Ptolemy's Ancient Planetary Observations

Summary

The Almagest of Ptolemy (mid-second century ad) contains eleven dated reports of observations of the positions of planets made during the third century bc in Babylon and Hellenistic Egypt. The present paper investigates the character, purpose, and conventions of the observational programmes from which these reports derive, the channels of their transmission to Ptolemy's time, and the fidelity of Ptolemy's presentation of them. Like the Babylonian observational programme, about which we have considerable knowledge through cuneiform documents, the Greco-Egyptian ones were not directed towards the deduction of mathematical models of celestial motion but appear to have investigated patterns, correlations, and periodicities of phenomena. Ptolemy's immediate sources most likely were not the original series of observational records, but treatises by various astronomers of the intervening four centuries, including Hipparchus. While Ptolemy does not appear to have tampered with the wording of the reports, he faced difficulties and uncertainties in interpreting them; critically, he lacked sufficiently detailed information about the ancient calendars to be able to convert the reported dates accurately into his own chronological framework based on the Egyptian calendar.

I am grateful to Robert van Gent (Utrecht), Teije de Jong (Amsterdam), and John Steele (Durham) for comments on drafts of this paper.

Notes

¹A chronological list of the observation reports in the Almagest is in O. Pedersen, A Survey of the Almagest, Acta Historica Scientiarum Naturalium et Medicinalium, 30 (Odense, 1974), 408–22 (note that there are some typographical errors); for accurate texts and calendrical equivalents in the Julian calendar, see G.J. Toomer, Ptolemy's Almagest (London, 1984). Observations are listed in Toomer's index according to the body observed, the observer, or the type of phenomenon. Nothing is known of Theon; he is certainly not to be identified with the Platonist philosopher, who lived about the right time but whose astronomical knowledge was entirely second-hand.

²A papyrus fragment from the second century ad, P. Oxy. astron. 4133, preserves at most one word of an observation report from 241 bc; this is discussed below in section 3.4. Undated reports such as Aristotle's statement in De Caelo, 292a, that he had once seen the moon occult Mars, are obviously in a different category, and we have no evidence that anyone in antiquity anticipated modern astronomers (beginning with Kepler) in deducing dates for such reports; see F.R. Stephenson, ‘A Lunar Occultation of Mars observed by Aristotle’, Journal for the History of Astronomy, 31 (2000), 342–44.

³See J.M. Steele, ‘Applied Historical Astronomy: An Historical Perspective’, Journal for the History of Astronomy, 35 (2004), 337–55, for a general discussion of the practice in antiquity and modern times, with an interesting discussion of Ptolemy (338–46). Steele distinguishes applied historical astronomy from the generality of astronomers’ use of their predecessors’ data by stipulating that the data originate from a different cultural setting; it appears to me that this criterion applies to Ptolemy's use of four-centuries-old observations even when they were first recorded in his own language and locality, because the scope and methods of astronomy had changed radically in the mean time.

⁴Toomer, Ptolemy's Almagest (note 1), 453 note 70.

⁵Texts 1–3 in A. Jones, ‘A Posy of Almagest Scholia’, Centaurus, 45 (2003), 69–78.

⁶Jones, ‘Posy’ (note 5), text 1: ‘Dionysius, who made his abode in Alexandria . . .’. Apparently, the first scholar to assert the connection between the Dionysian era and the first regnal year of Philadelphus was J. Funck, Chronologia (Wittenberg, 1601), sig. M 6^v (non vidi), cf. A.T. Grafton, Joseph Scaliger. A Study in the History of Classical Scholarship. II. Historical Chronology (Oxford, 1993), 271–72. Crusius, Liber de epochis seu aeris temporum et imperiorum (Basle, 1578), 23–26 [non vidi] and J.-A. Letronne, Oeuvres choisis de A.-J. Letronne. Deuxième série. Géographie et cosmographie, 2 vols (Paris, 1883), 513–14 are practically alone in denying significance to the coincidence.

⁷Ptolemy's chronological system is discussed together with a rather circumspect review of the other calendars mentioned in the Almagest in Toomer, Ptolemy's Almagest (note 1), 9–14.

⁸Modern theory ecliptic coordinates of the planets and fixed stars were computed by the software Alcyone Ephemeris version 2.4, which is based for the planets on an analytical ephemeris by Steve Moshier (see http://www.alcyone.de for details). Planetary longitudes were checked by the JPL ephemeris (http://ssd.jpl.nasa.gov/horizons.html); discrepancies never exceeded 1′, which is insignificant for our purposes. Figures 1–11 are adapted from planetarium simulations generated by the software Starry Night version 3.0.

