Abstract
Tycho Brahe made several thousand observations of the celestial bodies, in general with an unprecedented accuracy and precision. A group of observations of a nebulous object known as Præsepe differs, however, significantly from the general picture. Over a period of 3 years, Tycho observed different astronomical coordinates for Præsepe; the values of meridian altitude differed by as much as 8 arcminutes for repeated observations, and the declination values by up to 5 arcminutes, systematic discrepancies such as these never seen before or since for Tycho’s stellar observations. In this article it will be demonstrated that these differences were due to the observation of three or four individual stars and not of a single arbitrarily defined centre in Præsepe, the open star cluster M44 as it is known today. Individual stars had not been resolved in Præsepe before, and consequently neither had their celestial coordinates been determined. Tycho selected a single of the observed stars to represent Præsepe and included its celestial coordinates in his star catalogues.
Introduction
The Danish Renaissance astronomer Tycho Brahe recorded several thousand celestial coordinates for the sun, the moon, the stars and the planets. His ambition was to obtain an accuracy for his observations of one arcminute (1′) or better. 1 This claim gains support by an investigation of the accuracy of Tycho’s astronomical instruments based on primary data from observations of stars 2 and not on reduced data such as Tycho’s star catalogues. 3
In contrast to this high accuracy, there is a small group of stellar observations that deviate significantly from the general picture. They relate to a celestial body in the constellation of Cancer called Præsepe and were recorded in 1586, 4 1587 5 and 1589. 6 Meridian altitude values differed by as much as 8′ for repeated observations of Præsepe while declination values differed by up to 5′. No other group of stellar observations recorded by Tycho have shown repeated discrepancies similar to these.
To find the reason for this apparent, low accuracy, it was determined to make a detailed analysis of all observations of Præsepe performed by Tycho and his team of observers. As the stars in Præsepe are fainter than the vast majority of stars observed by Tycho, different aspects of this issue will also be discussed.
Præsepe Cancri
The celestial object Præsepe (Latin for manger) in Cancer has been known since antiquity. Aratus, a Greek poet, born about 260 BC, was the first who described this object: ‘Watch, too, the Manger. Like a faint mist in the North it plays the guide beneath Cancer’. 7 In his star catalogue from 129 BC, Hipparchus listed it as Nephelion (little cloud). 8 Ptolemy called it ‘The middle of the nebulous mass in the chest [of Cancer] called Præsepe’ in his Almagest (about 140 CE). 9
The term Præsepe relate to a Greek myth recounted by Eratosthenes: ‘When the gods waged war against the Giants, Dionysus, Hephaestus and Silenus rode to battle on donkeys. But even before they had arrived in sight of the Giants, the donkeys drawing near were braying with a terrible growling. When the Giants heard this, they were terrified and fled. On that account they [the donkeys] were placed in honor westerly in the sign of Cancer. These are the stars in the shell of the crab, called the donkeys. But there is a nebula nearby, which they call Præsepe where they are seen to stand’. 10
Today Præsepe is commonly known as the Beehive Cluster, M44 or NGC 2632. It is an open star cluster which contains at least 1000 faint stars of which only about 10 in the central region have an apparent magnitude (MagV 11 ) of less than 7, 12 and the brightest has a MagV value of 6.343. The faintest star visible to the naked eye under a dark sky has generally been reported to have an apparent magnitude value of 6.0–6.5. 13 Depending on the apparent magnitude of the individual stars, some if not all of the 10 stars in M44 with MagV values less than 7 should be visible without optical aid, an issue that is important for this work and that will consequently be discussed in detail below. In contrast to the individual stars in M44, this object as a whole has an apparent magnitude of 4.5, making it easily visible to the naked eye.
As stated above, Præsepe was described as a nebulous entity by the astronomers of antiquity, a practice that lasted well into the Renaissance. In the Persian astronomer al-Şūfī’s star catalogue, The Book of the Fixed Stars, dated at 964 CE, which is illustrated with drawings of the constellations, Præsepe is described as follows: ‘The first of its [i.e. Cancer’s] stars is the smear which resembles a piece of cloud surrounded by four close stars with the patch in the middle. Two stars are in front and two are behind’. 14
Thus, it appears that al-Şūfī was following Ptolemy in his description of Præsepe. In the drawing depicting the constellation Cancer (Figure 1), 15 Præsepe is, however, shown as a circular group of points, which might indicate that al-Şūfī may in fact have imagined Præsepe as composed of faint, individual stars even though it was not possible to resolve them.
al-Şūfī’s drawing of the constellation Cancer. Bodleian Library, University of Oxford, MS Marsh 144, p. 257.
Another Persian scholar, Abu Rayhan al-Bīrūnī, made the following comment on nebulous objects in his work al-Qānūn u’l-Masʿūdī dated 1030 CE: ‘In the skies we have some objects not resembling the stars in their roundness and light. They are the white patches called the Nebulae. Some of these are considered to be composed of the clusters of the stars’. 16 These suggestions that Præsepe was possibly a cluster of faint stars and not an unspecified nebulous patch did not, however, find support in the following five centuries.
Tycho Brahe was well acquainted with the works of the astronomers of antiquity and it is conceivable that he knew of al-Şūfī’s and al-Bīrūnī’s works. In any case, in his depiction of Cancer in the observation log for 1589 (Figure 2), Præsepe is shown as a cluster of 10 small points in the front part of the breast of Cancer between the stars labelled ‘4’ and ‘5’. Most likely these points represent individual stars. Tycho did, however, still follow the traditional nomenclature for Præsepe as shown by the names that he used for this object in his observation logs and star catalogues (e.g. ‘Præsepe and the nebulosity in the breast [of Cancer]’ 17 and ‘The nebulosity in the breast [of Cancer] which is called Præsepe’ 18 ).
Tycho Brahe’s drawing of Cancer in his observation log of 1589. GKS 312 b Folio, f. 224b, courtesy Det Kongelige Bibliotek, Copenhagen.
As will be demonstrated below, it seems certain, however, that Tycho and his assistants did in fact resolve individual stars in Præsepe. As Tycho generally determined the position of stars with sub-arcminute precision, it seems probable that he formulated a strategy for the observation of Præsepe as a cluster of individual faint stars and communicated this strategy to his assistants who would be performing the actual observations. Unfortunately, Tycho’s records do not contain any information regarding this. Analysis of the observations does, however, indicate that an observation strategy was indeed developed and used by the observers for recording of astronomical coordinates for Præsepe, as will be discussed below.
The observations
A main objective for Tycho in his restoration of astronomy was to prepare a new star catalogue comprising celestial coordinates for 1000 stars with an accuracy significantly superior to that of the existing catalogues. The star catalogues traditionally listed ecliptic coordinates, and while these could be determined by direct reading off zodiacal armillary instruments, the complex construction of these instruments resulted in inferior accuracy and precision. Ecliptic coordinates could, however, be calculated using trigonometric calculations from a combination of horizontal and equatorial coordinates as well as angular distances between two stars.
Around 1586, Tycho Brahe had at his disposal several very precise astronomical instruments that allowed him to determine horizontal and equatorial coordinates as well as angular distances between stars with unprecedented accuracy. Thus, in the period from 1586 to 1589, Tycho and his assistants recorded a vast number of horizontal and equatorial coordinates for numerous stars, including those in the zodiac and thus also for Præsepe in Cancer. The direct determination of right ascension for the stars was rather cumbersome and was not frequently used by Tycho. Instead, this coordinate was most often determined indirectly using the angular distance between the target star and one of Tycho’s fundamental stars whose coordinates had previously been determined with very high accuracy and precision (α Leonis or γ Geminorum was used for Præsepe). The right ascension of the star in question might then be calculated from these measurements.
The first observation of Præsepe was recorded in the observation log for 7 Feb 1586. 19 Observations of this celestial object continued in 1587, 20 and while none were recorded in 1588, the observations were continued in 1589 when the last were made on 3 Dec. 21 A total of 38 observations of Præsepe were recorded for these years.
An object as faint as Præsepe is preferably observed under a dark sky. All observations of Præsepe were carried out in the months of January, February, March and December, when this object passed the meridian at times between 9 PM and 3 AM the following morning, that is, at least 3 hours after sunset or before sunrise. In all cases except two, which will be discussed below, the observations of Præsepe were performed when the moon was below the horizon when Præsepe passed the meridian and the moonlight would thus not encumber the determination of celestial coordinates for this faint object.
Although it is not necessary to determine the declination of a celestial object at the meridian, it is advantageous to do so, since atmospheric refraction is minimal at the meridian transit and it is assumed that Tycho measured the coordinates of celestial bodies on the meridian whenever possible. For the determination of the right ascension of Præsepe as described above, it is obviously not possible to measure the angular distance between Præsepe and either α Leonis or γ Geminorum when both objects transit the meridian. It may be assumed, however, that Tycho made these determinations close to the meridian transit of Præsepe when the other observations of this object were optimal.
Meridian altitude determinations
Meridian altitude determinations for Præsepe were performed in February 1586 22 and in January and February of 1587 23 with two instruments, the Quadrans Muralis (the mural quadrant) and the Quadrans Volubilis (the revolving quadrant). The results are presented in Table 1. The two meridian altitude values for 7 Feb 1586 24 (observations 1 and 2) are probably not correct as the value of meridian altitude closest to these for any star in M44 is 55°09ʹ3ʺ (for HIP 42549). The discrepancy may be due to a copying error mistaking the digit ‘0’ for ‘9’. For the subsequent calculations in this article, the values of meridian altitude for 7 Feb 1586 are corrected by subtraction of 9′. The validity of this correction will be corroborated in a later section analysing the data in a star table based on the data of 7 Feb 1586. It should be mentioned that the provenance of the values of meridian altitude for 7 Feb 1586 in the Tychonis Brahe Dani Opera omnia has not been established. 25
Meridian altitude values of Præsepe Cancri.
