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 degrees / 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), Earth moves faster in its orbit, so the Sun appears to move about 1.02 degrees per day. At aphelion (farthest point, around July 4), Earth slows down and the Sun moves only about 0.95 degrees per day. This ~7% variation is the fundamental reason 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 with uniform angular speed. The mean anomaly M = 357.529° + 35999.050° x T tracks how far Earth has traveled from perihelion along its orbit, again assuming uniform speed. These are "mean" quantities — averages that ignore the real elliptical variation. The Equation of Center will correct them.