Kepler's Equation

Kepler's Equation relates the position of a body orbiting a star to time. Specifically, it connects the mean anomaly (a measure of time passed since last closest approach) with the eccentric anomaly (a geometric parameter describing the orbit's shape). The equation is expressed as \( M = E - e \sin E \), where \( M \) is the mean anomaly, \( E \) the eccentric anomaly, and \( e \) the orbit's eccentricity. Solving this equation helps determine the body's position along its elliptical path at any given time, which is essential for precise navigation and understanding of orbital mechanics.