Eccentricity

Eccentricity measures how elliptical Earth’s orbit is. A value of 0 is a perfect circle; higher values mean a more elongated ellipse. Earth’s current eccentricity is 0.01671022 — a nearly circular orbit.

What Eccentricity Means in Practice

The eccentricity value represents the offset distance between the centre of Earth’s orbit and the Sun, as a fraction of the semi-major axis (1 AU).

• At perihelion (closest, ~January 3): Earth is 147,098,057 km from the Sun.
• At aphelion (farthest, ~July 4): Earth is 152,097,684 km from the Sun.
• Earth receives about 6.9% more solar energy at perihelion than at aphelion.

One Law: the H/3 Eccentricity Line

Earth’s eccentricity follows a single law on the H/3 inclination cycle — not the ~100k and ~400k-year cycles predicted by Milankovitch theory:

e(t) = base′ · (1 + cos θ₃(t) / 2)

θ₃ = the H/3 inclination-cycle phase on the System-Reset anchor (θ₃ = 81.18° at J2000)

This is the same law the Moon’s eccentricity channel, the eclipse-chain Sun and the cardinal-point (seasons) chain ride — one eccentricity movement for the whole model, with base′ derived (not fitted) from the observed J2000 eccentricity and the shared anchor. The magnitude |e| and the perihelion direction ϖ are cleanly separated:

The familiar ~20,957-year cycle is still real — it is the meeting frequency of two counter-rotating motions (axial precession H/13 clockwise, inclination precession H/3 counter-clockwise; 13 + 3 = 16), and it governs where the perihelion points relative to the seasons. The beat moves the perihelion direction, not the orbit’s shape.

The modern-epoch test. The one law’s rate of change at J2000 is a prediction with zero fitted inputs: −0.0000431 per century, against the observed −4.2037e-5 (JPL/Meeus) — agreement to 2.5%.

The wobble centre survives as a marker. Earth’s visible wobble-centre in the simulation circles Earth at ~202,846 km once per axial precession — that distance is the Law-4 amplitude A, an exactly derived quantity (the 1246 triangle closure; see Fibonacci Laws — Law 4). It marks the precession direction and does not enter e(t).

Eccentricity Values

The mean base′ is not fitted: it is fully determined by the observed J2000 eccentricity and the same System-Reset anchor that already fixes the inclination law, the Moon’s eccentricity channel and the Sun’s imprint — their extremes coincide by construction.

Extremes and the 1246 Alignment

The eccentricity extremes ride the H/3 System-Reset anchor:

The 1246 AD alignment keeps its meaning — for the perihelion direction. In 1246 the perihelion pointed at the December solstice (and around ~11,725 AD it will point at the June solstice, half an H/16 beat later). That alignment anchors the perihelion-direction chain and the Law-4 A derivation; it is not an eccentricity extreme — the shape extremes belong to the H/3 line above.

We are currently at θ₃ ≈ 81.18° of the cycle: the value (0.01671022) is decreasing and will reach the minimum (~0.0078) around 32,682 AD, then return to maximum around 88,568 AD.

Why Not Milankovitch’s 100k/400k Cycles?

Conventional Milankovitch theory proposes eccentricity cycles of ~100k and ~400k years. The model proposes a single H/3 line (~111,772 years) instead. Five open questions in the conventional eccentricity theory:

The 100-kyr cycle in ice cores is a multi-planet eigenmode-beat signal, not direct eccentricity forcing. Empirical analysis on LR04 places the energy-weighted centroid at the s₁ − s₄ nodal eigenmode beat at n = 25 = 107.3 kyr, with adjacent contributions at n = 28 = 95.8 kyr (g₄ − g₅ eccentricity, Berger’s 95-kyr peak) and n = 22 = 121.9 kyr (s₂ − s₄ nodal). The 405-kyr g₂−g₅ term is essentially absent in post-MPT LR04 (amplitude ratio 0.12); bispectral analysis finds no significant 95k+125k phase coupling. Earth’s own H/3 inclination precession (n = 24) is a real cycle on the 8H lattice but does not directly drive climate — the L1 fit places near-zero amplitude there. Full empirical case: Climate Formula.

