The biggest spectacle in the sky are the Sun and the Moon, while the planets, comets, northern lights, novas and supernovas, etc. are only distant thirds. Good data are available since 3000 years in various quality. The Babylonians collected and analyzed numbers, and the Greeks interpreted most observations geometrically. Even Keppler could not find anything as good for the Moon as the ellipses for the planets. Newton obtained crude estimates for the period of the perigee and for the node in terms of the main motions of the sun and the Moon. The French mathematicians in the middle of the 18-th century calculated good values. Even a heroic effort a century later got the period of the perigee down only to a about 30 seconds, whereas the Greeks had gotten it to 1 second. Finally G.W. Hill in 1877 found the necessary help in a periodic orbit, which Brown and Eckert used further in the 20-th century. A century after Hill it was D. Schmidt and myself who used the same method with computing equipment, and ran into Poincare?s limit.