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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Commentariolus | 2/3 | https://en.wikipedia.org/wiki/Commentariolus | reference | science, encyclopedia | 2026-05-05T08:32:52.246082+00:00 | kb-cron |
Including the annual revolution around the Sun, which the Moon shares with the Earth in his system, Copernicus explains the Moon's motion as composed of five independent motions. Its motion around the Earth lies in a plane which is inclined at an angle of 5° to the plane of the Earth's orbit, and which precesses from east to west around an axis perpendicular to that plane, with a period of between 18 and 19 years with respect to the fixed stars. The remaining three motions, which take place within this orbital plane, are depicted in the diagram to the right. The first of these is that of the first, and larger, of two epicycles, whose center (represented by the point e1 in the diagram) moves uniformly from west to east around the circumference of a deferent centred on the Earth (represented by point T in the diagram), with a period of one draconitic month. The centre of the second, smaller epicycle (represented by the point e2 in the diagram) moves uniformly from east to west around the circumference of the first so that the period of the angle β in the diagram is one anomalistic month. The Moon itself, represented by the point M in the diagram, moves uniformly from west to east around the circumference of the second epicycle so that the period of the angle γ is half a synodic month. Copernicus states that whenever the point e1 lies on the line joining the Earth to the centre of its orbit (represented by the dotted line OTC in the diagram, of which only the point T here lies in the Moon's orbital plane), the Moon M will lie precisely between e1 and e2. However, this can occur only once every 19 years, when this line coincides with the line of nodes WTE. At other times it does not lie in the moon's orbital plane and the point e1 cannot therefore pass through it. In general, then, while the Moon will be close to conjunction or opposition to the Sun whenever it lies precisely between e1 and e2, these events will not be precisely simultaneous. The ratio which Copernicus took as that for the relative lengths of the small epicycle, large epicycle and deferent is 4:19:180.
=== The outer planets, Saturn, Jupiter and Mars === The theories Copernicus gives in the Commentariolus for the motions of the outer planets all have the same general structure, and only differ in the values of the various parameters needed to specify their motions completely. Their orbits are not coplanar with that of the Earth, but do share its centre as their own common centre, and lie in planes that are only slightly inclined to the Earth's orbital plane. Unlike the Moon's orbital plane, those of the superior planets do not precess. Their inclinations to the Earth's orbital plane do oscillate, however, between the limits 0°10′ and 1°50′ for Mars, 1°15′ and 1°40′ for Jupiter, and 2°15′ and 2°40′ for Saturn. Although Copernicus supposes these oscillations to take place around the orbits' lines of nodes that he assumes to remain fixed, the mechanism he uses to model them does cause tiny oscillations in the lines of nodes as well. As Kepler later pointed out, the necessity for assuming oscillations in the inclinations of the outer planets' orbital planes is an artefact of Copernicus's having taken them as passing through the centre of the Earth's orbit. If he had taken them as passing through the Sun, he would not have needed to introduce these oscillations.