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.

The ~20,957-Year Cycle

Earth’s eccentricity oscillates in a ~20,957-year cycle — not the ~100k and ~400k-year cycles predicted by Milankovitch theory.

Two motions work in opposite directions:

Because they move in opposite directions, they meet more frequently than either cycle alone:

Meeting frequency = 1/~25,794 + 1/~111,772 = 1/~20,957

They meet every ~20,957 years — the perihelion precession cycle.

Why alignment affects eccentricity. Earth’s perihelion point defines where Earth’s closest approach to the Sun occurs. Earth itself orbits its wobble center at a small radius (~202,847 km). When Earth and its perihelion point are on the same side of the wobble center, their distances add → maximum eccentricity (~0.0167). When on opposite sides, the distances partially cancel → minimum eccentricity (~0.0140).

Eccentricity Values

The base value (0.015386) cannot be measured directly because we only have observations from recent centuries. It was derived from three constraints: minimum eccentricity occurred in ~9,233 BC when perihelion aligned with the June solstice; maximum occurred in 1246 AD when perihelion aligned with the December solstice; current eccentricity (0.01671022) is near the maximum and decreasing. The 3D simulation was calibrated to satisfy all three.

The Solstice Connection

Eccentricity extremes correlate with solstice alignments:

When perihelion aligns with the December solstice (Northern Hemisphere winter), Earth and its perihelion point are positioned such that their orbital offsets add. When aligned with the June solstice, they partially cancel.

We passed maximum eccentricity around 1246 AD. The current value (0.01671022) is decreasing toward the mean; it will reach minimum (~0.0140) around 11,725 AD and return to maximum around 22,203 AD.

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

Conventional Milankovitch theory proposes eccentricity cycles of ~100k and ~400k years. The model proposes a simpler ~20,957-year cycle 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 predictions are compared with polynomial formulas from Newcomb (1898), Harkness (1891), and Meeus (1998). All four converge at J2000 (e = 0.01671022). Standard polynomials predict continued decrease toward ~0.01 by 20,000 AD; the model predicts bounded oscillation within ~0.0140–~0.0167 with minimum at ~11,725 AD followed by increase.

The graph below shows both predictions over 300,000 years. The model’s ~20,957-year cycle (blue) oscillates within a narrow bounded range of ~0.0140–~0.0167 around a base value of 0.015386 (red). Standard Milankovitch eccentricity (grey) varies over much larger amplitudes (up to ~0.06) on ~100k and ~400k-year timescales.

The two predictions diverge significantly: the model predicts eccentricity never leaves its narrow band; standard theory predicts it has varied by a factor of ~4 over the past 200,000 years. Since direct measurements only cover recent centuries, neither prediction 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 ~20,957-year perihelion cycle. 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

These differences are significant but 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:

For Earth the wobble period coincides with the perihelion precession period (H/16) because axial precession (H/13) and ICRF perihelion precession (H/3) meet at this rate (13 + 3 = 16). For other planets the two component periods are different, so the wobble period is a derived beat frequency.

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.