Carolingian Planetary Observations: The Case of the Leiden Planetary Configuration

Eastwood B. E. , “Origins and contents of the Leiden planetary configuration (ms Voss. Q.79. fol. 93v): An artistic astronomical schema of the early Middle Ages”, Viator, xiv (1983), 1–47; reprinted in Eastwood Bruce S. , The revival of planetary astronomy in Carolingian and post-Carolingian Europe (Variorum Collected Series; Ashgate, 2002), chap. IV. This book includes many other papers by Eastwood related to this topic. A review of all sorts of diagrams was recently published by Eastwood Bruce Grasshoff Gerd , Planetary diagrams for Roman astronomy in medieval Europe, ca. 800–1500 (Transactions of the American Philosophical Society, xciv; Philadelphia, 2004).

Pingree D. , “The Preceptum canonis Ptolemei”, in Hamesse J. Fattori M. (eds), Rencontres de cultures dans la philosophie médiévale: Traductions et traducteurs de l'Antiquité tardive au XIVe siècle. Actes du Colloque International de Cassino, 15–17 juin 1989 (Louvain-la-Neuve and Cassino, 1990), 355–75, esp. p. 373 and fn. 76.

Mostert Richard Mostert Marco , “Using astronomy as an aid to dating manuscripts: The example of the Leiden Aratea planetarium”, Quaerendo, xx (1990), 248–61, esp. pp. 252–3. Eastwood later changed his opinion on his own proposed date to support the hypothesis of Mostert and Mostert, see Eastwood B. , “The astronomies of Pliny, Martianus Capella and Isidore of Seville in the Carolingian world”, in Butzer P. L. Lohrmann D. (eds), Science in Western and Eastern civilisation in Carolingian times (Basel, 1993), 161–80, esp. p. 173. Still later Eastwood, The revival of planetary astronomy (ref. 1), Addenda and Corrigenda, added: “While I agree with this important correction to my dating of the configuration, some of the assumptions made by the Mosterts are highly questionable”.

Mostert Mostert , op. cit. (ref. 3), 252.

The quotation is taken from Mostert Mostert , op. cit. (ref. 3), 251, where also, in fn. 7, their reference is given: Annales regni Francorum qui dicuntur annales Laurissenses majores s.a. 807, ed. and transl. by Rau R. , Quellen zur karolingischen Reichsgeschichte, i (Darmstadt, 1955) [=Ausgewählte Quellen zur deutschen Geschichte des Mittelalters, v], 85. The following English translation is from the Mosterts:. DCCCVII: In the above year there was an eclipse of the Moon on 2 September; at that time the Sun stood in the sixteenth degree of Virgo, the Moon in the sixteenth degree of Pisces. In this year now, 31 January fell on the seventeenth day of the Moon, when the star of Jupiter seemed to go through the Moon, and on 11 February there was an eclipse of the Sun in the middle of the day, when both stood in the twenty-fifth degree of Aquarius. Again there was an eclipse of the Moon on 26 February, and that same night appeared a glow of wondrous magnitude, and the Sun stood in the eleventh degree of Pisces, the Moon in the eleventh degree of Virgo. On 17 March, on the other hand, the star of Mercury appeared in the Sun as a small black spot, slightly above the middle of that same star, and she was visible to us during eight days. But we could not at all notice when it entered and left the Sun, because of the obstructing clouds. Again, on 22 August, there was an eclipse of the Moon in the third hour of the night, with the Sun placed in the fifth degree of Virgo and the Moon in the fifth degree of Pisces. And thus from last September till September this year the Moon has been obscured thrice and the Sun once.

Tuckerman B. , Planetary, lunar, and solar positions: A.D. 2 to A.D. 1649 at five-day and ten-day intervals (Philadelphia, 1964). The tables present the planetary positions for 7 p.m. Baghdad time. This corresponds to a (local) Greenwich time of 4 p.m. The meridian of Aachen is 6° east of Greenwich, so Greenwich time is a good indication for observations made in Aachen or thereabouts.

Bedae Opera de temporibus , ed. by Jones Charles W. (Cambridge, MA, 1943), XX, 221. An English translation is Faith Wallis, Bede: The reckoning of time, with introduction, notes and commentary (Liverpool, 1999), XX, 64. The age of the Moon on 1 February, the regularis lunaris, in the first year of the 19-year lunar cycle was 10. To find the age of the Moon in 807 the epact of 807 has to be added. That epact was 9, implying that the age of the Moon on 1 February 807 was 19, and that on 31 January it was 18 days old. An error of one day is not unusual in medieval calendar calculations.

The aurora interpretation is explored by Link F. , “Observations et catalogue des aurores boréales apparues en Occident de –626 à +1600”, Geofysikalni Sbornik, x (1962), 297–392, esp. p. 318.