Note that the two altitude values recorded on 5 Feb 1587 (observations 8 and 9) differ by no less than 4′. These determinations were made with two different instruments, the first with the revolving quadrant in the underground observatory Stjerneborg and the second with the mural quadrant mounted on the western wall in the southwestern room of Tycho’s castle Uraniborg. As these observation locations were physically separated, the two observation teams had no way of correlating the observations with each other and the readings must consequently be considered reliable. Both quadrants had a mean accuracy better than 40ʺ, 26 and a review by Tycho of the observations for 5 Feb 1587 must have revealed the uncommonly large deviation between the two determinations; no comment, however, was entered in the observation log to explain the large difference between the two simultaneous altitude determinations.
The meridian altitude determinations are distributed in three discrete groups. Group 1 (observations 1 and 2) with a mean value of 55°19ʹ13ʺ, Group 2 (observations 7, 8 and 22) with a mean value 55°1ʹ50ʺ and Group 3 (observations 9 and 23–27) with a mean value of 55°5ʹ20ʺ. This grouping clearly indicates that the altitude determinations were made on different stars, a hypothesis that has been further investigated below.
Right ascension determinations
The difference in right ascension between Præsepe and α Leonis was determined on 7 Feb 1586, 27 probably with the Armillæ Æquatoriæ Maximæ (the great equatorial armillary sphere). The results are listed in Table 2, observations 3–5. Also shown in the table is the arithmetic mean of the determinations (row 4) and Tycho’s recorded mean value for the observations 28 (row 5) which agrees well with the arithmetic mean value.
Difference in right ascension between Præsepe and α Leonis.
The actual right ascension of Præsepe was obtained from the measured difference with respect to α Leonis by a simple subtraction of this value from the right ascension of the latter star. α Leonis was one of Tycho’s fundamental stars and its coordinates had been determined previously with great accuracy. 30
The considerable difference between the three values of right ascension will be discussed below in the context of identification of the star observed, based on this celestial coordinate.
Declination determinations
A total of 15 determinations of declination for Præsepe were recorded in Feb 1586, 31 Feb 1587 32 and in Jan and Feb 1589. 33 They were determined with the great equatorial armillary sphere and the results are shown in Table 3.
Declination values of Præsepe.
From the table it is noted that the values are distributed in two discrete groups, the first of declination values recorded on 7 Feb 1586 through 23 Feb 1587 (observations 6, 10–17 and 28–29) with a mean value of 20°59ʹ23ʺ and a standard deviation of the mean of 37ʺ and the second of declination values recorded on 29 Jan 1589 and 10 Feb 1589 (observations 30–31 and 34–35) with a mean value of 21°4ʹ15ʺ and a standard deviation of the mean of 34ʺ.
The difference in the values of declination, 4ʹ52ʺ, for the two groups is 7.5 times larger than the average error of the great armillary sphere (38ʺ.6) 34 and the low standard deviations of the mean of the values in the two groups clearly indicate that they represent declination values for two different celestial objects. This was confirmed by a t-test which shows that the probability that the data represent two different populations is higher than 99.9%.
For the observations made on 10 Feb 1589 (observations 34–35), Tycho added three notes in the observation log relating to the fact that the moon was visible in the sky on that date. 35 Stars as faint as those in Præsepe should, as mentioned above, preferably be observed in a dark sky and the presence of the moon was obviously a concern. The moon was also above the horizon on 5 Feb 1587 (observations 10–17), but in that case Tycho made no comments regarding this issue. Whether the moonlight did in fact make the observations of Præsepe less accurate and precise will be evaluated in a later section.
Determination of the angular distances between Præsepe and α Leonis or γ Geminorum
In 1582, Tycho introduced his Sextans Astronomicus Trigonicus pro Distantiis (triangular astronomical sextant for distances). This instrument was used to measure angular distances between two celestial objects and it became one of Tycho Brahe’s favourite astronomical instruments. Tycho used the sextant to measure the angular distance between Præsepe and two of his fundamental stars, α Leonis and γ Geminorum. The distance to α Leonis was measured on 5 Feb 1587 36 and 29 Jan 1589 37 observations 18–21 and 32–33) and the distance to γ Geminorum on 3 Dec 1589 38 (observations 36–38). The results are shown in Table 4. As seen in this table, the angular distances between Præsepe and α Leonis (observations 18–21 and 32–33) are very similar, with a mean value of 22°31ʹ41ʺ and a standard deviation of the mean as low as 24ʺ, that is, a very high precision. Furthermore, it should be noted that the determinations made on 5 Feb 1587 and 29 Jan 1589, that is, separated by almost 2 years, resulted in essentially the same angular distance. This fact indicates that the observers pointed the sextant at an individual star in Præsepe and not at a less well defined ‘middle of a nebulous swirl’.
Distances from Præsepe to α Leonis and γ Geminorum.
The first of the three distance measurements between Præsepe and γ Geminorum (observation 36) differs about 2ʹ from the other two (observations 37–38). This rather high discrepancy might be due to a misreading of the numeral ‘16’ in place of ‘18’ in the observation log. This is, however, hypothetical and the values as recorded in the observation log will be used for the calculations discussed below.
Influence of moonlight on the accuracy and precision of the observations of Præsepe
As mentioned above, the moon was above the horizon on two of the nights when Tycho determined the declination values for Præsepe, namely on 5 Feb 1587 39 and 10 Feb 1589. 40 This section will investigate whether the accuracy and precision of the measurements were negatively affected by this issue.
On 5 Feb 1587, the moon was 51% illuminated and was 25° above the horizon. There are, however, no remarks in the observation log for that day to indicate that Tycho deemed the moonlight to negatively affect the observations. Unfortunately, there are no observation data in the log to evaluate if the moonlight did in fact reduce the accuracy for the Præsepe observations. The observations were, however, very precise as shown by the fact that the declination values for this date have a mean of 20°59ʹ9ʺ with a standard deviation of the mean of no more than 30ʺ, indicating that the moonlight did not degrade precision of the observations.
On 10 Feb 1589, the moon was 37% illuminated and only 16° above the horizon and the conditions were thus somewhat more favourable than on 5 Feb 1587. In this case, however, Tycho was concerned about the moonlight as is evident from three notes he made to the observations of 10 Feb 1589. 41 The first note was entered prior to the data from the observations: ‘Repetition of declination [determination] for as many stars in Cancer as could be seen in the bright light of the moon’. The second was entered as a comment to the observations of Præsepe and read: ‘Præsepe (dubious because of the moon)’. The third was made at the end of the declination determinations: ‘The declination of several stars in Cancer could not be observed this evening due to the light of the new moon or were obscured by it at other times. Thus, maybe these declinations will be repeated sometime when the moon is hidden, although they essentially may be acceptable’. As stated in Tycho’s first note, the declination determination made on 10 Feb 1589 was a repetition of determinations made on 29 Jan of the same year when he observed all 15 stars that he had registered in Cancer. 42 On 10 Feb 1589, however, Tycho was able to record the declination for only 7 of these 15 stars.
A comparison of the declination values for the seven stars determined on both dates was made to evaluate the potential negative effect of the moonlight on the accuracy and precision of the determinations made on 10 Feb 1589. In addition to Præsepe, the six other stars were: HIP 40167 (Tegmine), HIP 42911 (Asellus Australis), HIP 42806 (Asellus Borealis), HIP 43103, HIP 44066 (Acubens) and HIP 44798.
The true declination values for these stars on the two dates were calculated using the following procedure.
Values of right ascension, declination, parallax, proper motion in right ascension and declination as well as radial velocity for the stars were obtained from the Extended Hipparcos Compilation (XHIP) catalogue 43 accessed using the Vizier online catalogue.
The values of right ascension and declination were then corrected for proper motion in right ascension, declination and radial velocity as described by Nash. 44
The coordinates corrected for proper motion were subsequently precessed, using the precession matrix, equation 1 in Hilton et al. 45 with the P03 expressions for equatorial coordinates set out in equations 40 of Capitaine et al. 46
The precessed coordinates were then corrected for nutation with the IAU 2000A procedure described by Kaplan, 47 using the IAU 2000A Nutation Series included in the same document.
Finally, aberration was calculated and corrected for, using the procedure described by Meeus. 48
In the following these methods will collectively be referred to as the ‘current procedure’.
Assuming that Tycho’s declination determinations were made at, or close to, the meridian, his values were corrected for refraction as described in a report in preparation. 49
The error in declination for Tycho’s observations of the seven Cancer stars on 29 Jan and 10 Feb, respectively, was calculated as the difference between Tycho’s values corrected for refraction and the true declination values calculated as described above. These results are shown in Table 5 together with the mean error (accuracy) and standard deviation of the mean error (precision) for the measurements made on the two dates.
Error in declination determinations made on 29 Jan and 10 Feb 1589.
The results in Table 5 show that the mean error for the observations made on 10 Feb 1589 was 1ʹ5ʺ compared to 26ʺ for the observations made on 29 Jan 1589, while the standard deviation of the mean error for both sets of measurements was essentially the same (38ʺ vs 31ʺ). This would indicate slightly inferior but not significantly worse conditions on 10 Feb 1589, possibly due to the moonlight.
For Præsepe the difference between the two declination values on 10 Feb 1589 was 1ʹ30ʺ. Thus, this variation in the measurements of declination for Præsepe on this date is similar to the mean error for the other stars investigated. It may thus be concluded that even if the other stars in Cancer have greater apparent magnitudes, the measured declination value for Præsepe was determined with almost the same accuracy as the brighter stars on 10 Feb 1589, even in the presence of moonlight.
The conclusion is that Tycho was correct in assuming that the results of the declination determinations for the stars in Cancer including that of Præsepe made on 10 Feb 1589 were in fact slightly inferior due to the moonlight. The error in accuracy is, however, quite small, and Tycho’s conclusion that the determinations ‘essentially may be acceptable’ was also correct.
