The ancient Greeks observed that the positions of ascending and descending nodes at which the Moon passes through the fixed plane of the Earth's orbit around the Sun, the ecliptic, decrease, i.e. orbit the Earth in the opposite direction to the Moon, in such a rate that the cycle of that regression amounts almost exactly 18.6 Earth's years. In other words, if the Moon, during the spring or autumn equinox, when viewed from stationary point on Earth, ascends at a certain position on the east horizon, describes the curve of its path and descends at another particular point on the west horizon, it would take 18.6 years for this trajectory to be repeated. In past centuries, developing lunar theory, many famous mathematicians and astronomers have dealt with described problem (Newton, Clairaut, D'Alembert, Euler, Laplace, Damoiseau, Plana, Poisson, Hansen, De Pontécoulant, J. Herschel, Airy, Delaunay, G.W. Hill, E.W. Brown) indicating its inherent difficulty and the theoretical and practical importance. Presented geometry accurately predicts the described cycle. Relative to Earth, Moons trail draws torus. For artistic purposes, in this video, geometry is adapted to exactly mach 18 years cycle. Its mathematical description can be red at: http://www.principiauniversi.com/blogs/11-2-dot-1-regression-of-lunar-nodes The background sound is a clip from the soundtrack "Symphonies of planets" recorded by NASA's Voyager.
Video Creator Bio
Andrej Rehak finished High School for Mathematics and Informatics and graduated sculpture on Academy of Fine Arts in Zagreb. He does computer animation and searches for patterns in motions and shapes.