Retrograde Motion: Geocentric vs Heliocentric (2D)

Earth and an outer planet both orbit the Sun on circular paths, but Earth — closer in, faster — periodically laps the outer planet. This 2D simulator integrates both real orbits forward in time and, every frame, computes the outer planet's true apparent bearing as seen from Earth using plain vector geometry. The top-down panel shows the real heliocentric orbits; the lower strip chart plots that apparent bearing against time, revealing the characteristic forward-retrograde-forward pattern precisely when Earth overtakes the outer planet — timed to match the synodic period formula exactly, the same phenomenon Ptolemy needed epicycles to fake and Copernicus explained with nothing more than two circles at different speeds.