Identification of Tycho’s Præsepe
It seems evident from the analysis of Tycho’s astronomical measurements for Præsepe listed in the sections above that the values of meridian altitude, declination and the angular distances of this object to either α Leonis or γ Geminorum, and possibly also the difference in right ascension to α Leonis, were not the result of inaccurate observations of some arbitrarily defined centre of M44. On the contrary, there is little doubt that the different values for these celestial coordinates refer to individual stars in the open star cluster M44.
As a consequence of this conclusion, an investigation was carried out to determine which stars may have been observed during Tycho’s different observation campaigns. As mentioned above, there are 10 stars in the central part of M44 with MagV values below 7. Of these, six could be excluded based on large differences between Tycho’s observed values for the measured coordinates and the theoretical coordinate values for the stars in question. The remaining four stars (HIP 42497, HIP 42549, HIP 42556 and HIP 42600) were used as reference stars in the procedure used for the identification of individual stars observed in Præsepe. In the following sections, theoretical values of meridian altitude, right ascension and declination for these reference stars as well as their distances to Tycho’s fundamental stars α Leonis or γ Geminorum were calculated and compared with Tycho’s values. Based on this comparison it has been possible to identify the individual stars in M44 that Tycho and his assistants observed as they determined the different coordinates for Præsepe.
Meridian altitude
Declination values for the four reference stars listed above were calculated for all relevant dates by the current procedure; the declination values were then converted to the corresponding meridian altitude values by addition of the colatitude. Tycho’s meridian altitude values were corrected for refraction as described. 50
To identify individual stars in M44 based on Tycho’s meridian altitudes for Præsepe, the theoretical values for the reference stars were subtracted from Tycho’s values [as mentioned, Tycho’s two meridian altitude values for 7 Feb 1586 were corrected by subtraction of 9ʹ]. The results are presented in Table 6.
Identification of Præsepe stars from values of meridian altitude.
For each of Tycho’s meridian altitude determinations, the reference star with the lowest difference in meridian altitude relative to Tycho’s value was assumed to be the one observed. These are marked in bold font. Where the difference values were similar, the selection between the reference stars was evaluated further (see below).
The identifications in Table 6 may be summarised as follows:
7 Feb 1586, observations 1 and 2 HIP 42549
27 Jan 1587, observation 7 HIP 42497 or HIP 42556
5 Feb 1587, observation 8 HIP 42497 or HIP 42556
5 Feb 1587, observation 9 HIP 42600
17 Feb 1587 observation 22 HIP 42497 or HIP 42556
21 Feb 1587, observation 23 HIP 42600
23 Feb 1587 observations 24–27 HIP 42600
For the observations made on 27 Jan 1587 (observation 7), 5 Feb 1587 (observation 8) and 17 Feb 1587 (observation 22), the identification is not straightforward as the difference between Tycho’s meridian altitude values and those of the indicated reference stars is less than 1ʹ, which is within the range of uncertainty for the altitude determinations. This is illustrated in Figure 3 51 which is a photograph of the pertinent part of M44. The figure shows five stars of apparently similar magnitude. The three stars TYC 1395-1677-1, TYC 1395-1993-1 and TYC 1395-2711-1 do, however, have MagV values of 7.481, 7.473 and 7.310 respectively and they were considered so faint that it would be questionable if they could be observed; they were therefore not included in the evaluation. Thus, only the two reference stars HIP 42556 and 42497 with MagV values of 6.343 and 6.756, respectively, were considered relevant as the possibly observed stars.
The ‘1′ band of stars’ in M44. Author’s photo.
It is actually rather difficult to select between these two stars as the meridian altitude values are very similar. For the observations made on 27 Jan 1587 and 17 Feb 1587 (observations 7 and 22), the most obvious choice for the star observed by Tycho is HIP 42556, as it has a lower difference with respect to Tycho’s value than HIP 42497 and it is somewhat brighter. For observation 8 made on 5 Feb 1587, it is possible that HIP 42497 was the target, as it has the lowest difference in meridian altitude value (6ʺ) relative to that of Tycho’s for the two stars in question. It cannot be ruled out, however, that the star observed was HIP 42556 as the difference in meridian altitude relative to that of Tycho’s is quite low (38ʺ), but, more importantly, it is the brightest star in M44.
In conclusion, it may be stated that based on the meridian altitude determinations for Præsepe, 8 out of 11 observations could be linked to individual stars with a high probability: HIP 42549 (two observations), HIP 42600 (six observations). Two of the meridian altitude values of the remaining three observations could be assigned to HIP 42556 with a reasonable probability, while the last one was tentatively assigned to HIP 42497.
Right ascension
To investigate if Tycho’s determinations of right ascension for Præsepe, calculated from its difference to α Leonis, could be related to individual stars in M44, the values of right ascension for the four reference stars were calculated by the current procedure and compared with those determined by Tycho. As mentioned above, Tycho’s values were calculated from the observed difference in right ascension between Præsepe and α Leonis. These values were not corrected for refraction as it was assumed that Præsepe was at, or close to the meridian where the correction for refraction in right ascension is zero.
For the comparison, the difference between the right ascension values for the reference stars and Tycho’s stars were calculated and the results are shown in Table 7, observations 3–5. In each row the reference star with the lowest difference in right ascension with respect to Tycho’s values was assumed to be the one observed by Tycho. These are marked in bold font.
Identification of Præsepe stars from right ascension values.
There is great variation in the results; but as there were only three observations, it is not meaningful to calculate the standard deviation to assess precision. To improve the basis for an identification of the Præsepe star for these observations, the mean error and the variance of the error relative to the four reference stars were calculated, rows 4 and 5. Instead of the standard deviation, the variance was used as a measure for the precision of the results. Based on this parameter, it is indicated that HIP 42549 was observed. From Table 7, row 4 it is furthermore seen that HIP 42549 has the lowest mean error compared to Tycho’s values. Taken as a whole, the results in Table 7 suggest a tentative identification of HIP 42549 as the Præsepe star based on the right ascension data.
In a note below the three entries in the log, Tycho has added the following comment: ‘One may use 22°27ʹ’. 52 This might indicate that he was not certain which value to trust and consequently used all the recorded values to get a mean value of 22°27ʹ, in good agreement with the arithmetic mean of 22°26ʹ40ʺ which is quite close to the value for HIP 42549 (22°26ʹ16ʺ).
Declination
To investigate if the declination values for Præsepe listed above could be related to individual stars in M44, the values of declination for the reference stars were calculated by the current procedure. Tycho’s values of declination were corrected for refraction as described. 53 The differences between the declination values for the reference stars and those determined by Tycho were calculated and are presented in Table 8. In each row the reference star with the lowest difference in declination with respect to Tycho’s values was assumed to be the one observed by Tycho. These are marked in bold font.
Identification of Præsepe stars from declination values.
The results for 7 Feb 1586, 5 Feb 1587 and 23 Feb 1587 (observations 6, 10–17 and 28–29) clearly indicate that HIP 42600 was the star whose declination was determined by Tycho on these dates. The number of declination values related to HIP 42600 (11) furthermore allows a validation of this identification by statistical means. A one sample two tail t-test shows that the declination values of observations 1–11 are identical to those of HIP 42600 with a confidence level of 96%. The same test applied to the centre of M44 shows that the probability that these declination values could be related to the centre of M44 is less than 0.1%.
Finally, it seems clear from Table 8, observations 30–31 and 34–35, that it was HIP 42549 that was the target of the observations on 29 Jan and 10 Feb 1589.
It may thus be concluded that, based on the declination values, two stars in M44 have been identified beyond reasonable doubt as those observed by Tycho: HIP 42600 (11 observations) and HIP 42549 (4 observations).
Distances between Præsepe and the fundamental stars, α Leonis and γ Geminorum
The distances between the four reference stars and either α Leonis or γ Geminorum were calculated as described by Meeus. 54 The required values of right ascension and declination for the four reference stars were calculated by the current procedure. The distances calculated in this way were then deducted from the distances listed by Tycho and the resulting differences are shown in Tables 9 and 10, respectively.
Identification of Præsepe stars from distances to α Leonis.
Identification of Præsepe stars from distances to γ Geminorum.
In each row the reference star with the lowest difference in distance with respect to Tycho’s values was assumed to be the one observed by Tycho. These are marked in bold font.
For the six determinations where the distance between Præsepe and α Leonis was measured, it is clear that it was HIP 42549 that was the target star.
The three determinations of the distance between the reference stars and γ Geminorum point clearly to HIP 42549, as the star to which the distance to γ Geminorum was measured.
Summary
Based on the evaluation presented in the previous sections, the following stars have been identified as probable candidates for Tycho’s Præsepe:
HIP 42497 1 Meridian altitude value (tentative)
HIP 42549 2 Meridian altitude determinations (certain)
− 4 Declination determinations (certain)
− 9 Distance determinations (certain)
− 3 Right ascension determinations (probable)
− In total, 15 certain identifications and 3 probable identifications
HIP 42556 2 Meridian altitude determinations (certain)
− In total, 2 certain identifications
HIP 42600 6 Meridian altitude determinations (certain)
− 11 Declination determinations (certain)
− In total, 17 certain determinations
The identified stars are all faint with MagV values as follows: HIP 42497–6.756, HIP 42549–6.589, HIP 42556–6.343 and HIP 42600–6.824.
The tentative identification of HIP 42497 as Præsepe may be questionable. It is possible that the star should be HIP 42556 as the difference in meridian height with respect to Præsepe is only 32ʺ and this difference could easily be explained as an error of observation. Furthermore, HIP 42556 is brighter than HIP 42497.
It is remarkable that the brightest star in M44, HIP 42556, was the target of only two, possibly three observations.
Hence, it has been shown that the analysis 34 out of 38 Præsepe observations resulted in certain identifications of individual stars in M44, three resulted in probable identifications and one was tentative. None were inconclusive.
