The Sun's Apparent Motion

From Earth's perspective, the Sun appears to trace a great circle around the sky once per year. This path is the ecliptic, and the Sun moves along it at roughly 1 degree per day (360° / 365.25 days). But "roughly" is the key word – the motion is NOT uniform. Earth orbits the Sun in an ellipse with eccentricity e ≈ 0.017. At perihelion (closest approach, around January 3), the Sun appears to move about 1.02°/day. At aphelion (farthest, around July 4), only about 0.95°/day. This ~7% variation is why we need the Equation of Center.

Two fundamental quantities track the Sun's position. The geometric mean longitude L₀ = 280.466° + 36000.770° x T tells us where the Sun would be if Earth's orbit were a perfect circle. The mean anomaly M = 357.529° + 35999.050° x T tracks how far Earth has travelled from perihelion. These are "mean" quantities – averages that ignore the real elliptical variation. T is Julian centuries from J2000.0.