Earth’s Clock
The model reads Earth’s long cycles against one clock: the mean lunisolar precession period, the time Earth’s spin axis takes to trace one circle on the sky.
- Period at J2000: 25,771.4 years — the model’s one J2000 precession reading, the beat of its own sidereal and tropical year laws (the IAU value agrees to eight parts in a million).
- Rate: 50.3″ per year, of which the Sun’s torque supplies 31.6 % and the Moon’s the rest.
This page states the clock, reads Earth’s five long periods against it, and follows the clock through geological time. The section at the end records the framing this page used to carry.
What the clock is made of
Earth’s spin axis precesses because the Sun and the Moon pull on its equatorial bulge. The rate is a composition of the two torques on the spin:
ψ̇(t) = [ω(t)/ω₀] · p₀ · [f_S + (1 − f_S) · (a₀/a_M(t))³]
where ω is Earth’s spin rate, p₀ the J2000 rate, f_S the Sun’s share of the J2000 torque, and a_M the Moon’s distance. Two things change the clock through time: the tides slow the spin (ω falls), and the Moon recedes (its torque weakens as the inverse cube of its distance). Both are measured histories, not fitted constants — the same recession history that carries the length-of-day record. Expanding Resonance is the time-evolution layer.
One reading, every surface. The J2000 period is derived, not fitted: the certified year laws’ beat at 2000. Every face of the model — the simulator’s panels, the published packages, this site — reads the same value. An older device reading (a fitted timing anchor divided by 13) sat 0.086 % higher and is retired as a period; see the record below.
Earth’s five long periods, against the clock
Earth’s orbit and spin carry five long periods. Each is now the model’s own dynamical value — read from its N-body chain and its composed spin rate — and each is best understood as a ratio to the clock.
| Period | J2000 value | How it is derived | Ratio to the clock |
|---|---|---|---|
| Axial precession (the clock itself) | ~25,771 yr | the of-date year laws’ beat at J2000, T_sid/(T_sid − T_trop) | 1 |
| Perihelion of date — the perihelion against the moving equinox | ~20,936 yr | the perihelion-of-date beat of the one-family route at J2000: 1/T_peri = 1/T_p + 1/T_aps | 0.8124 |
| Obliquity beat — the tilt’s oscillation | ~41,224 yr | the beat of the axial precession against the nodal mode s₃, 1,296,000/(ψ̇ − |s₃|) | ≈ 1.6 |
| Nodal (ecliptic) precession — the orbit plane’s turn on the invariable plane | ~68,751 yr | the N-body chain’s dominant nodal mode s₃, 1,296,000/|s₃| | ≈ 2.7 |
| Apsidal precession — the perihelion against the stars | ~111,570 yr | the N-body chain’s secular apsidal tangent at J2000 | 4.329 |
Three of these are frame arithmetic once the other two are known. The perihelion-of-date period is the beat of the clock with the apsidal period (1/T_peri = 1/T_p + 1/T_aps): the equinox precesses one way, the perihelion drifts the other, and the two rates add. The obliquity beat is the clock against the dominant nodal mode of Earth’s orbit (2π/(ψ̇ − |s₃|)): the tilt oscillates at the rate the spin axis gains on the orbit plane.
The ratios are readings, not constants. The apsidal ratio reads 4.329 at J2000 but wanders between 0.83 and 9.89 across the past and coming 26,000 years, because the perihelion’s motion is a sum of planetary modes with no single period, while the clock itself is nearly flat over that window. Earlier versions of this page read the ratios as fixed integers (13 : 3, 13 : 5, 13 : 8, 13 : 16). Those integers were J2000 coincidences of the readings, and the model no longer claims them.
The clock through geological time
Because the spin slows and the Moon recedes, the clock lengthens:
| Epoch | Precession period | Obliquity beat |
|---|---|---|
| J2000 | 25,771.4 yr | 41.2 kyr |
| Devonian (−380 Myr) | 21,699 yr | — |
| +200 Myr | 28,208 yr | — |
| 1.4 Gyr ago | — | 19.1 kyr |
| 2.46 Gyr ago | — | 15.1 kyr |
The obliquity beat shortens faster than the clock itself, because the nodal mode s₃ is an orbital quantity that does not follow Earth’s spin: as the precession rate rises into the past, the beat 2π/(ψ̇ − |s₃|) closes in. This split — spin quantities ride the clock, orbital quantities do not — is the model’s pre-registered deep-time prediction, tested against Precambrian cyclostratigraphy at 1.4 and 2.46 Gyr. The climate formula’s precession-band lines ride the clock; its eccentricity-band lines, planetary beats, do not (Climate Formula).
Within the last few million years the clock is not constant either: the axial period itself wanders between 24,813 and 26,556 years over the ±26,000-year window as the orbit’s eccentricity and inclination modulate the torques, and the perihelion-of-date period between 11,697 and 26,193 years.
The fitted anchor
The model’s correction terms — the small periodic corrections that bring its analytic motions onto the observed cardinal points, day lengths and eclipses — are Fourier series on a fixed grid. That grid’s unit is a fitted timing anchor of 335,317 years, calibrated so that Earth’s perihelion and the December solstice align at the verified 1246 AD epoch (Configuration: Why 1246 AD?). The anchor is 13.011 clock periods long: it was fitted on the perihelion-of-date alignment, not on the axial rate, so the 0.086 % gap is the fit’s convention, constant at every epoch, and not physics. The anchor and the clock scale together through time; their ratio is a fit constant, not structure.
The anchor is a unit of the correction bases, the way a metre is a unit of a ruler. It is not a cycle, nothing in the sky returns after one anchor interval, and no published quantity is defined by dividing it by an integer.
Retired framing: the “Solar System Resonance Cycle”
Earlier versions of this page described an Earth Fundamental Cycle (the anchor read as Earth’s master cycle, with the five periods as its integer divisors H/3, H/5, H/8, H/13, H/16) and a Solar System Resonance Cycle of eight anchor intervals, into which every planet’s six principal long periods were said to divide as integer fractions, with a System Reset epoch when all eight planets reach their inclination extremes together, and a per-planet “Fundamental Cycle” tiering that made Earth unique.
That framing is retired, on the model’s own evidence:
- The Earth periods are not integer divisors. Read from the model’s dynamical chain, the apsidal, nodal, obliquity and perihelion-of-date periods sit 0.18 %, 2.5 %, 1.7 % and 0.10 % from the integer-divisor values, and the axial period 0.086 % — small, but real, and the ratios wander far from the integers across the ±26,000-year window (table above).
- The planetary fractions carry no information. The model’s N-body eigenfrequencies, computed from its own integration, land on the eight-unit grid no more often than chance: the labels were readings of J2000 values with a dense enough grid to fit anything. The planets’ periods are now stated as the N-body chain’s own values (Moon & Planets, N-body Exploration).
- The System Reset and the tiers followed from the fractions and retire with them. The simulator’s period table and reset controls were removed.
What survives is the physics the framing was reaching for: the composed spin clock, its measured tidal history, the five dynamical periods and their beats, and the long-eccentricity metronome of 405 kyr that the planets’ modes set. The public record of the retired claims, with the measurements that retired them, is kept in the simulator repository’s retired record.
See also
- Precession — the axial and apsidal motions in detail, and how each is observed
- Obliquity & Inclination — the obliquity beat and the orbit plane
- Expanding Resonance — the clock through geological time
- Configuration: Why 1246 AD? — the fitted anchor’s calibration