Accuracy and precision of the determinations
The validity of the above identifications was further evaluated by calculation of the mean error (accuracy) and the standard deviation of the mean error (precision) for the difference determinations that were used as basis for the identification of the individual stars in M44.
The accuracy and precision for the differences in meridian altitude, declination and angular distance to a reference star between Tycho’s values and those of the reference stars are presented in Table 11. The table does not include calculations based on right ascension as the data was insufficient (three observations).
Accuracy and precision of the determinations.
From Table 11 it is seen that the values of the mean error and the standard deviation of the error are very low. This is a strong indication that the observations of Præsepe by Tycho and his assistants were indeed aimed at the individual stars identified above and not at an arbitrarily defined centre of a nebulous object.
Tycho’s strategy for the observations of Præsepe
Tycho conducted three observation campaigns of 15 stars in Cancer during the period 1586–1589. They included a total of 162 observations; Præsepe accounted for 6 out of 22 observations in 1586, 23 of 34 in 1587 and 9 of 106 in 1589. The disproportionately high number of Præsepe observations in 1586 and 1587 compared to other stars in Cancer indicates that Tycho in the first 2 years focused his efforts on improving the observation techniques for the faint stars in Præsepe. This is corroborated by the fact that the observers determined coordinates for three different stars in 1586 and 1587 (HIP 42549, HIP 42556 and HIP 42600). In 1589, the situation had changed completely. Only 9 of 106 observations in Cancer were aimed at Præsepe and all nine exclusively at HIP 42549, a clear indication that Tycho’s team could now observe individual stars in M44.
Apparent magnitude of the observed stars
The main objective of the investigation reported in this article has been to determine whether the seemingly inaccurate measurements of celestial coordinates for Præsepe in Cancer were indeed that, or whether they were the result of observations of individual stars in the open star cluster M44, the central part of which constitutes Præsepe. As discussed above, it seems clear that the observed coordinates did indeed relate to individual stars. It is, however, remarkable that Tycho did not list the three stars observed in Præsepe by individual names in his observation logs or star catalogues but only by terms such as ‘Præsepe’ or ‘Nebulosa ♋’. Furthermore, for these stars he always referred to their apparent magnitude by the term ‘nebulosa’, or abbreviated forms of this word. How might we explain these naming practises?
In the star catalogue contained in Tycho’s major work, Astronomiæ Instauratæ Progymnasmata, 55 Tycho generally specified a value of apparent magnitude which he called ‘Magnit.’ with a range of 1–6, where 6 indicates the faintest stars. For 20 stars, however, he added a dot after the Magnit. value 6 to indicate that the star in question was slightly fainter. For Præsepe he did not, as mentioned, specify a conventional Magnit. value but used the term ‘nebulosa’ or abbreviated forms of this word. This seems strange as there is little doubt that he must have been aware that the observed coordinates and angular distances referred to individual stars in Præsepe. This is corroborated by his choice of a single set of coordinates (that of HIP 42549) that was inserted in all of Tycho’s star tables and catalogues, as will be demonstrated below.
Maybe Tycho considered the Præsepe stars to be so faint that he did not want to assign them a Magnit. value that would be out of the conventional range of 1–6 or his own scale extended with 6 dot.
Tycho’s use of the term ‘Nebulosa’ or equivalent in his star catalogues
To investigate this further, Tycho’s star catalogues and observation logs were analysed to find out if the terms ‘nebulosa’, ‘ne’ or similar abbreviations were used for celestial objects other than the Præsepe stars and whether these terms were used for individual stars, as suggested above, or also for truly nebulous objects like M31.
Twelve records with these terms were found and are shown in Table 12. Of these, 11 can be positively identified to be individual stars while one could be tentatively identified as such (HIP 92761). And note that this analysis of Tycho’s star catalogues did not reveal the existence of any records for truly nebulous objects.
Celestial objects with Tycho’s Magnit. values of ‘nebulosa’ or equivalent.
In column 3 of Table 12 it is seen that for 5 of the 12 entries, Tycho used the term ‘nebulosa’ in the name of the objects just as he did for Præsepe. Columns 4 and 5 show that one of the terms ‘Nebulosa’, ‘Nebul.’, ‘Ne.’ or ‘Neb’ was used to characterise the apparent magnitude for all but one of these objects in either Tycho’s star catalogues or his observation logs. These terms were used indiscriminately with the regular Tychonic Magnit. values ‘6’ or ‘6·’. As mentioned above, Tycho used the notation ‘6·’ to specify a Magnit. value slightly higher than 6, that is, a fainter star. Of particular interest is the Magnit. entry for HIP 4510, ‘6 min. fere nebulosa’ 73 which translates to ‘fainter than 6, nearly nebulosa’. This can only mean that ‘nebulosa’ in this context was used to specify a Magnit. value slightly higher than 6·, that is, a very faint star.
From column 2 in Table 12 it is evident that these stars are indeed faint and that Tycho used terms as ‘nebulosa’ and abbreviated forms of this word to denote apparent magnitude equal to or fainter than indicated by 6 or 6·. The faintest star in Table 12 is HIP 87045 with a MagV value of 6.509, similar to those for the three positively identified Præsepe stars (HIP 42556–6.343, HIP 42549–6.589 and HIP 42600–6.824).
From the data discussed above, it may be concluded that Tycho used the term ‘nebulosa’ or equivalent forms of this term to denote stars with a Magnit. value of 6 or 6·, that is, very faint stars, in his visual magnitude system.
Ptolemy and other astronomers prior to Tycho all included Præsepe as the first entry for the constellation Cancer in their star catalogues. Thus, it is possible that Tycho considered it important that his star catalogue should contain an entry for this object as well and in the same prime position. In any case he selected HIP 42549 which is near the centre of M44 to represent Præsepe even though it was faint. Tycho recorded coordinates for at least seven stars with MagV values between 6 and 7 in his observations logs and they were not included in his star catalogues and that was also the case for the other two stars identified in M44.
Nebulous objects in the star catalogues of other astronomers
In addition to Præsepe (M44), other nebulous objects had been listed in star catalogues since antiquity. Thus, the Double Cluster (NGC 869 & NGC 884), M22, Mel 111 and M7 were included in the star catalogue of Ptolemy 74 and not surprisingly in catalogues of later astronomers who copied Ptolemy’s coordinates and precessed them to their epochs. The names of the four celestial objects in these catalogues often included terms as ‘the middle of the nebulosity’ or equivalent. Although Ulugh Beg based his catalogue on his own observations, he still used terms as ‘Nebulosa’ for Præsepe, as well as for the Double Cluster, Mel 111, M22 and M7. 75
In Tycho’s star catalogues it was different. The Double Cluster is not listed at all in Tycho’s star catalogues. This open star cluster contains a few stars that Tycho might have observed, that is, HIP 11020 (MagV 6.555) in NGC 884 as well as HIP 10805 (MagV 6.695) and HIP 10816 (MagV 6.777) in NGC 869. These stars have MagV values similar to those of the three positively identified stars in Præsepe and yet Tycho did not record any observations of them and consequently, they were not included in his star catalogues. The reason for this may be that NGC 869 and NGC 884 are both surrounded with a very extended halo. Thus, it seems likely that it would have been very difficult, if not impossible, to discern the three faint stars against the luminous background of these halos. M44 in contrast is not surrounded by a halo and the stars identified in this open star cluster were thus seen on a dark background, making it possible to discern the individual faint stars.
Neither is the globular star cluster M22 included in Tycho’s star catalogues. The brightest stars in this cluster have MagV values of 11 and are thus invisible to the naked eye. The apparent magnitude of M22 is, however, 5.1 making it possible to see it as a truly nebulous object without optical aid. Thus, Tycho would have been able to observe M22 as a nebulous object, but nevertheless he did not include it in his star catalogues.
In Tycho’s star catalogues there are no references to the open star cluster Mel 111 as a nebulous object. On the other hand, Tycho included no less than eight individual stars of this star cluster in his star catalogues. In contrast to the stars in the Double Cluster and M22, these stars have MagV values in the range 4.516–5.571 and they are thus significantly brighter. And in contrast to the Double Cluster, there is no halo in Mel 111 to interfere with the resolution of the stars. It must therefore have been easy for Tycho’s observers to resolve the eight stars in this open star cluster that were included in his star catalogues.
M7 or stars in this star cluster are not mentioned by Tycho. The simple reason is that M7 never rises above the horizon at the latitude of his observation site at Hven and he was thus not able to observe it.
Finally, the Andromeda galaxy, M31, which had been described by al-Şūfī as a small cloud in his Book of the Fixed Stars and which is readily visible to the naked eye, does not appear in Tycho’s star catalogues even though he must have been aware of this object.
The conclusion is that Tycho only recorded observations of stars but not of truly nebulous celestial objects.
Sighting faint stars and extended nebular objects with Tycho’s instruments
The design of his advanced parallel slit sights as well as the aiming process are described in detail in Tycho’s De Mundi Ætherei Recentioribus Phænomenis 76 and in the description of his instruments, Astronomiæ Instauratæ Mechanica. 77 Based on information in these documents, Tycho’s procedure to frame a celestial object and determine a given coordinate for it may be described as follows (Figure 4):
To record for example, the altitude of a star, the upper and lower parallel slits of the near pinnacidium 78 were initially adjusted to a large width in order to make the star visible in the slits. The star should be seen through the upper slit on the near pinnacidium lined up against one edge of the cylinder constituting the pinnacidium on the far side of the alidade. At the same instant the star should be visible through the lower slit lined up against the other edge of the cylinder.
Keeping the star visible in the slits, the width of these was reduced ‘in relation to the light from the stars that is observed’, 79 that is, to a narrow slit for faint stars. Tycho assigned an angular size of ⅓′ to a star of magnitude 6 80 and it seems likely that the slits were adjusted in relation to this parameter.
