ClimateOrbitOrbital forcing · seasonal climate · attribution

Orbital parameters

Three slow clocks behind every seasonal cycle

Eccentricity sets how far the orbit departs from a circle, obliquity sets how far the seasons swing, and precession sets which season meets perihelion. Scrub back through a million years of the La2004 solution to see how they combine, and how Kepler's second law turns them into seasons of unequal length.
SunMar equinoxJun solsticeSep equinoxDec solsticeperihelionaphelion
Seen from above the north ecliptic pole; the Earth moves counter-clockwise. Dots mark where the Earth is at each solstice and equinox; the diamond is perihelion.
Eccentricity
0.01670
Obliquity
23.439°
Longitude of perihelion ϖ (heliocentric)
102.9°
Climatic precession e·sin ϖ̃
-0.0163
Perihelion date*
3 Jan
Sun's longitude at perihelion
282.9°

Season lengths (Kepler's second law)

  • NH spring92.8 d
  • NH summer93.6 d
  • NH autumn89.8 d
  • NH winter89.0 d

*Calendar anchored to the March equinox on its modern date, the usual palaeoclimate convention. The unequal season lengths come from eccentricity alone: with a circular orbit every season would last 91.3 days.

La2004 orbital elements, 0–1000 ka

The vertical line marks the selected epoch

Eccentricity

Obliquity (°)

Climatic precession e·sin ϖ̃

65°N June-solstice insolation (W m⁻²)

Age (ka BP)

Laskar et al. (2004) nominal solution at 1 kyr (plotted every 2 kyr). Precession index e·sin ϖ̃ with ϖ̃ = ϖ + 180°: positive when perihelion falls near the northern summer solstice.

Conventions, stated once

La2004 distributes ϖ as the heliocentric longitude of perihelion measured from the moving equinox (102.9° today). The Sun's apparent longitude at perihelion is ϖ + 180°. The analysis pins this convention with a test: the present-day elements must place perihelion in early January, and an off-by-π error would place it in July.

Time runs as ka BP, thousands of years before 1950, positive into the past. La2004 stores it as negative kyr; the loader negates it and asserts the present-day elements (e = 0.01670, ε = 23.439°, ϖ = 102.92°) before any analysis proceeds.