How elliptical orbits of planets clinch Newton’s laws of motion and gravitation

Abstract Following a geometrical analysis in the historical tradition of Euclid, we show how Newton’s axioms (subsequently regarded as laws) of motion and gravity, when applied to an orbiting body, lead to the elliptical orbit, with the Sun at one focus, that had been empirically established by Kepler. This constitutes a cross-check on Newton’s hypothesis, which already have Kepler’s other two laws built in. Thus, ‘elliptical orbits clinch Newton’s laws.’