When the star was visible, ‘divided in the middle’ 81 in either slit of the near pinnacidium lined up against the respective sides of the cylinder, the reading of the desired coordinate would be made off the transversal scale on the circumference of the instrument to allow the maximum accuracy possible.
Tycho’s sight. TBOO, vol. V, p. 154.
Given the procedure outlined above, Tycho must have realised that it would be difficult for the different observers to repeatedly locate the same, faint star in Præsepe amidst the other faintly visible stars that were located within a distance of no more than 16′ from each other. Consequently, it seems probable that Tycho devised a strategy for the observation of Præsepe according to which the observer should first locate the group of faint stars in the extended object of Præsepe, then select a star as close to the centre as possible and adjust the sights as described above. Once a faint star had been framed and kept visible in the slits during the sighting process, the accuracy of the required coordinate would not be inferior to that for a brighter star.
Tycho’s sighting process was, without doubt, developed to frame point-like objects as stars. With the method described above it would actually have been extremely difficult to sight a vaguely defined centre of an extended nebulous object. In the case of Præsepe, the brightest stars are situated in a region with a diameter of approximately 40′ near the centre of M44. If Præsepe were indeed a nebulous object, there would be no visible object in the central cluster of the brightest, but putatively invisible stars for the observer to aim at and keep fixed in the narrowing slits of the near pinnacidium during the adjustments. For example, a misalignment of the sight on the mural quadrant of just 5.6 mm would result in a sighting error of 10′, clearly possible in a nebulous expanse with a diameter of 40′.
Naked eye visibility of the stars in M44
As mentioned in the introduction, the faintest star visible with the naked eye under a dark sky has commonly been accepted to have an apparent magnitude value of 6.0–6.5, but sightings of stars with apparent magnitude values as high as 7.0 82 and even 8.0 83 have been reportedly possible for observers with excellent acuity at very dark observation sites.
The MagV values for the identified stars in Præsepe are as follows: HIP 42556–6.343, HIP 42549–6.589 and HIP 42600–6.824. These values are close to or slightly higher than 6.5 but all are below 7 and it would thus be reasonable to assume that they were visible to Tycho’s team as the observations were conducted at a very dark site and as it is certain that Tycho selected his assistants for their observation abilities and skills. 84 That Tycho’s teams were indeed capable of observing stars with MagV values in this range is supported by the fact that they observed the star HIP 87045 in Hercules with a MagV value 6.509; Tycho assigned this star a Magnit. value ‘ne’ (Table 12, row 3) in the star catalogues. This is a documented example that a star with a MagV value as high as 6.5 could be observed by Tycho’s observers.
There are, however, matters that might limit the visibility of faint stars and that need to be considered in the context of this work. These are discussed in an article by Włodarczyk et al. 85 While the focus of their article is planetary conjunctions, some of the issues discussed are relevant for the current article.
The first issue is the darkness of the sky against which the stars are seen. It is certain that the night sky at Tycho’s observation site on the sparsely populated island of Hven at Tycho’s time was very dark, as light pollution was absent. That Tycho was aware of the necessity of a dark sky for stellar observations is clear from the fact that for the vast majority he restricted these to the period from September until March with the exceptions of stars that were visible only outside of this period. Regarding the observations of Præsepe, there is one record indicating that the night sky was not satisfactorily dark, namely on 10 Feb 1589, where Tycho added the comment ‘Præsepe (dubious because of the moon)’. This has been discussed above and it was shown that the light of the new moon did in fact affect the observations but only to an insignificant extent.
A dark sky is a prerequisite for detecting faint objects but it is also necessary that the observers conduct the observations with dark adapted vision. In the article referenced above, it is noted that spatial resolution is reduced with a dark-adapted eye, as the retinal rods are larger than the cones. The resolution is, however, still 1′ with dark adapted vision. The spatial resolution of 1′ would be reduced if the purpose of an observation were to resolve two stars of very different apparent magnitudes. As discussed above, this would not apply to the situation for Tycho’s observers where the stars in Præsepe are all faint with roughly the same apparent magnitude and there are no bright stars in the whole expanse of M44 to interfere with the observations.
Another issue that might reduce the accuracy of stellar observations is the stability of the atmosphere, often referred to as the ‘seeing’. Especially temperature gradients in the atmosphere are detrimental to accurate observations. Tycho was, however, well aware of this phenomenon and he sometimes referred to the seeing conditions with remarks such as ‘It has not been adequately calm’ 86 and ‘For the last observations, it has not been adequately calm’. 87 These remarks clearly refer to the seeing conditions. Importantly, there are, however, no notes indicating degraded seeing conditions for any of the observations of the stars in Præsepe.
Conclusions
Based on the assessments made in the preceding sections, the following conclusions may be drawn:
Tycho used the term ‘nebulosa’ in the names of faint stars other than Præsepe. He also used this term and or abbreviated forms to denote the apparent magnitude of stars as faint as or fainter than those where he used the values ‘6’ or ‘6·’, that is, very faint stars.
Tycho recorded no observations of stars in the Double Cluster though the MagV values of three stars in this object were similar to those of the stars in M44, probably due to bright halos around the Double Cluster. Nor did he, however, as his predecessors had done, include the Double Cluster as a nebulous entity in his star catalogues.
In the open star cluster Mel 111, Tycho recorded eight individual stars in this celestial object but did not record Mel 111 as a nebulous object, again in contrast to previous astronomers.
No truly nebulous celestial objects, for example, the Double cluster, M22 or the great Andromeda galaxy (M31), appear in Tycho’s star catalogues even though he must have been aware of them. It thus appears that Tycho included celestial coordinates in his catalogues exclusively for stars.
Tycho’s slit sights were developed to sight stars with high accuracy. The sights and the sighting process would, however, not allow observation of a vaguely defined centre of an extended nebulous object with the great precision that has been demonstrated for the Præsepe stars.
An evaluation of the aspects discussed in the work of Włodarczyk et al. do not result in any indications that the identified stars in Præsepe could not have been observed by Tycho’s team.
The Cassel observations of Præsepe
Apart from the observations made by Tycho as described above, there are no documented records of previous or contemporary sightings of individual stars in Præsepe. A few observations of Præsepe made under the auspices of Landgrave Wilhelm IV of Hesse-Cassel may, however, have been aimed at HIP 42549, a star which is very close to the centre of M44.
The observations made in Wilhelm’s observatory in Cassel were part of an observation programme carried out during the years 1585–1587 for the construction of a star catalogue. For 1586, the Cassel observation log has two entries of meridian altitude for Præsepe. 88 There are also recordings of the angular distance between Præsepe and two reference stars, Procyon and Castor. 89 These readings for Præsepe are listed in rows 1–3 in Table 13.
Measurements and coordinates from the Cassel observatory.
The table also contains the entries of equatorial and ecliptic coordinates for Præsepe as they appear in the manuscript for the Cassel star catalogue (row 4). 90
From the meridian altitude and the geographical latitude of Wilhelm’s observatory, determined to be 51°19ʹ as reported in the Cassel records, 91 it was possible for Wilhelm’s astronomer, Christopher Rothmann, to calculate the declination for Præsepe to be 21°4ʹ, identical to the value in the star catalogue (row 4). The right ascension of Præsepe may be calculated based on its angular distance to either Procyon or Castor combined with the values of right ascension and declination for either of these stars, coordinates that are recorded in the Cassel star catalogue. The right ascension value for Præsepe based on the distance to Procyon was calculated to be 124°10ʹ5″ in excellent agreement with the value in the star catalogue (row 4). If, however, the calculation is based on the distance to Castor, a value for the right ascension of 124°13ʹ36″ is obtained, differing by more than 3ʹ from the value obtained using Procyon. The subsequent conversion into ecliptic coordinates was done using the declination value and the right ascension value obtained from the distance between Præsepe and Procyon. The angular distance value between Præsepe and Castor was not used at all.
The ecliptic coordinates calculated based on the declination value of 21°4ʹ and the right ascension value of 124°10ʹ5″ were calculated to be 121°36ʹ53″ longitude and 1°14ʹ0″ latitude. These values correspond exactly to the values in the manuscript star catalogue. The longitude differs, however, by 3ʹ from a value of this coordinate communicated to Wilhelm by Tycho Brahe. 92 As demonstrated in a recent study of the Cassel star catalogue, 93 Wilhelm’s ecliptic longitudes differed, however, by 6ʹ from the true value, a fact that Tycho had pointed out in a letter to the Landgrave already in 1587. 94
To evaluate the possibility that the Cassel observations of Præsepe might have been directed at HIP 42549, the primary observation data were compared with the true values for HIP 42549.
Thus, the meridian altitude (59°45ʹ) was corrected for refraction to enable comparison with the true value for HIP 42549. The resulting value, 59°44ʹ24″, is very close to the true value for HIP 42549 (59°44ʹ32″) calculated by the current procedure. It should be noted that the Cassel observatory made two identical meridian altitude determinations with an interval of 8 months, indicating that the quadrant had been aimed at a single star in M44. The other primary observations were the angular distance between Præsepe and either Procyon or Castor. The theoretical values for these two distances were calculated as described by Meeus 95 with the precessed equatorial coordinates calculated by the current procedure. The true angular distance to Procyon was calculated to be 20°35ʹ14″, differing by −2ʹ14″ from the Cassel values. The corresponding value for Castor was 19°8ʹ49″, differing by 1ʹ11″ from the Cassel values. The latter results combined with the results of the meridian altitude determinations might indicate that HIP 42549 could have been the target for these observations. It should be noted that, while the value of right ascension based on the angular distance to Procyon was inferior to that based on Castor, it was the former that was used by Rothmann for the Cassel star catalogue.
In conclusion, it seems possible that the observations of Præsepe in Cassel were indeed directed at a single star in M44, HIP 42549. The recorded data of only four observations from the Cassel observatory and the inferior results based on the distance between Præsepe and Procyon do, however, make uncertain any identification of the object in M44 observed as Præsepe at the Cassel observatory.
