Abstract
Having developed the theories of the Sun and Moon with the theory of eclipses as a beautiful corollary, and having described the fixed stars, Ptolemy now turns to the theory of the remaining planets - Saturn, Jupiter, Mars, Mercury, and Venus. They are dealt with in Book IX-XI of the Almagest. The old question of the order of the planets (page 295) is raised at the beginning [IX, 1; Hei 2, 206], where Ptolemy has to admit that there are no objective criteria of planetary distances because of the imperceptible planetary parallaxes. Nevertheless, he thinks it the best course to follow those ancient astronomers who placed the sphere of the Sun in the middle, with Saturn, Jupiter, and Mars above it as superior planets, and Venus, Mercury, and the Moon below it. Mercury and Venus are therefore known as the inferior planets. This has the advantage that the sphere of the Sun divides the planets into two natural groups, the superior having oppositions, and the inferior not.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Copernicus also began his planetary theory with Saturn, examining Ptolemy's theory (De Rev. V, 5) before adjusting it by means of his own observations (ibid. V, 6). A possible reason why Ptolemy started with Mercury is indicated below (note 15).
- 2.
See Klibansky, Saxl, and Panofsky, Saturn and Melancholy, London 1964.
- 3.
There is no doubt that the statement is an argument post hoc, offered after Ptolemy for other reasons had decided to relate the second anomaly to the motion on the epicycle; cf. Aaboe 1963 p. 3.
- 4.
See O. Neugebauer, Astronomical Cuneiform Texts, II, 281-283.
- 5.
In the Hypotheses (I, 17; Opera minora p. 79) this relation is changed. Here Ptolemy states that Saturn performs 313 anomalistic revolutions minus 0°; 12,26,19,14,25,48 in 324 tropical years, or 324 Egyptian years and 83 days. Similar relations comprising long periods and ignoring the number of revolutions in longitude are given for the other planets.
- 6.
Thus it is misleading when later than the deferent centre, Dreyer (1906, p. 197) believes the equant or “the centre of distances”. centre to be introduced
- 7.
In De Revolutionibus Copernicus returns several times to this break with the established opinion of how uniform, circular motion is to be understood; see the preface (fol. iii verso) where his criticism is stated in general terms, and his remarks on the Ptolemaic theories of the Moon (IV, 2) and Mercury (V, 25). - A later author like Tannery (1893, p. 256) still speaks of Ptolemy's little heresy as le vice fondamental of his system.
- 8.
Robert Small wrote (1804, pp. 55-56) that as Ptolemy gives no account of the means by which this was discovered, nor of the observations from which it was infer ed, his assuming it has justly excited the wonder of all astronomers. The greater part believed him to have assumed it merely from conjecture, and not to have derived it, as Kepler more generously supposed, from any observations. Small himself suggested that there seems some reason for thinking, that it came to him by tradition, from the more ancient astronomy of the east. This is without any support whatever and only rejects the general ignorance of eastern astronomy at the time when Small wrote his survey.
- 9.
The gist of Kepler's long and complicated argument is the following: Assuming the bisection of the eccentricity Ptolemy had shown how λa and e = TD = DE could be found from three oppositions. Discarding this assumption Kepler investigated a model for Mars - later called the hypothesis vicaria - in which λa, the total eccentricity TE and the ratio TE: DE could be determined from four oppositions (see Astronomia Nova (De motibus stellae Martis) II, 16, Opera omnia III, p. 151 ff.). Using four of Tycho Brahe's observations, Kepler found (p. 168) a total eccentricity TE = 0.18564 divided in the ratio TD:DE = 0.11332:0.07232. This model was found to reproduce the longitudes of 12 oppositions to within about 0°;2 (II, 18; pp. 171 ff.), but was unable to reproduce the latitudes of the planet. However, Kepler proved that the latitudes could be accounted for if the total eccentricity was bisected as TD = DE = 0.09282; but in this case the errors in longitude rose to 0°;8 (II, 19; p. 177). Without any evidence whatever Kepler surmised that Ptolemy might have found himself in a similar situation, accepting the bisection of the eccentricity in order to save the latitudes, and tolerating an error of 0°;8 in longitude (assuming that the was aware of it) as acceptable within the general accuracy of his observations. A similar course was not open to Kepler because of the greater accuracy of Tycho's observations, and he had to discard both the hypothesis vicaria, and the bisection of the eccentricity.
- 10.
This explanation was put forward by Dreyer (1906, p. 197) who also gave a good account of Kepler's explanation (ibid., pp. 384 ff.).
- 11.
In decimal notation Ptolemy's result is e = 0.0569444 Calculating the same parameter from a Kepler orbit Czwalina (1958, p. 299) found e =0.0568451.
- 12.
Determining the elliptic Kepler orbit from Ptolemy's observations Czwalina (1958 p. 299) found the longitude of the apogee to be λa = 180° + 53°;3. This compares well with Ptolemy's result.
- 13.
Concerning the Ptolemaic theory of Mars, see Max Caspar's introduction to the German translation of Kepler's Neue Astronomie, München-Berlin, 1929, pp. 9*—12*.
- 14.
There is some evidence that Greek astronomers investigated also models in which the planet has a retrograde motion on the epicycle (as in the lunar theory). A model of this kind is implied in Papyrus Michigan 149 dating from the 2nd century A.D. It reminds one of the models vaguely described by Pliny, Hist. nat. II, 12-14. This type of models has been examined by Aaboe (1963) who proved that it is impossible to provide them with such parameters that retrogradations will occur for all the five planets.
- 15.
This is an assumption in the theories of Saturn, Jupiter, and Mars. In the case of Mercury Ptolemy had reasons to believe that the fixed position of the apogee relative to the fixed stars was an observational fact (see below page 312). This may have been a reason for dealing first with the inferior planets, before going on to the superior ones.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Pedersen, O. (2011). The Superior Planets. In: Jones, A. (eds) A Survey of the Almagest. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84826-6_9
Download citation
DOI: https://doi.org/10.1007/978-0-387-84826-6_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-84825-9
Online ISBN: 978-0-387-84826-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)