The sunspot possibility is mentioned in Dietrich Lohrmann, “Alcuins Korrespondenz mit Karl dem Grossen über Kalender und Astronomie”, in Butzer Lohrmann (eds), op. cit. (ref. 3), 89–114, esp. p. 114.

McCluskey Stephen , “Changing contexts and criteria for the justification of computistical knowledge and practice”, Journal for the history of astronomy, xxxiv (2003), 201–17, espec. p. 207.

McCluskey , op. cit. (ref. 10), 206–7. It is not clear precisely how McCluskey obtained his data. 12. The calendar is edited in Borst A. , Die karolingische Kalenderreform (Hanover, 1998), 254–98. The same dates of the Sun's entries in the signs are found in the reconstruction of Bede's lost calendar published in Wallis, op. cit. (ref. 7), Appendix I, 379–91.

Juste David , “Neither observation nor astronomical tables: An alternative way of computing the planetary longitudes in the early Western Middle Ages”, in Burnett Charles Hogendijk Jan P. Plofker Kim Yanu Michio (eds), Studies in the history of the exact sciences in honour of David Pingree (Leiden, 2004), 181–222, esp. pp. 186–7, predicted longitudes using a simple rule (employed by Hrabanus) that the Sun enters a sign on the 15th kalends of the month. In order to meet the value quoted in the record for 26 February he made an exception to this rule for the entry of the Sun into Pisces, which he placed on the 14th kalends of February, as marked in the Lorscher calendar. Note that the use of Hrabanus's rule (15th kalends of the month) would predict a solar longitude on 26 February 807 of Pisces 10° (instead of 11°) and that using the Lorscher calendar one finds a solar longitude on 11 February 807 of Aqr 26° (instead of 25°). On this difference, see also Borst, op. cit. (ref. 12), 435–6.

The Mosterts, op. cit. (ref. 3), 252, compared the solar positions to the longitudes listed by the Tuckerman Tables, and on this based the conclusion quoted by us above.

Bedae Opera de temporibus (ref. 7), XXX.1–5, 235. Stevens Wesley M. , “Astronomy in Carolingian schools”, in Butzer P. Kerner M. Oberschelp W. (eds), Karl der Grosse und sein Nachwirken: 1200 Jahre Kultur und Wissenschaft in Europa (2 vols, Turnhout, 1997), i, 417–87, esp. pp. 433–39, discusses the difficulties in finding the dates of the equinoxes and solstices through observation.

On conventions, see Neugebauer Otto , History of ancient mathematical astronomy (New York, 1975), 600. The Ari 0°-convention was used in Antiquity by Hipparchus and Ptolemy and by all later mathematical astronomers. However, there is no evidence that Carolingian astronomers would be aware of it. They might have known instead the Ari 8°-convention, which formed part of Plinian astronomy.

Maurus Rabanus , De computo , 48, edited by Stevens Wesley (Corpus Christianorum Continuatio Medievalis, xliv; Turnhout, 1979), 259. The following English translation is from Juste, op. cit. (ref. 13), 182–3:. Today, that is the year of the Lord's Incarnation 820, on the 9th of July, the Sun is in Cancer 23°, the Moon is in Taurus 9°, Saturn is in the sign of Aries, Jupiter in Libra, Mars in Pisces and the position of Venus and Mercury are not visible because they are at the moment close to the Sun in daylight.

Pingree , op. cit. (ref. 2), 372. Juste , op. cit. (ref. 13), 188–222, showed that in Carolingian times a so-called method of ‘the years of the world’ was available for calculating planetary longitudes. The early history of this method is not yet clear, but Juste notes that none of the records dated from 770–820 was computed by it, and therefore this method is not of interest for the present paper.

Juste , op. cit. (ref. 13), 182.

Juste , op. cit. (ref. 13), 184–5. For calculating the position of the Moon a method used by Bede described in Bedae Opera de temporibus (ref. 7), XVII, 215, and by Hrabanus, op. cit. (ref. 17), is used which is based on the fact that the distance between the Sun and the Moon increases daily by about 12° or 4 puncti. The result would be that on 9 July 820, when the age of the Moon was 24 days, the Moon had moved away from the Sun 9 whole signs and 6 puncti, or 288°. By adding this to the longitude of the Sun in the zodiac (Cnc 23°) the place of the Moon is found to be Tau 11°. Another method was discussed by Alcuin in a letter to Charlemagne. It was based on the constant daily increment of 360/(27+1/3) degrees of the Moon with respect to its position on a given day and time. This method requires a suitable initial position of the Moon at a given hour of the day, which is difficult to predict, and so its applicability is limited. The letter was published by Lohrmann D. , “Alcuins Korrespondenz mit Karl dem Grossen über Kalender und Astronomie”, in Butzer Lohrmann (eds), op. cit. (ref. 3), 78–114, esp. pp. 105–12.