Comparison with Standard Formulas

The model’s eccentricity is compared with the Meeus (1991) polynomial, Berger (1978) and La2004 (Laskar) over ±20,000 years. All four converge at J2000 (e = 0.01671022) — and the one law also matches the observed rate: −0.0000431/century predicted vs −4.2037e-5 observed (2.5%). Beyond a few thousand years the curves part: the secular solutions decline faster toward their deep minimum, while the model’s single H/3 line declines more gently toward its own minimum (~0.0078 at ~32,682 AD) and then rises again.

Over the longer span (the figure in the Extremes section above, −250,000 to +100,000 years) the contrast is structural: the model’s H/3 line oscillates within ~0.0078–~0.0233 around the derived mean base′ = 0.0155200, while Berger and La2004 vary over larger amplitudes (up to ~0.05) on the ~100k and ~400k-year beats of the secular eigenmodes. The single line reproduces the timing of the present decline and the existence of one minimum; it does not reproduce the multi-mode envelope. Since direct measurements only cover recent centuries, neither picture can be verified for deep time — but they offer testable, fundamentally different forecasts.

Saturn coupling — an additional effect

The eccentricity curve above reflects only Earth’s own H/3 line. Saturn’s eccentricity is independently predicted by Law 5 — the global eccentricity balance equation determines Saturn’s value from the other seven planets to 0.27%. The two predictions are not independent: Saturn participates in the same balance system that includes Earth, so changes in Earth’s eccentricity feed into Saturn’s via Law 5.

The physical Earth–Saturn coupling comes from Saturn being the only planet whose precession formula requires Earth’s time-varying obliquity and eccentricity as inputs (GROUP 15 terms; see Formulas), and from Saturn’s perihelion cycle (−8H/65 = 41,270 years, ecliptic-retrograde) coinciding with Jupiter’s ICRF perihelion — the gas-giant lock that drives Earth’s obliquity (Law 6). Saturn’s axial precession (~1.8 Myr, driven by a spin-orbit resonance with Neptune; Saillenfest et al. 2021) is unrelated.

Numerical comparison: Model vs La2004

Both curves decline smoothly to a single minimum, in remarkable near-term agreement (exact at 3,000 AD). They part company at the minimum itself: La2004 is already in its minimum region at 27,000 AD (0.00263), while the one law bottoms later and shallower — ~0.0078 at ~32,682 AD. A single harmonic line cannot reproduce Laskar’s multi-mode beat exactly; the framework’s own N-body derivation of the full mode vector (which does track La2004) is recorded as a research result, deliberately outside the shipped zero-fitted-constants doctrine. These differences require geological timescales to verify directly. See Climate Formula: eccentricity attribution headwinds for the three discriminating empirical tests (405-kyr absence, bispectrum, wrong-family centroid).

Climate Implications

Eccentricity affects Earth’s climate through two mechanisms:

Total annual energy. Higher eccentricity gives Earth slightly more total annual solar energy. Orbit-averaged flux scales as 1/√(1−e²); perihelion’s intense, close-range flux more than compensates for the longer time spent near aphelion.

This effect is small — too small alone to cause ice ages.

Seasonal contrast. The more important effect is when perihelion occurs relative to seasons:

Eccentricity Cycles for Other Planets

The same two-counter-rotating-motion principle applies to every planet. Each planet has its own wobble period — the meeting frequency of its axial precession and ICRF perihelion precession — the period over which its eccentricity completes one full oscillation:

Earth is the family’s exception. Its wobble beat — axial precession (H/13) meeting ICRF perihelion precession (H/3), 13 + 3 = 16, the ~20,957-year perihelion precession — governs the perihelion direction only. Earth’s |e| itself oscillates on the H/3 line above, so the table lists H/3. For the seven other planets the two component periods differ, the wobble period is a derived beat frequency, and their eccentricities do oscillate on it.

Calculate Eccentricity at Any Year

See Formulas for the complete formulas.

Summary

Continue to Days & Years to learn how these cycles affect the length of our days and years.