Why a Year Is 365 Days: Earth's Orbit

Presets

Orbit Parameters

Semi-major axis a 1.00 AU

Star mass 1.00 M☉

Eccentricity e 0.02

Time speed 0.60 yr/s

Click anywhere in the orbital plane to drop the planet at that distance from the star. Drag to pan, scroll/pinch to zoom.

Live Readouts

Orbital period T

1.000 yr

In days

365.25 d

vs. Earth's real year

= 1.000× (identical)

Kepler's third law

A planet's orbital period depends only on its distance from the star and the star's mass — not on the planet's own mass or size. In units of astronomical units (AU), years, and solar masses (M☉), Kepler's third law takes its cleanest form:

T² = a³ / M
T = period in years
a = semi-major axis in AU
M = central star's mass in solar masses (M☉)

Earth sits at a ≈ 1 AU around a 1 M☉ star, so T² = 1³/1 = 1 → T = 1 year (365.25 days) — that's the entire reason Earth's year is the length it is. Push the planet farther out (larger a) and the period grows as a^1.5; make the star heavier (larger M) and its stronger pull shortens the period for the same distance. This view plots the true Kepler ellipse — the planet visibly speeds up near the star (perihelion) and slows down far from it (aphelion), exactly as conservation of angular momentum requires for a non-zero eccentricity.

t = 0.00 yr

Star Planet Earth's real orbit (ref.)