McCluskey Stephen , Astronomies and cultures in early medieval Europe (Cambridge, 1998), 148; Juste, op. cit. (ref. 13), 183, note 7.

No calibrated angular measuring instruments for finding longitudes expressed in signs of the zodiac are known from Carolingian times. Neither was there any knowledge of the numerical values of the longitudes of the stars used in observations. Stevens, op. cit. (ref. 15), 433–44, discusses some instruments for finding the dates of the equinoxes and solstices and for finding the time during the day and at night, but none would have been suitable for measuring the position of the planets.

MacRobius , Commentary on the Dream of Scipio, transl. with an introduction by Stahl W. H. (New York, 1952, 1990), 177–80.

Neugebauer , op. cit. (ref. 16), 36.

Suppose one tries to estimate the positions of the planets on 9 July 820, knowing that the calendar predicts the place of the Sun in Cnc 23°. To find the sign in which a planet is on the same day, one has to determine the ecliptic distance between the planet and the Sun. Using a water clock, the method described by Macrobius (op. cit. (ref. 23)), one can find the time between sunset and the moment a planet rises or sets. Assuming with Macrobius that 1 hour corresponds to a rise of the ecliptic of 15°, one finds the following: Mars rises c. 3 hours after sunset, when the longitude of the point on the ecliptic that is setting is Cnc 23° + 45°, and that of the point that is rising with Mars is Cnc 23° + 45° + 180° = 338°. This places Mars in Pisces in agreement with the record. Saturn rises c. 4 hours after sunset, when the longitude of the point on the ecliptic that is setting would be Cnc 23° + 60°, and that of the rising point Cnc 23° + 60° + 180° = 353°. Thus Saturn would also be in Pisces (the record says Aries). Finally, Jupiter sets c. 3.5 hours after sunset, when the longitude of the point on the ecliptic that is setting with Jupiter would be less than Cnc 23° + 60° = 173°. This places Jupiter in Virgo (the record says Libra). Note that on 9 July 820 the Moon became visible a few hours after Jupiter had set, so the position of the Moon could not be used to correlate a position of this planet. Six hours after sunset Mars and Saturn were respectively 2.5 and 1.5 signs separated from the Moon and therefore their locations could have been derived from the lunar longitude; but without specifying the position of the Moon at a given time this method cannot be applied.

Bedae Opera de temporibus (ref. 7), XXXVIII, 33–36, says that learning to recognize the constellations is part of elementary schooling, so we may assume that it was possible to know the main outlines of the zodiacal constellations through observation.

This distinction between constellations and signs is not always significant but — As shown below in the discussion of the Leiden planetary configuration — When it does, it offers a good criterion by which to adjudicate between dates.

Tuckerman , op. cit. (ref. 6).

Eastwood , “Origins and contents” (ref. 1), 2–3 and fn. 3.

We do not believe that refinements of 1° introduced by Mostert and Mostert, op. cit. (ref. 3), 254, are significant.

In Carolingian manuscripts with images of the individual constellations illustrating Germanicus's Aratea, scholia and star catalogues, Libra is without exception presented as a part of Scorpio. This is also the case in many early celestial planispheres. A different situation is seen in zodiacs where, understandably, Libra is presented separately as a figure carrying a pair of scales. The images in the zodiac in the Leiden planetary configuration seem to fit in this latter tradition and may have come with the images of the months included in it. As a rule, pictures of zodiacs are based on signs. We argue that the images in the zodiac in the Leiden planetary diagram have been used as if they were zodiacal constellations and this may have been a cause for confusion unless it was realized that signs differed from constellations.

The maximum elongation of Mercury is not mentioned in the texts of the diagram. If the maker utilized a text by Martianus Capella he would have known it to be one sign, which is what is seen in the diagram. A Plinian text would have told him that it is twenty degrees but the maker may have used a rounded-off value of one sign.

The Paschal Moon is by definition the first full moon after the vernal equinox. Astronomically the vernal equinox was the date on which the Sun entered the sign of Aries. In 816 this took place on 16 March around 8 o'clock (GMT). So the full moon around 18 March would in principle be the Paschal Moon. However, the date of the Paschal Moon was part of an Easter calculation in which the agreed date for the vernal equinox in Carolingian times was 21 March. This excludes a full moon around 18 March and places the date of the Paschal Moon in 816 in April.

Wallis , op. cit. (ref. 7), Appendix II, reproduces Bede's 532-year Paschal Tables. The Paschal Moon in 816 is on 17 April.