⁹The reading ‘21’ had already been proposed as an emendation by K.R. Lepsius, as reported in [Anonymous], ‘10. Febr. Gesammtsitzung der Akademie. Hr. Lepsius theilte einige Abschnitte mit aus einer Abhandlung, welche folgende Punkte behandelt: . . .’, Monatsberichte der königlichen Preußischen Akademie der Wissenschaften zu Berlin, 1859, 182–86 (183) and adopted by A. Böckh, Ueber die vierjährigen Sonnenkreise der Alten, vorzüglich den Eudoxischen (Berlin, 1863), 294–95.

¹⁰A. Jones, Astronomical Papyri from Oxyrhynchus, 2 vols. in 1, Memoirs of the American Philosophical Society, 233 (Philadelphia, 1999), I, 70.

¹¹Toomer, Ptolemy's Almagest (note 1), 451 note 64.

¹²Most Greek manuscripts have +9° 30′, but the reading +9° 40′, found in D and (according to Toomer) in the Arabic tradition, is confirmed by the list of zodiacal stars in the Handy Tables (for which I have consulted Vat. gr. 1291, ff. 90v–94v and Laur. 28, 26, ff. 124v–127r).

¹³G. Graßhoff, ‘Normal Star Observations in Late Babylonian Astronomical Diaries’, in Ancient Astronomy and Celestial Divination, edited by N.M. Swerdlow (Cambridge, MA, 1999), 97–147; A. Jones, ‘A Study of Babylonian Observations of Planets Near Normal Stars’, Archive for History of Exact Sciences, 58 (2004), 475–536.

¹⁴Jones, ‘Study of Babylonian Observations’ (note 13), 520.

¹⁵Month length data in an astronomical tablet from Babylon, BM 32327 would be consistent with the month in question having begun on the evening of October 16; unfortunately, this text is elsewhere inconsistent with apparently more reliable documentation, as is shown by J.M. Steele, ‘The Length of the Month in Babylonian Calendars of the First Millennium bc’, in Calendars and Years: Astronomy and Time in the Ancient World, edited by J.M. Steele (forthcoming). The text is no. 39 in A.J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylonia, vols. I, II, III, and V to date, Österreichische Akademie der Wissenschaften, Philosophisch-historische Klasse, Denkschriften, 195, 210, 247, and 299, V.

¹⁶Toomer, Ptolemy's Almagest (note 1), 477 note 17 maintains that the word kateilephos (‘having overtaken’) probably signified an occultation; B.R. Goldstein and A.C. Bowen, ‘The Introduction of Dated Observations and Precise Measurement in Greek Astronomy’, Archive for History of Exact Sciences, 43 (1991), 93–132 (98–99) argue that only a passage of the star by the planet is intended.

¹⁷Goldstein and Bowen, ‘Introduction of Dated Observations’ (note 16), 93 and 98 assert that Ptolemy derived Venus’ longitude on this later date from Timocharis’ report for the earlier date, but this cannot be correct.

¹⁸J.M. Steele, ‘Planetary Latitude in Babylonian Mathematical Astronomy’, Journal for the History of Astronomy, 34 (2003), 269–89 (283–86); Jones, ‘Study of Babylonian Observations’ (note 13), 515.

¹⁹Diary text -229B in Sachs and Hunger, Astronomical Diaries (note 15), II.

²⁰On the Callippic calendrical system, see A. Jones, ‘Calendrica I: New Callippic Dates’, Zeitschrift für Papyrologie und Epigraphik, 129 (2000), 141–58.

²¹Toomer, Ptolemy's Almagest (note 1), 13 asserts that Hipparchus used a Callippic year count adapted to the Egyptian calendar; Jones, ‘Calendrica I’ (note 20), 148–50 argues that this was not the case.

²²The meaning of ‘opposite’ is not clear, but might mean either ‘at the same longitude’ or ‘rising simultaneously’. In either sense, the term would apply only rather roughly to η Vir's position relative to ε Vir.

²³The nomenclature of the Babylonian observational (or more accurately ‘non-mathematical astronomical’) texts was established by A. Sachs, ‘A Classification of the Babylonian Astronomical Tablets of the Seleucid Period’, Journal of Cuneiform Studies, 2 (1948), 271–90.

²⁴Edition of the dated fragments of Diaries in Sachs and Hunger, Astronomical Diaries (note 15) I–III.

²⁵Goal year texts are described, with a specimen translation, in H. Hunger, ‘Non-Mathematical Astronomical Texts and Their Relationships’, in Ancient Astronomy and Celestial Divination (note 13), 77–96.

²⁶Edition of most of the Excerpt texts in Sachs and Hunger (note 15) V.

²⁷Jones, ‘Study of Babylonian Observations’ (note 13), 530–34.