Discussion
In the first sections of this article, it has been demonstrated that the seemingly inaccurate assemblage of observations of celestial coordinates for the nebulous object Præsepe in Cancer were in fact discrete groups of observations of individual stars in the open star cluster M44. In the following sections it was shown that three or possibly four the stars, HIP 42497, HIP 42549, HIP 42556 and HIP 42600 as they are labelled today in the Extended Hipparcos star catalogue, could be identified as targets for the observations. These stars are all located in the central part of M44 which contains the brightest stars in this cluster.
The validity of the identification of these stars is shown by the fact that out of Tycho’s 38 measurements of astronomical coordinates for Præsepe, 34 could be positively assigned to one of the four stars. The identification of these stars is further corroborated by the high accuracy and precision of the determination of Tycho’s coordinates when compared to the equivalent coordinates calculated for the reference stars.
Tycho must have realised that it would be difficult for the different observers to repeatedly locate the same, faint star amidst the other faintly visible stars that were located within a distance of no more than 16ʹ from each other. Consequently, it seems probable that Tycho devised a strategy for the observation of Præsepe, optimised in the years 1586 and 1587 when a disproportionately high number of observations of Præsepe were carried out compared to the 14 other stars in Cancer. The details of this strategy are not known, but it may be assumed that the observers should first locate the extended object of Præsepe, then select a star as close to the centre as possible and finally determine the celestial coordinate in question by the aiming procedure described above. The average number of Præsepe observations in 1589 indicates that a reliable procedure for the observations of the faint stars was at hand at that time and that it was used by Tycho’s team to determine the definitive coordinates for Præsepe.
A spectacular demonstration of the ability to consistently aim the sights at the same object is given for observations made with the triangular sextant to measure the angular distance between Præsepe and α Leonis. On 7 Feb 1587 a mean value of 22°31ʹ42″ was obtained while almost 2 years later, on 29 Jan 1589, a mean value of 22°31ʹ38″ was recorded. It is inconceivable that these almost identical results could have been achieved had the sextant been aimed to determine the angular distance between α Leonis and an arbitrarily defined centre of an extended nebulous object.
It has finally been shown that Tycho did not include truly nebulous objects in his star catalogues but only individual stars. Names of very faint stars as those in Præsepe often contained the term ‘nebulosa’ and values of apparent magnitude – Magnit. in Tycho’s terminology – were frequently given as ‘Nebulosa’, ‘Nebul.’ or ‘Ne.’ indicating that they were fainter than stars with a Magnit. value of 6 or even 6·.
Præsepe in Tycho’s star catalogues
As mentioned above, one of Tycho’s objectives for his astronomy project was to compile a star catalogue containing the celestial coordinates for 1000 stars. In the course of this process, a number of preliminary star catalogues and tables were compiled, all of which contain equatorial and/or ecliptic coordinates for Præsepe.
All entries were reduced by precession to an epoch 96 specific to the particular catalogue or table. Tycho was not explicit regarding his calculation of precession for the equatorial coordinates. His table of 100 stars 97 does, however, contain values of right ascension and declination for the end of the years 1600 and 1700 CE as well as the difference between these. The text prior to this table explains that the equatorial coordinates for any year between 1600 and 1700 for the stars in the table may be obtained by interpolation. The difference values in this table are in fact Tycho’s precession values for a 100-year period. These precession values may as well be used for the period a few decades prior to this, that is, the epochs for all of Tycho’s star catalogues. Importantly, the table contains values for the stars relevant for this article, viz., Præsepe, α Leonis and γ Geminorum. These values were used to calculate Tycho’s precession for the equatorial coordinates.
For the ecliptic coordinates Tycho used a value of 51″ per year for precession in longitude 98 and although he had demonstrated that latitude changes slightly over several centuries it was sufficiently constant in the context of his star catalogues that Tycho did not correct this coordinate for precession. 99
In an explanatory note made for one of his star catalogues Tycho explains how the coordinates in the different star catalogues and tables were obtained: ‘Catalogue containing right ascensions, declinations and derived from these, ecliptic longitudes and latitudes for all stars of the zodiac (that were observable) which have been faithfully measured in the heavens at the subterranean observatory of Uraniburg in the year of 1589’. 100 The different star catalogues and tables are described below in order of their times of compilation:
On 18 Jan 1587 Tycho sent a letter to Wilhelm IV, Landgrave of Hesse-Cassel, regarding observations that both parties had carried out of the comet of 1585. 101 Tycho had noted that the ecliptic longitudes of some stars that Wilhelm previously had communicated to him in this context differed by as much as 5′ or 6′ from his own. 102 Thus, in return he sent Wilhelm some tables with his own coordinates for the same stars. Among these was a table containing the ecliptic longitudes and latitudes of 52 stars, including those of Præsepe. 103 The ecliptic coordinates in this table were reduced to the beginning of 1587 [epoch 1587]. Below, this table will be labelled The 52 Star Table of 1587.
An appendix to the observations of 1589 contains a list of ecliptic longitudes and latitudes as well as values of right ascension and declination for 312 stars in the zodiac. 104 Below, this will be termed The Zodiac Catalogue. This catalogue is based on observations made in 1589 as stated by Tycho in an explanatory note to the catalogue. It is not mentioned to which epoch the coordinates have been precessed, but in a list of right ascension values for a number of Tycho’s fundamental stars preceding the catalogue, Tycho has stated that the right ascension for α Arietis was reduced ‘ad init. 89’, 105 that is, to the beginning of 1589 [epoch 1589]. It will be assumed that the coordinates in this catalogue have been reduced to this epoch as well.
An appendix to the observations of 1592 offers a catalogue containing ecliptic longitudes and latitudes as well as values of right ascension and declination for stars of all constellations 106 reduced to the end of 1588 [epoch 1589]. This catalogue contains 777 named stars, but it is incomplete as some coordinates, especially values of right ascension and declination for several stars, are missing. This catalogue will be labelled The Draft Catalogue. The zodiacal stars included in this catalogue have coordinates that, with few exceptions, are identical to those listed in The Zodiac Catalogue.
The star catalogue contained in Tycho’s main opus, Astronomiæ Instauratæ Progymnasmata, labelled The Progymnasmata Catalogue in this article, lists the ecliptic longitude and latitude for 777 stars 107 ; it is complete and the coordinates are reduced to the end of 1600 [epoch 1601]. The listed stars are, with a few exceptions, identical with those of The Draft Catalogue and it is very probable that this catalogue was used by Tycho as a template for The Progymnasmata Catalogue.
The star table mentioned above, containing right ascension and declination values for 100 selected stars precessed to epochs 1601 and 1701, 108 was included in Astronomiæ Instauratæ Progymnasmata and was a supplement to The Progymnasmata Catalogue. It presents equatorial coordinates for 100 important stars. This table will be referred to as The 100 Star Table.
Tycho’s final star catalogue with 1004 entries expands The Progymnasmata Catalogue from 777 to 1004 stars, reduced to epoch 1601. 109 The catalogue lists ecliptic longitudes and latitudes for the stars; it was prepared by Tycho in Wandsbeck in 1598 after his departure from Denmark. It includes the 777 stars of The Progymnasmata Catalogue supplemented with coordinates for stars observed in 1595 ‘that were desired for the catalogue’ 110 and in 1597 ‘60 [stars] that are desired to fill a number of 1000’. 111 The catalogue was not printed in Tycho’s time but was circulated in manuscript to some of his correspondents as well as to the Holy Roman Emperor, Rudolph II. Below, it will be termed The 1004 Star Catalogue.
A star table appended to The 1004 Star Catalogue contains equatorial and ecliptic coordinates for 36 selected stars, one for each sign in the zodiac, that is, 12 stars, as well as 12 stars each north or south of the ecliptic. 112 The coordinates in this table were precessed to 1552, the year of birth of Rudolph II. Obviously, Tycho hoped that this detail would improve his prospects of obtaining the position as Rudolph’s imperial mathematician. It has been labelled The 36 Star Table of 1552. This table is based on The Progymnasmata Catalogue and does not contain any additional information. Thus, it will not be discussed in detail below.
Tycho’s 1004 star catalogue, as well as excerpts from it, appear in several works published by his successors, the most notable being the Tabulæ Rudolphinæ of Johannes Kepler. 113 As this catalogue contains some amendments made by Kepler, it will not be included in this analysis.
Evaluation of the Præsepe coordinates in the star catalogues
Using the general procedure described below, Tycho’s coordinates for Præsepe in each of the star catalogues or tables listed above were investigated to determine (i) which sets of primary observation data were used to calculate the listed equatorial and or ecliptic coordinates and (ii) to determine the star whose coordinates were listed in the star catalogues and tables.
Identification of dates where observations sufficient for the calculation of the equatorial coordinates (right ascension and declination) were made. A priori, it is not clear whether Tycho combined observation data from different dates for the calculation of the coordinates for the star catalogues. It will, however, be assumed that Tycho used data obtained during a single observation session as this would eliminate uncertainty due to any instrument adjustments made between the observation dates.
In cases where multiple determinations of a celestial coordinate were made at a single date and the data clearly belonged to a discrete population, the calculations in this work were carried out using the mean value of the determinations. Otherwise, the determinations were treated as separate observations.
For each relevant date, the declination and right ascension were determined as follows:
ο In most cases, the declination for Præsepe had been determined directly. Otherwise, it was calculated from the meridian altitude by subtraction of the colatitude for Uraniborg. It should be noted that Tycho, as described in Progymnasmata, 114 did not correct altitude and declination determinations for atmospheric refraction for stars that were observed at altitudes exceeding 20°. As the observations of Præsepe, α Leonis and γ Geminorum were all made at altitudes higher than 20°, no corrections for refraction were made for Tycho’s declination and meridian altitude values in the calculations used to determine the set of primary observation data. For the identification of the star observed in Præsepe, correction for refraction was made before comparing the coordinates with those of the reference stars.
