Earth’s Clock

The model reads every long cycle of Earth’s orbit and spin against one clock: the mean lunisolar precession period, the time Earth’s spin axis takes to trace one circle on the sky. The clock is not a constant of nature. It is composed from the Sun’s and the Moon’s pull on Earth’s equatorial bulge, and both of those change on geological timescales, so the clock lengthens — and every period read against it is a reading of date, not a fixed number.

This page establishes:

• What the clock is made of, and its J2000 value, 25,771.4 years — What the clock is made of.
• Earth’s five long periods as ratios to it, three of them frame arithmetic once two are known — Earth’s five long periods.
• How the clock lengthens through geological time, and which periods follow it and which do not — The clock through geological time.
• What the model’s fitted timing anchor is, and is not — The fitted anchor.
• The framing this page used to carry, and why it was retired — Retired framing.

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. At J2000:

• Period: 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: 50.2883″ per year, of which the Sun’s torque supplies 31.6 % and the Moon’s the rest.

The J2000 period is derived, not fitted, and 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 (the record below).

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.

Earth’s five long periods, against the clock

Earth’s orbit and spin carry five long periods. Each is 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.

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 spin axis’s own inertial precession (ψ̇ᵢₙ, 0.097 ″/yr faster than the equinox clock — the planetary precession) against the dominant nodal mode of Earth’s orbit (2π/(ψ̇ᵢₙ − |s₃|)): the tilt oscillates at the rate the spin axis gains on the orbit plane. The two motions themselves — what moves, in which direction, and how each is observed — are the subject of Precession; the obliquity beat and the orbit plane are Obliquity & Inclination.

The clock through geological time

The period is not a constant even within the modern era: it oscillates by about two thousand years as the orbit’s own plane moves, and Vondrák’s expression — drawn here across the span it is valid for — follows the same oscillation. Within the ±26,000-year window the axial period wanders between 24,801 and 26,559 years as the orbit’s eccentricity and inclination modulate the torques, and the perihelion-of-date period between 11,303 and 26,698 years. What changes at geological time is the mean the oscillation rides on.

Because the spin slows and the Moon recedes, the clock lengthens:

The precession period shortens monotonically into the past. The equinoxes completed one circuit in ~15,972 years at 1 Gyr ago against ~~25,771 yr today, and the period collapses toward zero at the rigid-Roche crossing (the Earth–Moon genesis, ~4.498 Ga) — the asymptote of the recession history, not a period the model reads off. The classical observable known since Hipparchus is not a fixed astronomical constant but a now-snapshot of a slowly-evolving clock.

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. A dated record sees the beat of the pole rate’s mean over the record’s window, not the J2000 instant: over the LR04 record (0–5.32 Ma) that mean is 50.517 ″/yr and the realized obliquity period ~40,927 yr, measured on the model’s own obliquity history (~40,919 yr) and on La2004’s (~40,900 yr) alike (Supporting Evidence §7). 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).

At today’s rate the clock lengthens by ~0.025 % per million years, about 6 yr per Myr at the modern epoch — small on human timescales but in principle observable in high-precision IAU precession-rate measurements over decades; distinguishing it from mainstream tidal-LOD contributions and planetary-precession evolution is the open observational question. The strongest evidence comes from deep time, where the cumulative shift is large: paleontological day counts and cyclostratigraphic period drift across the Phanerozoic (Supporting Evidence §11 for the Wells 1963 Devonian-coral validation table).

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 1246 AD epoch of the IAU mean elements (the model’s own series crosses at 1247.2 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 read the anchor as Earth’s master cycle with the five periods as its integer divisors, and a “Solar System Resonance Cycle” of eight anchor intervals into which every planet’s long periods divided as integer fractions, with a “System Reset” when all eight planets reached their inclination extremes together. That framing is retired on the model’s own evidence. 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 %, and the ratios wander far from the integers across the ±26,000-year window (table above). The planets’ N-body eigenfrequencies land on the eight-unit grid no more often than chance, so the fractions, the reset and the tiers carried no information; the planets’ periods are the N-body chain’s own values (Moon & Planets, N-body Exploration). The full record is doc 109 in the 3d repository .

Continue to Precession for the two motions behind the clock and how each is observed, Obliquity & Inclination for the obliquity beat and the orbit plane, and Expanding Resonance for the clock through geological time.