not future observation
The 2031–2040 reference values are predictions from a fitted JUP365 ephemeris, not measurements collected in those future years.
Planetary dynamics · replicated research product v1.0.0
What holds Jupiter’s moons in rhythm?
Io, Europa, and Ganymede do not simply orbit at nearly 4:2:1. Their three mean longitudes combine into a Laplace angle that stays close to 180°. A second, frozen study now tests whether the model result survives a new decade and stricter numerical checks.
- Reference
- JPL JUP365
- Validation
- 2031–2040
- New samples
- 3,653 days
Interactive JPL ephemeris
Watch a three-body clock emerge.
The moon angles come from a 60-day JUP365 vector extract. Distances and body sizes are deliberately rescaled so all four moons remain visible.
Measured angular motion · illustrative radial spacing · exaggerated radii
Epoch (TDB)2001-01-01
Speed: 1 sample per frame
- Io
- Europa
- Ganymede
- Callisto
Do not read this as raw observation. JUP365 is a fitted ephemeris. The animation preserves timing and projected direction, not physical scale.
The observable
One angle compresses three orbits.
180°
2031–2040 JUP365 circular mean
179.988°φL = λIo − 3λEuropa + 2λGanymede
If the three-body relationship circulated freely, this angle would roam through the full circle. Across the new frozen validation interval it spans only 0.776° peak to peak around 180°.
- Within ±2°
- 100%
- Half-range
- 0.388°
- Combined registry
- 14,610 days
Frozen temporal replication
Add physics. Test a new decade.
Each model starts from the same 2031 JUP365 state and uses the same 0.0025-day step. Lower circular RMSE means a closer Laplace-angle trace.
Selected modelG4J2
Maximum residual1.53°
G4J2 replicated the frozen ordering at the common validation step.
Confirmatory v1 result
Every frozen replication and convergence gate passed.
G4J2 again had lower RMSE than K2, G3, and G4 at a common 0.0025-day step. Its finest trace reached 0.470° RMSE against JUP365. The model is initialized again from JUP365 in 2031, so this is a temporal replication—not an uninterrupted forty-year forecast or a precision ephemeris.
Frozen numerical gate
Halve the step. Watch the error settle.
Choose a G4J2 step to see its daily circular residual against JUP365. The thresholds were committed before the validation data were retrieved.
Selected step0.00125 day
RMSE vs JUP3650.470°
The finest trace passes the frozen 1° reference-adequacy gate.
| Gate | Observed | Threshold | Outcome |
|---|---|---|---|
| Medium–fine trace RMSE | 0.5735° | ≤ 0.75° | Pass |
| Estimated convergence order | 1.984 | 1.5–2.5 | Pass |
| Fine trace vs JUP365 | 0.4699° | ≤ 1.0° | Pass |
Research architecture
A result you can inspect, not just watch.
- 01
Freeze twice
Both protocols were committed before their corresponding scored extracts and model runs.
- 02
Separate time
The validation uses 3,653 new daily JUP365 epochs that do not overlap the v0.1 interval.
- 03
Compare fairly
All four validation models use one common step; G4J2 receives two additional convergence runs.
- 04
Keep failures possible
Ordering, trace agreement, estimated order, and reference adequacy had fixed pass criteria.
Stop at the boundary
What this study does not establish.
Not a forty-year forecast
The validation restarts from JUP365 in 2031; it tests a new propagation interval, not continuous error from 2001.
Not an ocean detector
No claim follows about tidal Q, interior heating, subsurface oceans, or habitability.
Not a universal ranking
G4J2’s win belongs to these models, states, frame choices, intervals, and endpoint.
Primary record