Model scope and corrections — read first

Kepler's laws approximate two-body orbital motion about a common gravitating center. For planets orbiting the Sun, T²/a³ is approximately constant in a consistent unit system, with corrections from planetary masses and gravitational perturbations. Earth travels faster near perihelion (early January) and slower near aphelion (early July). Northern Hemisphere winter is not caused by Earth being farther from the Sun; Earth is actually near perihelion then. Nevertheless, Earth–Sun distance still affects incoming solar radiation. Axial tilt, through changes in solar angle and day length, is the main driver of the seasons.

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KeplerThree laws
Module 10 · Kepler's Laws
Semimajor axis a (AU) 1.00
Eccentricity e 0.017
① Elliptical orbit: r = a(1-e²)/(1+e·cosθ)
② Equal areas: dA/dt = const
③ T² / a³ = constant
e: eccentricity (0=circle, 0.999=highly elongated ellipse)
a: semimajor axis (AU)
T: orbital period (years)
Earth: a=1AU, e=0.0167, T=1 year
Orbital parameters
Semimajor axis a—
Semiminor axis b—
Eccentricity e—
Perihelion distance—
Aphelion distance—
Orbital period T—
Real-time position
Current r (AU)—
Speed (relative)—
True anomaly θ—
T²/a³ for the eight planets
Planeta(AU)T(yr)T²/a³
Mercury0.3870.2411.001
Venus0.7230.6151.000
Earth1.0001.0001.000
Mars1.5241.8810.999
Jupiter5.20311.860.998
Saturn9.53729.461.000
Uranus19.1984.010.999
Neptune30.07164.81.000
Counterintuitive insight
"Earth is farther from the Sun in winter, so the Northern Hemisphere is colder" —False!In early January, Earth is near perihelion (about 147.1 million km); in early July, it is near aphelion (about 152.1 million km). During Northern Hemisphere winter, Earth is actuallycloser to the Sun! Seasonal temperatures are determined by solar altitude and day length, not distance.