ο In a single case the right ascension of Præsepe was calculated from the difference of this coordinate between Præsepe and α Leonis. Otherwise, the measured distance between Præsepe and either α Leonis or γ Geminorum was used to calculate the right ascension for Præsepe. This method was a standard procedure for Tycho. In both cases the coordinates for α Leonis or γ Geminorum recorded in Tycho’s list of fundamental stars 115 were precessed to the relevant date of observation prior to the calculation of right ascension for Præsepe.
For the determination of the primary observation data, the equatorial coordinates for Præsepe determined as described above were then precessed by the procedure used by Tycho 116 to the epoch of the star catalogue or table in question and converted to the desired ecliptic coordinates.
Finally, the observation data identified as described above to be those that the equatorial and/or ecliptic coordinates in Tycho’s star catalogues and tables were based on, were corrected for refraction and precessed to the relevant epoch by the current procedure. They were then compared with the coordinates of the reference stars precessed similarly with the purpose of identifying the star that had the best fit to Tycho’s celestial coordinates in the different star catalogues and tables.
The 52 star table of 1587
This star table was included in a letter of 18 Jan 1587 that Tycho sent to Wilhelm IV. It lists the ecliptic longitude and latitude for a number of stars including Præsepe. The observations that were used to calculate the coordinates in the table must obviously have been made prior to the date of the letter and the only Præsepe observations available to Tycho were those made on 7 Feb 1586. They included two values of meridian altitude, a single value of declination and three values of difference in right ascension to α Leonis.
For the calculation of the ecliptic coordinates of The 52 Star Table of 1587, three options exist:
Using the measured declination in combination with the right ascension obtained from the measured difference of this coordinate between Præsepe and α Leonis, and as noted above it seems probable that Tycho would have used the mean of the three determinations (22°27ʹ) 117 for this parameter and this value was used when Tycho’s method of precession was employed. For the modern precession calculations, the arithmetic value of 22°26ʹ40″ was used.
Converting the measured meridian altitude as listed in the observation log to declination by subtraction of the colatitude for Uraniborg and using it with the right ascension as in the first option.
As mentioned above, it may be assumed that the meridian altitude values of 55°19ʹ0″ and 55°19ʹ25″ for Præsepe in the Tychonis Brahe Dani Opera omnia 118 are erroneous and should instead read 55°10ʹ0″ and 55°10ʹ25″. Using the corrected meridian altitude values together with the right ascension as in the second option will be used as a third option for the calculations.
The ecliptic coordinates for Præsepe from The 52 Star Table of 1587 are shown in Table 14, row 1. The observation data of the three calculation options were processed using the general method described above and the resulting ecliptic coordinates are listed in Table 14, rows 2–4 respectively. For the results obtained using the measured declination (row 2) it is noted that while the longitude is in reasonable agreement with the value of the star table, the deviation for the latitude is significant. This is not surprising as the declination used in the calculation referred to HIP 42600, while the right ascension was probably related to HIP 42549.
Præsepe coordinates in The 52 Star Table of 1587.
When the declination was derived from the meridian altitude values listed in the observation log of the Tychonis Brahe Dani Opera Omnia (row 3), it is seen that the ecliptic longitude differs by 2ʹ19ʺ from Tycho’s value in the star table. The value of the ecliptic latitude differs, however, again significantly from Tycho’s value.
In a reverse calculation based on the ecliptic coordinates in this star table, a value of 55°10ʹ36ʺ for the meridian altitude is obtained, being strong evidence that the meridian altitude values listed in the Tychonis Brahe Dani Opera omnia are erroneous. Thus, the correction of −9ʹ to the meridian altitude determinations of 7 Feb 1586 seems justified.
The ecliptic coordinates calculated based on the corrected meridian altitude values (row 4) are in excellent agreement with those of The 52 Star Table of 1587. It seems highly probable that Tycho used these values of meridian altitude for the calculation of the coordinates listed in this star table as the results for the other options differ significantly from those in the star table and as he had no other observation data at his disposal.
Identification of the star in The 52 Star Table of 1587
The primary data for this star table, that is, the mean value of the adjusted meridian altitude, was corrected for refraction and converted to declination by subtraction of the colatitude. The resulting mean value of declination and the arithmetic mean value of right ascension were then precessed to epoch 1587 using the current procedure and converted to ecliptic coordinates. The coordinates as shown in Table 15, row 1 were then compared with those of the four reference stars precessed similarly to epoch 1587 (rows 2–5).
Identification of the star listed as Præsepe in The 52 Star Table of 1587.
The reference star with ecliptic coordinates closest to those calculated based on Tycho’s primary data was considered to be the one observed by Tycho’s team and whose ecliptic coordinates he entered in the The 52 Star Table of 1587.
The results in Table 15 clearly indicate that the ecliptic coordinates for Præsepe that were entered by Tycho in the table sent to Wilhelm IV on 18 Jan 1587 were those of the star HIP 42549.
The Zodiac and the Draft Catalogues
The Zodiac Catalogue lists both equatorial and ecliptic coordinates for the 312 stars including Præsepe. As mentioned in the overview of the catalogues above, the epoch for this catalogue is not stated explicitly but is assumed to be 1589.
The Draft Catalogue similarly lists equatorial and ecliptic coordinates for 777 stars and for this catalogue the epoch is explicitly stated to be the end of 1588 [epoch 1589]. The entries for Præsepe are identical to those of The Zodiac Catalogue except for the ecliptic longitude where a difference of 10ʺ occurs as seen from rows 1 and 2 in Table 16. The difference of 10ʺ for the ecliptic longitude between the two catalogues is probably not due to rounding of this coordinate in The Draft Catalogue, as ecliptic longitude values were often specified to ⅙ or ⅚ of an arcminute in this catalogue. With this insignificant exception the coordinate values for Præsepe in these two catalogues are identical and they will consequently be discussed together in this section.
Præsepe coordinates in The Zodiac and Draft Catalogues.
All of Tycho’s 38 observations of Præsepe performed in the years 1586, 1587 and 1589 were at hand for the calculation of the coordinates for The Zodiac and Draft Catalogues. As mentioned above, it seems reasonable to assume that Tycho used data obtained during a single observation session as this would eliminate uncertainty due to the frequent adjustments that were performed on the instruments. If he did indeed use data from observations made on a single date, he would have had six options with observation data sufficient to determine the desired coordinates for Præsepe for these star catalogues.
7 Feb 1586, 1 Meridian altitude and Difference in right ascension to α Leonis
7 Feb 1586, 2 Declination and Difference in right ascension to α Leonis
5 Feb 1587, 1 Meridian altitude 1 119 and Angular distance to α Leonis
5 Feb 1587, 2 Meridian altitude 2 and Angular distance to α Leonis
5 Feb 1587, 3 Declination and Angular distance to α Leonis
29 Jan 1589 Declination and Angular distance to α Leonis
Below it has been evaluated which of these options Tycho most probably used for the calculation of the coordinates for Præsepe that were included in The Zodiac and The Draft Catalogues. The observation data for the three dates were converted to equatorial and ecliptic coordinates and precessed to epoch 1589 by the general procedure outlined at the beginning of this section. The results are shown in Table 16.
7 Feb 1586. The coordinates of Præsepe were calculated as described above and precessed to epoch 1589. It is seen that the coordinates calculated based on the (corrected) meridian altitude (row 3) agree reasonably well with those of the two star catalogues. In contrast, the declination and ecliptic latitude based on the declination (row 4) disagree significantly from the values in the star catalogues.
5 Feb 1587. For this date, the situation is more complex. The ecliptic coordinates might be calculated based on the two values of meridian altitude. They differed, however, by as much as 4ʹ between each other and it is doubtful if Tycho would have based his calculations on these. Still, both values have been included in this evaluation (rows 5 and 6). It is seen that the resulting coordinates differ significantly from those of the two star catalogues. The coordinates based on the declination (row 7) are quite similar to those of row 6 and differs as well significantly from those of the star catalogues discussed in this section.
29 Jan 1589. The declination for Præsepe and the angular distance to α Leonis were the only data recorded on this date, but they were obtained with Tycho’s optimised observation procedure for faint stars and were sufficient for the calculation of the equatorial and ecliptic coordinates according to the procedure described above. The results are shown in Table 16, row 8 and it is seen that they agree very well with those of The Zodiac and Draft Catalogues (rows 1 and 2).
The question is whether Tycho used the data of 7 Feb 1586 or those of 29 Jan 1589 to calculate the coordinates for these star catalogues. The coordinates based on the data of 29 Jan 1589 agree better with those in the catalogues than those based on the data of 7 Feb 1586. Furthermore, it appears that Tycho generally had more confidence in his most recent data. 120 In conclusion, it is most likely that the observations made on 29 Jan 1589 were those used by Tycho for the calculation of the coordinates in The Zodiac and Draft Catalogues.
Identification of the star in The Zodiac and Draft Catalogues
The identification of the star whose coordinates were entered in The Zodiac and Draft Catalogues was made as described for the previous star catalogue. The primary data for these star catalogues, that is, those obtained on 29 Jan 1589 as described in the previous section, included two values of declination and two of the angular distance between Præsepe and α Leonis. The mean value of the declination values was corrected for refraction and together with the mean value of right ascension then precessed to epoch 1589 by the current procedure. The precessed equatorial coordinates were finally converted to ecliptic coordinates. Both sets of celestial coordinates are listed in Table 17, row 1; they were then compared with those of the four reference stars precessed similarly to epoch 1589 (rows 2–5).
Identification of the star in The Zodiac and Draft Catalogues.
The reference star with equatorial and ecliptic coordinates closest to those calculated for Præsepe based on Tycho’s primary data was considered to be the one observed by Tycho’s team and whose ecliptic coordinates he entered in the The Zodiac and Draft Catalogues.
