How this orrery works Every planet starts with a position on its orbit and a velocity computed from the vis-viva equation, v = √(μ · (2/r − 1/a)). Nothing follows a drawn ellipse: a velocity-Verlet integrator advances each body under Newton's law of gravitation, and the orbits emerge from the accelerations. A solar eclipse is detected from geometry alone. Seen from Earth, when the Moon sits within a narrow cone of the Sun and on the sunward side, its shadow falls on Earth. The Moon's ~5° orbital tilt is why this happens only a couple of times per simulated year. The forecast re-integrates a private copy of the system forward and reports the next alignment. Back to the sky