²⁸Normal Star Almanacs are described, with references to published examples, in H. Hunger and D. Pingree, Astral Sciences in Mesopotamia, Handbuch der Orientalistik, 1.44 (Leiden, 1999), 162–67.

²⁹A.J. Sachs, ‘The Latest Datable Cuneiform Tablets’, in Kramer Anniversary Volume: Cuneiform Studies in Honor of Samuel Noah Kramer, edited by B.L. Eichler, J.W. Heimerdinger, and Å.W. Sjöberg, Alter Orient und Altes Testament, 25 (Neukirchen-Vluyn, 1976), 379–98.

³⁰Steele, ‘Applied Historical Astronomy’ (note 3) 340–43.

³¹Jones, ‘Posy’ (note 5), text 4.

³²A similar view is put forward in B.R. Goldstein and A.C. Bowen, ‘On Early Hellenistic Astronomy: Timocharis and the First Callippic Calendar’, Centaurus, 32 (1989), 272–93 (274–76), though in Goldstein and Bowen, ‘Introduction of Dated Observations’ (note 16), 98–99, it is proposed that Timocharis’ observations of lunar occultations may have been intended to investigate the length of the moon's sidereal month and that his observation of Venus ‘reflects an interest in the phase of Venus’ greatest elongation’ and might have been part of an attempt to establish a periodicity of the planet. (The observation was not in fact near a date of greatest elongation.) Incidentally, I do not think that much significance should be ascribed to the circumstance that all the stars mentioned in the surviving Dionysian reports were Babylonian Normal Stars, since the Normal Stars in fact include most of the brightest stars in the zodiacal belt.

³³B.L. van der Waerden, ‘Greek Astronomical Calendars. III. The Calendar of Dionysios’, Archive for History of Exact Sciences, 29 (1984), 125–30 (129).

³⁴For the date of the beginnings of Greek astrology, see D. Pingree, From Astral Omens to Astrology. From Babylon to Bi_ka_ner, Istituto Italiano per l'Africa e l'Oriente, Serie Orientale Roma, 78 (Roma, 1997), 21–29.

³⁵Jones, Astronomical Papyri (note 10), I, 69–80.

³⁶E.g. Pedersen, Survey (note 1), 13.

³⁷R. Bagnall, ‘Alexandria: Library of Dreams’, Proceedings of the American Philosophical Society, 146 (2002), 348–62, esp. 359. The considerable modern literature on the library of Alexandria is not distinguished by sobriety; Bagnall's paper is almost the only sensible thing written on the subject.

³⁸Toomer, Ptolemy's Almagest (note 1), 421 note 11.

³⁹A. Jones, ‘A Likely Source of an Observation Report in Ptolemy's Almagest’, Archive for History of Exact Sciences, 54 (1999), 255–58; for the common provenance of the three papyri see A. Jones, ‘An Almagest Before Ptolemy's?’, in Studies in the History of the Exact Sciences in Honour of David Pingree, edited by C. Burnett, J.P. Hogendijk, K. Plofker, and M. Yano, Islamic Philosophy, Theology, and Science, Texts and Studies, 54 (Leiden, 2004).

⁴⁰Toomer, Ptolemy's Almagest (note 1), 464 note 99.

⁴¹Jones, ‘Study of Babylonian Observations’ (note 13), 522.

⁴²In Geography 1.12 (ed. Nobbe 1.25–26) Ptolemy deprecates the notion of ‘not doing right according to the philosophically appropriate manner if one was not going to get caught’. See J.L. Berggren and A. Jones, Ptolemy's Geography. An Annotated Translation of the Theoretical Chapters (Princeton, NJ, 2000), 73.

⁴³D. Rawlins, ‘Ancient Heliocentrists, Ptolemy, and the Equant’, American Journal of Physics, 55 (1987), 235–39 (236–37 and 239 notes 23–24).

⁴⁴N.T. Hamilton, N.M. Swerdlow, and G.J. Toomer, ‘The Canobic Inscription: Ptolemy's Earliest Work’, in From Ancient Omens to Statistical Mechanics, edited by J.L. Berggren and B.R. Goldstein, Acta Historica Scientiarum Naturalium et Medicinalium, 39 (Copenhagen, 1987), 55–73 (65–67); A. Jones, ‘Ptolemy's Canobic Inscription and Heliodorus’ Observation Reports’, SCIAMVS, 6 (2005), 53–97 (88 and 90). The epoch positions in the Canobic Inscription are for the Era Augustus rather than the Era Nabonassar; conversion between the eras is straightforward.

⁴⁵The regulation of month lengths in the Babylonian calendar during the late period is discussed in Steele, ‘Length of the Month’ (note 15).

⁴⁶Alternatively, if one had observations of the moon such as lunar passages by Normal Stars from the same months as the planetary observations, one could in principle use astronomical theory to fix the date of the beginning of the Babylonian month, as has been done for the Diaries in modern times; but the use of such methods in antiquity seems a remote possibility.

