page_title: Commentariolus
section_title: The Moon
hierarchical_section_title: Commentariolus / Summary / The Moon
caption_attribution_description: Diagramatic representation of Copernicus's model of the Moon's motion as presented in Commentariolus
context_page_description: The Commentariolus is Nicolaus Copernicus's brief outline of an early version of his revolutionary heliocentric theory of the universe. After further long development of his theory, Copernicus published the mature version in 1543 in his landmark work, De revolutionibus orbium coelestium.
  Copernicus wrote the Commentariolus in Latin by 1514 and circulated copies to his friends and colleagues. It thus became known among Copernicus's contemporaries, though it was never printed during his lifetime. In 1533, Johann Albrecht Widmannstetter delivered a series of lectures in Rome outlining Copernicus' theory. Pope Clement VII and several Catholic cardinals heard the lectures and were interested in the theory. On 1 November 1536, Nikolaus von Schönberg, Archbishop of Capua and since the preceding year a cardinal, wrote to Copernicus from Rome and asked him for a copy of his writings "at the earliest possible moment".
context_section_description: 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.
caption: Diagram of the Moon's orbit, as described by Copernicus in his Commentariolus
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