The theoretical values for the coordinates of HIP 42549 (row 3) are in very close agreement with the precessed coordinates for Præsepe (row 1) and the identification of HIP 42549 as the star listed by Tycho in these two catalogues must be regarded as valid.
The Progymnasmata Catalogue, The 1004 Star Catalogue and The 100 Star Table
As the coordinates for Præsepe in The Progymnasmata and The 1004 Star Catalogues are identical and as they are reduced to the same epoch (1601), they will be discussed together. Closely related to The Progymnasmata Star Catalogue is The 100 Star Table. This table lists right ascension and declination for 100 selected stars, including Præsepe, for epochs 1601 and 1701.
As mentioned in the previous section, Tycho did not observe Præsepe after December 1589, and although he had all Præsepe observations ever made by his team at his disposal, it seems likely that he reused the coordinates from The Draft Catalogue for the catalogues discussed in this section. All Tycho had to do was to reduce the coordinates from The Draft Catalogue from epoch 1589 to epoch 1601.
The Progymnasmata and The 1004 Star Catalogues list ecliptic coordinates and they are presented In Table 18, row 1. The 100 Star Table lists equatorial coordinates (Table 18, row 2).
Præsepe coordinates in The Progymnasmata Catalogue, The 1004 Star Catalogue and The 100 Star Table.
To evaluate whether or not Tycho did in fact use the coordinates from The Draft Catalogue for The Progymnasmata and The 1004 Star Catalogues, the equatorial and ecliptic coordinates of The Draft Catalogue were precessed to epoch 1601 as described above. The results of this calculation are given in Table 18, row 3.
From Table 18 it appears that the coordinates listed in The Progymnasmata and The 1004 Star Catalogues as well as The 100 Star Table (rows 1 and 2) are in very good agreement with those of The Draft Catalogue precessed to epoch 1601 (row 3), corroborating the assumption that Tycho prepared the new catalogues from the older.
Identification of the star in The Progymnasmata, The 1004 Star Catalogue and The 100 Star Table
Since these catalogues were most likely based on The Draft Catalogue, it was expected that the star whose coordinates are listed in these catalogues would be identified as HIP 42549, as was the case for The Draft Catalogue, and the calculations (data not shown) have confirmed that this was the case.
Summary of the evaluation of the Præsepe coordinates in the star catalogues
In the previous sections it has been established which observational data Tycho used to calculate the equatorial and ecliptic coordinates for Præsepe that appear in his various star tables and catalogues.
For The 52 Star Table of 1587 Tycho only had the observation data of 7 Feb 1586 at his disposal. It is furthermore clear, that he could only have obtained the results listed in that table if the values of meridian altitude had been identical with those corrected by subtraction of 9′ from the values listed in the Tychonis Brahe Dani Opera omnia.
For all the other star catalogues and tables, Tycho almost certainly used the results of his most recent observations that would allow the calculation of the equatorial and ecliptic coordinates, that is, the observations of 29 Jan 1589. Finally, it has been demonstrated that the coordinates for Præsepe in all Tycho’s star tables and catalogues represent those for a single star, HIP 42549, in the open cluster M44.
Tycho’s selection of the star labelled Præsepe in the star catalogues
Ptolemy listed Præsepe as the first object in Cancer in his Almagest, 121 a practice that was repeated by several other astronomers well into the Renaissance. In all probability, Tycho must have felt it important that his star catalogues contained the coordinates for Præsepe and in the same prime position as his predecessors’.
Ptolemy described Præsepe in ‘the middle of the nebulous mass in the chest [of Cancer] called Præsepe’ and his practice was followed by several other astronomers until Tycho’s time. Tycho did, however, not include nebulous objects in his star catalogues – only stars. Thus, he was faced with the challenge of resolving the very faint stars in the centre of M44 to determine the coordinates for a star to represent Præsepe; in the previous sections it has been described how Tycho accomplished this.
The observations Tycho performed on Præsepe were thus directed at individual stars which resulted in recording of celestial coordinates for three or perhaps four individual stars in Præsepe in 1586 and 1587. In accordance with his general strategy of preferring his most recent observations, Tycho chose to base his selection of the star to represent Præsepe on his observations of 29 Jan 1589 when his observation methods for the faint stars in Præsepe had reached their final form and the observations were all directed at a single star, HIP 42549.
The decisive factors for Tycho’s selection of HIP 42549 must have been the proximity of this star to the centre of Præsepe (M44) and its brightness. HIP 42549 is just 13″ from the centre of M44 as it is defined today, while HIP 42556 (ε Cancri), the brightest star in M44, but only slightly brighter than HIP 42549, 122 is as distant as 7ʹ40″ from the centre of M44.
Thus, selecting HIP 42549 as the star representing Præsepe appears to be logical and it is remarkable that Tycho made that choice already in 1587, based on the few observations made on 7 Feb 1586; but nevertheless, it was a choice he adhered to for all his star catalogues and tables.
Rawlins’ identification of Præsepe
In an extensive study, Dennis Rawlins has analysed Tycho Brahe’s 1004 star catalogue from 1598. 123 He considered the individual stars in the centre of M44 to be too faint for observation. Consequently, he combined the MagV values for three stars, HR 3428 (HIP 42549), HD 73709 and HD 73785 to obtain a combined MagV value of 5.69 which he considered observable. For the coordinates of this combination of stars, the values for HIP 42549 were chosen because the true coordinates for this star had the best fit to Tycho’s positions.
There are, however, two problems with Rawlins’ procedure. First, the MagV value for HD 73709 cited by Rawlins to be 7.7 is listed as 8.7 in the HD catalogue; 124 the same value is given in the CCDM (Catalog of Components of Double & Multiple stars) 125 which, as the name implies, has focus on nearby stars such as HIP 42549 and HD 73709. Second, the distance between HIP 42549 and the third component star (HD 73785) in the combination is as much as 5ʹ47″, and there is no doubt that Tycho’s observers would have been able to resolve these two stars easily. If the MagV contribution of HD 73785 is omitted and the HD value for HD 73709 is used, the MagV value for the combination of HIP 42549 and HD 73709 is 6.444, not significantly different from 6.589, the value for HIP 42549 by itself. As Tycho’s observers in general would have been able to resolve two faint stars with an angular separation of 1ʹ, the resolution of HIP 42549 and HD73709 should not have been a serious problem. HD 73709 is, however, so much fainter than HIP 42549, that it is doubtful whether this star was even noticed by Tycho’s team of observers.
HIP 42549 has been identified in the sections above as the star representing Præsepe in Tycho’s star catalogues and Rawlins comes to the same conclusion regarding the coordinates for Præsepe. Thus, Rawlins’ assessment of Præsepe, corrected as described, does not contradict the claims of this article.
Conclusion
As part of Tycho’s work to prepare a new star catalogue for 1000 stars containing celestial coordinates with unprecedented accuracy, he made a group of observations of the nebulous celestial object Præsepe in Cancer. Unlike the vast majority of his observations, the determination of meridian altitudes for Præsepe show variation of up to 8′ for repeated determinations and up to 5′ for determination of the declination.
In this paper, it has been shown that these discrepancies were not the result of unprecise observations but rather derived from observation of three or possibly four individual stars in the central part of the open star cluster M44, as Præsepe is known today.
This has been demonstrated by the high accuracy and precision of the identifications of the individual stars based on 34 determinations of meridian altitude, declination as well as angular distance between Præsepe and two of Tycho’s fundamental stars, α Leonis and γ Geminorum. Four of the observations, one meridian altitude determination and the three determinations of right ascension, were tentatively related to a specific star.
Sighting of individual, faint stars in the centre of this open star cluster must have been very difficult, and it seems probable that Tycho devised a strategy whereby this could be achieved even under non-optimal conditions as in the presence of the moon. This strategy included a procedure for sighting the faint stars in M44 that was probably optimised in the years 1586 and 1587 indicated by a disproportionately high number of observations of Præsepe in these 2 years compared to the number of observations of other stars in Cancer. On 29 Jan 1589, the procedure in its final form was used to record the definitive determinations of coordinates for a single star in Præsepe, HIP 42549.
Tycho’s unorthodox use of the term ‘nebulosa’ and equivalent forms of this word has been shown to refer to very faint stars and not to truly nebulous objects as for example the Double Cluster in Perseus or the great Andromeda galaxy, M31. In fact, there are no records of such objects in Tycho’s observation logs or star catalogues, even though he must have been aware of these. Tycho used the phrase ‘Several, important fixed stars’ to describe the contents of his catalogues; and that was exactly what they were – catalogues of stars and not of nebulous objects.
It has finally been demonstrated that the coordinates of Præsepe in Tycho’s star catalogues may, with great confidence, be identified as those of the star HIP 42549. This was the case already in the star table sent by Tycho to Wilhelm IV in Jan 1587 and it has been demonstrated that he continued to list the coordinates for this star in all of his subsequent star catalogues. The selection of HIP 42549 seems logical, as this star is very close to the centre of M44 and it is the second brightest star, only slightly less so than HIP 42556 which, on the other hand, is much more distant from the centre of the open star cluster.
The observation of individual faint stars in Præsepe was an extraordinary achievement and without precedent. It has generally been accepted that Galileo Galilei with the use of his telescope in 1609 was the first astronomer to resolve individual stars [36] in Præsepe. 126 In the present article it has been demonstrated that Tycho and his assistants resolved three or possibly four individual stars in M44 more than 20 years prior to Galileo’s observation. Tycho and his team resolved just a few stars in Præsepe, but not only did they resolve them without optical aid, they also determined their coordinates with extraordinary accuracy and precision.
The observation of the individual stars in Præsepe is a unique example of Tycho Brahe’s and his assistants’ unparallelled observation skills in the era of pre-telescopic astronomy.
Footnotes
Acknowledgements
I wish to thank my wife Anna, for her patience and invaluable support during the preparation of this article.