⁴⁷Böckh generally gets the credit for this reconstruction on the basis of his detailed exposition of it in A. Böckh, Ueber die vierjährigen Sonnenkreise der Alten, vorzüglich den Eudoxischen (Berlin, 1863), 286–340, but Lepsius had previously announced it (with Böckh's endorsement) at a meeting of the Berlin Academy in 1859, for which see [Anonymous], ‘10. Febr. Gesammtsitzung’ (note 9). This followed papers on the same topic delivered by Lepsius and Böckh the preceding year ([Anonymous], ‘12. August. Gesammtsitzung der Akademie. Hr. Lepsius las über einige Berührungspunkte der Aegyptischen, Griechischen und Römischen Chronologie’, Monatsberichte der königlichen Preußischen Akademie der Wissenschaften zu Berlin, 1858, 450–53, and ‘Hr. Böckh trug vor: Eine Bemerkung über den zodiakalen Kalender des Astronom Dionysios’, Monatsberichte der königlichen Preußischen Akademie der Wissenschaften zu Berlin, 1858, 578–85). Letronne had already proposed in an extended review of L. Ideler, Ueber den Ursprung des Thierkreises (1838) in the Journal des Savants (1839), 480–95; 527–39, 577–92, and 651–68 [non vidi]; reprinted as J.-A. Letronne, Sur l'origine du zodiaque grec et sur plusieurs points de l'uranographie et de la chronologie des Chaldéens (Paris, 1840) [non vidi] and again in Letronne, Oeuvres choisis (note 6) 458–530) that the calendar year of Dionysius began on the summer solstice and comprised twelve thirty-day months and five epagomenal days, with a sixth epagomenal day every four years (509–20 in Oeuvres choisis). Several errors in Letronne's analysis of the dates were pointed out by T. Mommsen, Die Römische Chronologie bis auf Caesar (Berlin, 1858), 245 note 6 (non vidi), cf. the 2nd edition (Berlin, 1859), 271 note 21.

⁴⁸Van der Waerden, ‘Greek Astronomical Calendars’ (note 33); O. Neugebauer, A History of Ancient Mathematical Astronomy, 3 vols. (Berlin, 1975), III, 1066–67, with whom Toomer, Ptolemy's Almagest (note 1), 13–14 concurs.

⁴⁹For each Dionysian month and day number in the Almagest, if the month name is ‘read’ as the cognate zodiacal sign and the day number as degrees within the sign, the result is always close to the Sun's mean longitude computed by Ptolemy for the date in question. Goldstein and Bowen, ‘Introduction of Dated Observations’ (note 16), 123 strangely raise doubts about whether the Dionysian months Aigon and Hydron might not be named after the non-zodiacal constellations Capella (Aix in Greek) and Hydra rather than Capricorn (Aigokeros) and Aquarius (Hydrokhoos). The Dionysian year number manifestly increased by one after Didymon (the month associated with Gemini) and Leonton (associated with Leo), that is, between roughly the middle of June and late July. See also van der Waerden, ‘Greek Astronomical Calendars’ (note 32), 126–27.

⁵⁰For the correction of Aigon 25 to Aigon 26 see [Anonymous], ‘10. Febr. Gesammtsitzung’ (note 9), 183 and Böckh, Ueber die vierjährigen Sonnenkreise (note 45), 294.

⁵¹Jones, ‘Posy’ (note 5), text 2.

⁵²Jones, ‘Posy’ (note 5), text 3 also uses this expression, restating the contents of the last sentence of text 2.

⁵³L. Ideler, Historische Untersuchungen über die astronomischen Beobachtungen der Alten (Berlin, 1806), 267–68, citing Petavius [D. Petau], De Doctrina Temporum book 4 chapter 16.

⁵⁴A. Rehm, article ‘Parapegma’, in Realencyclopädie der classischen Altertumswissenschaft (‘Pauly-Wissowa’), 18.4 (1949), cols. 1295–366 (col. 1346–47); Neugebauer, History (note 47), II, 628–29 expresses scepticism about the attribution to Callippus, though the resulting season lengths are at least consistent with those ascribed to him in the ‘Eudoxus Papyrus’, P. Par. 1. A.C. Bowen and B.R. Goldstein, ‘Meton of Athens and Astronomy in the Late Fifth Century B.C.’, in A Scientific Humanist. Studies in Memory of Abraham Sachs, edited by E. Leichty, M. deJ. Ellis, and P. Gerardi, Occasional Publications of the Samuel Noah Kramer Fund, 9 (Philadelphia, 1988) 39–81 (58–63) have a useful discussion of possible derivations of such schemes.