COMPUTER TRACKING OF GEODESICS

It is demonstrated via a dynamic computer geometric analysis that in Newton’s Principia Propositions 55/56 the principle of geodesic uniform motion on a curved surface is implied. A 2D-elliptic orbit satisfying Kepler’s second law, expanding area in proportion to time, is transformed to a curved trajectory on 3D-ellipsoid surface traversed with uniform velocity. Vice versa, projections of computer tracked geodesic trajectories on ellipsoid surfaces expanding with increasing eccentricity give rise to precessing orbits in which Kepler’s Second and Third law approximated via triangle geometry become independent from the eccentricity and the magnitude of the time interval. The geodesics are identified as Viviani curves, intersections of ellipsoid surfaces with axes A=B, C and elliptic cylinders tangent in the aphelia. A circle is a projection of a geodesic equator of an ellipsoid with ratio of the axes A=B=1 C=2.