Holistic view of our universe — Expanding Solar System Resonance Theory

What if the orbits of all eight planets, the wobble of Earth’s axis, and the rhythm of ice ages are governed by the same physics, read against one clock? This holistic view proposes exactly that: Earth’s long cycles as periods and ratios against its lunisolar precession clock, with every planet’s motion derived from the model’s own N-body engine — explaining solar system dynamics and Earth’s climate record from formation to the present day.

Two Motions, One Ratio

The model starts from a single observation: two of Earth’s precession motions rotate in opposite directions.

Earth’s two counter-rotating precessions. The perihelion direction advances counter-clockwise around the Sun at T ≈ ~111,570 years (apsidal precession); Earth’s Wobble Center circles Earth clockwise at T ≈ ~25,771 years (axial precession, the clock). Their ratio reads 4.329 today — a reading that wanders, not a constant.

Because the two motions run in opposite directions their rates add, and their beat is the ~20,936-year perihelion-of-date cycle. From this starting point the model derives quantities normally calculated separately: precession of the equinoxes, obliquity oscillation, eccentricity cycles and Milankovitch beat frequencies, length of days and years, and climate patterns (ice ages) — while the eight planets themselves ride the model’s own N-body engine, derived from one cited J2000 state with zero fitted constants.

Everything is read against one clock: Earth’s other long periods are beats of the precession clock with its orbit’s own motions, and the planets’ periods are the N-body engine’s eigenfrequencies. A 3D simulation visualises it all in one interactive view. (Earlier versions of this site read the ratios as fixed integers dividing a 335,317-year “Earth Fundamental Cycle” and an eight-fold “Solar System Resonance Cycle”; that framing is retired — Earth’s Clock.)

Why This Matters

Modern celestial mechanics — JPL Horizons, Laskar’s secular theory, high-precision ephemerides — achieves sub-arcsecond accuracy on Myr timescales and remains the right instrument for high-precision position prediction. Several structural gaps remain:

1. No closed-form solution exists. The gravitational n-body problem cannot be solved exactly; positions must be computed step-by-step.
2. Each phenomenon has its own model. Precession, obliquity, eccentricity, and day/year lengths are all driven by gravity but modelled independently with different parameterizations.
3. No closed-form framework ties all eight planets’ tilts and eccentricities to a single timescale. Each planet’s orbital tilt and eccentricity are treated as independent outcomes of formation, with no structure linking them collectively.
4. No unified 3D simulation. Existing tools handle orbital mechanics or Milankovitch cycles in isolation. None bring axial precession, obliquity oscillation, perihelion precession, eccentricity cycles, day/year length variation, and all eight planets’ orbits into a single interactive view.

Observation First — A Bottom-Up Approach

Standard paleoclimate theory takes the climate record as its starting point. The 100-kyr, 41-kyr, and 23-kyr cycles observed in ice cores and ocean sediments are interpreted by selecting which combinations of planetary motions best fit each peak — eigenmode beats from classical Laplace–Lagrange theory. The math is rigorous, but the climate-to-planet attribution is fitted to the data. Several major puzzles remain unexplained: the 100,000-year problem (eccentricity forcing is too weak to drive ice ages directly), the absence of the theoretically dominant 400-kyr cycle in post-MPT climate records, and the Mid-Pleistocene Transition ~1 million years ago.

This holistic view reverses the direction. It starts from directly observed orbital motion — Earth’s measured precession periods, every planet’s measured orbital cycles — anchored against JPL Horizons / WebGeoCalc ephemeris data (1800–2100 AD, RMS < 0.09°) and historical astronomical records. From these observations the model’s own N-body engine yields the planets’ secular modes, and Earth’s spin clock is derived from its year laws. Only then are the beats of those quantities — the climate formula’s 28 orbital lines — overlaid onto the climate record. The line periods are fixed by the model’s dynamics, not fitted to climate — only the per-line amplitudes are fitted to LR04 / CENOGRID / EPICA / CenCO2PIP.

