Astronomical Images : Lines and motions of the Moon

Georg von Peuerbach

Astronomical Images

Georg Peuerbach (Georgius Aunpekh) was born in Peuerbach, near Linz. He studied at the University of Vienna, obtaining his BA in 1448 and MA in 1453. He held positions as court astrologer to the king of Hungary, and then to Emperor Frederick III. At the request of Cardinal Johannes Bessarion, Peuerbach began an abridgement of Ptolemy's Almagest, which was incomplete when he died in 1461. Peuerbach had also compiled Theoricae novae planetarum, a revision of the Theorica planetarum attributed to Gerard of Cremona. This originated as lectures given in Vienna in 1454, which were attended by Johannes Regiomontanus, who published the first edition in Nuremberg around 1474. This is the 1482 edition by Erhard Ratdolt, which contains copies of the original diagrams. As in the original edition, some woodcuts were coloured. Ratdolt was active in Venice and Augsburg, and was particularly interested in astronomical subjects. He also produced editions of Johannes Engel's Astrolabium planum in tabulis ascendens and G. Julius Hyginus' Poetica astronomica. Peuerbach's text was printed in a compilation that also included Johannes Sacrobosco's Sphaericum opusculum and Johannes Regiomontanus' Contra Cremonensia in planetarum theoricas delyramenta disputationes. This collection of astronomical treatises, and other similar ones, together comprised the main elementary texts available in the late fifteenth century. This woodcut is a slightly reduced copy of a diagram in the original edition of Peuerbach's treatise (c. 1474). The outermost circle around the centre of the World (c. mundi) probably represents the 'fourth concentric orb of the Moon carrying the Head of the Dragon', that is the ascending node, which 'moves on the axis of the zodiac, revolving westward uniformly about the centre of the World, about three minutes in every natural day' (orbis quartus concentricus Caput Draconis deferens movetur super axe zodiaci circa centrum mundi regulariter contra successionem omni die naturali tribus minutis fere). The same outermost circle may also represent the ecliptic of the eighth sphere along which the motion or longitude of the Moon is measured. The middle circle is the eccentric deferent of the epicycle of the Moon (deferens epicyclum Lunae), abbreviated as the deferent of the Moon. Its centre (c. deferentis) revolves around the centre of the World, describing the innermost circle in the diagram. This small circle is divided in two by the axis of the deferent orbs of the apogee, which is the line passing through the centre of the World, the centre of the deferent, and the points of the deferent that are most and least distant from the centre of the World (the apogee, or aux, and the perigee, or oppositum augis). This axis orbium augem deferentium is not labelled, but it is easily found: it coincides with the vertical middle axis of the diagram (and of the page). The point on this axis and on the innermost small circle, which is opposite to the centre of the deferent, is called the 'opposite point' (punctum oppositum). Four small circles are drawn around the middle circle (the eccentric deferent of the epicycle of Moon); they show the lunar epicycle in four different positions: when its centre is on the axis of the deferent orbs of the apogee (at the apogee and at the perigee), and in two intermediate positions. The epicycle, whose centre is on the eccentric deferent and that moves according to the motion of this deferent, also rotates around its own axis, so that the body of the Moon, which is attached to its circumference, successively occupies different positions, represented by black dots. The line of mean motion, or longitude, of the Moon (linea medii motus) is, in Peuerbach's words, the line 'extended from the centre of the World to the zodiac through the centre of the epicycle. The mean longitude of the Moon is the arc of the zodiac from the beginning of Aries up to the said position', that is to the point where the line of mean motion intersects the eighth sphere. The line of the true motion, or true longitude, of the Moon, not labelled on the diagram, is 'extended from the centre of the World through the centre of the body of the Moon up to the zodiac. The true longitude of the Moon is the arc of the zodiac from the beginning of Aries up to the said line' (to the point where the line of the true motion of the Moon intersects the eighth sphere). Another line that is not labelled passes through the 'opposite point' (punctum oppositum) and the centres of the epicycle in two intermediate positions. This line indicates the mean apogee of the epicycle (aux media epicycli), a rather important point. For Peuerbach specifies that the rotation of the epicycle around its centre is irregular, but that this irregularity can be reduced to uniformity, as 'the Moon is uniformly removed from the point of the mean apogee of the epicycle (a puncto augis epicycli mediae â?¦ regulariter elongetur), wherever that is, by receding in every natural day by thirteen degrees and about four minutes'. The mean apogee is defined by Peuerbach as 'the point of the circumference of the epicycle, which is determined by the line drawn through the centre of the epicycle from the point diametrically opposite the centre of the eccentric in the small circle'. This mean apogee is distinct from the true apogee of the epicycle (aux vera epicycli), defined as 'the point of the circumference that is determined by the line drawn through the centre of the epicycle from the centre of the World'. We may observe that the line of the mean motion, or longitude, of the Moon coincides with the line that determines the true apogee of the epicycle: both are drawn through the centre of the epicycle from the centre of the World. However, the mean motion is a point marked on the zodiac (or an arc of circle measured on the zodiac), whereas the true apogee of the epicycle of the Moon is a point marked on the circumference of the epicycle. In any case, the 'two apogees coincide when the centre of the epicycle is in the apogee or perigee of the deferent', that is on the axis of the deferent orbs of the apogee (represented by the vertical line); 'everywhere else, however, they diverge'. In later editions of the Theoricae novae planetarum, new diagrams were added to explain more clearly the motion of the epicycle. Translated quotations of Peuerbach's Theoricae are from Aiton (1987).