The framework makes a structural commitment the standard approach does not: the orbital layer carries only the engine’s own beat lines, a sharply falsifiable claim. A climate peak with no counterpart among those beats would refute the orbital layer.

The canonical Climate Formula on LR04 δ¹⁸O over the past 700,000 years. R² = 0.779 post-MPT — the 28 engine-derived orbital lines (with the 405-kyr carbon-thermostat family) and the step transitions capture most of the post-MPT climate signal.

From Software to Theory

This framework began as a software project — a 3D simulation built from just 6 free parameters. The simulation reproduces the positions of the Sun, Moon, and all seven planets — verified against JPL Horizons ephemeris data and historical astronomical observations. From the same geometric framework it simultaneously produces obliquity, eccentricity, perihelion precession, and inclination oscillation for all planets — quantities normally computed by separate models.

From this, a theoretical framework emerged:

• Observable patterns in obliquity, eccentricity, orbital longitudes, and planetary motions could be captured in closed-form formulas
• Precise measurements of day lengths and year lengths in the 3D model also reduced to formulas
• A clock emerged: Earth’s axial precession period, derived from the year laws, against which every other Earth period is a beat — and which lengthens through geological time on the measured tidal history
• The planets moved onto dynamics: an N-body engine seeded by one cited J2000 state supplies the secular modes; an earlier integer-label reading of the planets’ periods (the “Fibonacci Laws”, a Jupiter–Saturn “lock”, Saturn’s “anti-phase” balance role, a formation-epoch KAM story) was tested against the engine’s own eigenfrequencies, found to carry no information, and retired with its record (Earth’s Clock)

The simulation also serves as a test bed: existing results such as Souami & Souchay’s (2012) invariable plane definitions can be verified, and eight testable predictions — each naming the observation that would falsify it — can be checked against future observations.

Headline Findings — Climate Cluster

The model’s climate work is grounded in four independent proxy records (LR04 / CENOGRID / EPICA / CenCO2PIP). Three results stand out:

• R² = 0.779 — the 28 engine-derived orbital lines (L1, with the 405-kyr carbon-thermostat family inside) plus the boundary-condition step transitions (L3) on post-MPT LR04; 0.730 on EPICA CO₂, 0.692 on CenCO2PIP 0–66 Ma. (The comb-era formula with 33 integer-labelled lines fitted 0.87; the shipped physical-line formula pays the honest price of carrying only the engine’s own beats.) These are in-window descriptions: fitted on one half of a regime window, the lines have no skill on the other half (T7, pre-registered); the model’s own orbital histories predict 0.357 of post-MPT LR04 out of sample — the prediction, published beside the description.
• ΔR² ≈ 0 — adding classical Berger 1978 insolation features (ε, e, e·sin ϖ, e·cos ϖ) with the real orbital elements (Laskar 2004 / 2010) on top of the formula yields no cross-window-stable gain in any regime. Classical insolation features alone explain only R² = 0.0544 post-MPT — 16× less than the orbital lines alone. The beat lines subsume the Berger insolation parameterization.
• Two tiers at deep time — the formula’s precession-band and obliquity lines ride Earth’s lengthening clock; its eccentricity-band lines are planetary beats and do not. Every newly dated Precambrian section tests the split (Expanding Resonance).

Read the Climate Summary → for the full synthesis statement and empirical case in one table.

An open framework, not a closed theory

Explore the Model

Start reading: How It Works →

Quick Facts

• The clock — axial precession: 25,771.4 years at J2000 (derived; lengthens through geological time)
• The fitted anchor: 335,317 years — the unit of the correction bases, 13.011 clock periods
• Apsidal precession: ~111,570 years (4.329 clock periods — a reading that wanders)
• Perihelion precession (of date): ~20,936 years (0.8124 clock periods)
• Obliquity cycle: ~41,224 years (the beat of the clock against the orbit plane’s nodal turn)
• Obliquity range: ~22.21° – ~24.72°
• The planets: every planet’s orbital shape and tilt from the model’s own N-body engine — see Moon & Planets