Issue |
A&A
Volume 516, June-July 2010
|
|
---|---|---|
Article Number | A28 | |
Number of page(s) | 24 | |
Section | Catalogs and data | |
DOI | https://doi.org/10.1051/0004-6361/201014002 | |
Published online | 22 June 2010 |
Three editions of the star catalogue of Tycho Brahe
Machine-readable versions and comparison
with the modern Hipparcos Catalogue![[*]](/icons/foot_motif.png)
F. Verbunt1 - R. H. van Gent2,3
1 - Astronomical Institute, Utrecht University, PO Box 80 000,
3508 TA Utrecht, The Netherlands
2 - URU-Explokart, Faculty of Geosciences, Utrecht University, PO Box
80 115, 3508 TC Utrecht, The Netherlands
3 - Institute for the History and Foundations of Science, PO Box
80 000, 3508 TA Utrecht, The Netherlands
Received 6 January 2010 / Accepted 3 February 2010
Abstract
Tycho Brahe completed his catalogue with the positions and magnitudes
of 1004 fixed stars in 1598. This catalogue
circulated in manuscript form. Brahe edited a shorter version with
777 stars, printed in 1602, and Kepler edited the
full catalogue of 1004 stars, printed in 1627. We
provide machine-readable versions of the three versions of the
catalogue, describe the differences between them and briefly discuss
their accuracy on the basis of
comparison with modern data from the Hipparcos Catalogue. We also
compare our results with earlier analyses by Dreyer (1916, Tychonis
Brahe Dani Scripta Astronomica, Vol. II) and Rawlins (1993, DIO, 3, 1),
finding good overall agreement. The magnitudes
given by Brahe correlate well with modern values, his longitudes and
latitudes have error distributions with widths of 2,
with excess numbers of stars with larger errors (as compared
to Gaussian distributions), in particular for the faintest
stars. Errors in positions larger than
10
,
which comprise about 15% of the entries, are likely due to
computing or copying errors.
Key words: astrometry - history and philosophy of astronomy
1 Introduction
The astronomical observations of Tycho Brahe improved by an order of magnitude on the positional accuracy achieved by his predecessors. His measurements of the positions of stars on the celestial sphere resulted in a manuscript catalogue in 1598 (Brahe 1598). Astronomers and mapmakers throughout Europe used handwritten copies of this catalogue. Brahe edited a shorter version, with 777 stars, which was printed in 1602 as part of Astronomiae Instauratae Progymnasmata (Brahe 1602). The full list of 1004 entries with some modifications was published by Johannes Kepler in 1627 as part of the Tabulae Rudolphinae (Kepler 1627).
These catalogues are a monument in the history of astronomy, and as such have been studied repeatedly (e.g. Baily 1843; Dreyer 1890; Rawlins 1993).
In this paper we describe machine-readable versions of the catalogues. In addition to the numbers given by Brahe (and Kepler) the machine-readable tables provide cross-references between the catalogues, identifications with stars from the (modern!) Hipparcos Catalogue (ESA 1997) and on the basis of these the accuracy of the positions and magnitudes tabulated in the old catalogues.
The accuracy of the measurements of Brahe is best studied by
reference to his observational logs rather than by reference to his
reduced data, and Wesley (1978)
has shown that the measurement accuracy varies between the instruments
used by Brahe. For the mural quadrant, for example,
the average error is 34
6.
In his comprehensive study of Brahe's star catalogue, Rawlins (1993) also refers
to the observational logs to correct errors that Brahe made in
producing his star catalogue. An important conclusion drawn by
Rawlins is that errors exceeding 6
are usually the consequence of errors in the reduction of the
measurements, rather than in the measurements themselves. Such errors
include repetition of stars in several
entries, mixing data for different stars for one entry, and spurious
entries. Rawlins (1993)
produces an improved version of the star catalogue of Brahe,
the best version that Brahe could have published on the basis
of his measurements. The goal of our edition is to
present the star catalogue of Brahe as it was available for use to
a 17th century astronomer or map maker,
i.e. the versions as given by Brahe and Kepler.
Our analysis improves on earlier ones in three ways. First and foremost, our analysis is based on the Hipparcos Catalogue (ESA 1997), which is more accurate, complete and homogeneous than the stellar catalogues used in earlier analyses. Second, we grade each identification, discriminating between secure, probable and merely possible. Third, we provide images of each constellation comparing the positions and magnitudes from the Brahe catalogue with the posistion and magnitudes of all stars in the field, thus illustrating which stars were selected by Brahe for measurements and which ones not.
In describing the different versions of the catalogues we use the following notation: Manuscript refers to the manuscript version (Brahe 1598), Progym refers to the version edited and printed by Brahe (1602), Kepler refers to the version edited by Kepler (1627), and KeplerE to our emended version of the latter catalogue. Individual entries are numbered according to the order in which they appear in the different versions. For example, the third entry in Kepler corresponds to entry 338 in Manuscript, which we denote as K 3 and M 338, respectively. (Thus, our M numbers correspond to D numbers of Rawlins 1993.) The sequence number within a constellation is indicated by a number following the abbreviated constellation name: Oph 14 is the 14th star of Ophiuchus.
2 Description of the catalogues
The star catalogue of Brahe is organized by constellation. Manuscript starts with the zodiacal constellations, followed first by the Northern and then by the Southern constellations. Brahe added two constellations with respect to those given by Ptolemaios: Coma Berenices (between Bootes and Corona Borealis), and Antinous (between Aquila and Delphinus) and omitted the southern constellations that follow Centaurus in the catalogue of Ptolemaios, viz. Lupus, Ara, Corona Australis, and Piscis Austrinus. For many constellations the list of stars belonging to it is followed by a list of additional stars near to, but not considered to be part of, the constellation. In the case of Ophiuchus and Serpens the additional stars precede the stars of the constellations. The total number of entries in Manuscript is 1004, but as we will see below up to fourteen stars occur more than once, so that the actual number of stars present in the catalogue is closer to 990. The version we use is the one given in Volume 3 of the complete works by Tycho Brahe as edited by Dreyer (1916). Dreyer based his edition mainly on Codex 306 in the Copenhagen Royal Library, but also consulted various other manuscripts (Dreyer 1916: p. 332).
In Progym the additional stars and occasionally some more stars at the end of the constellation have been omitted, and the constellation Centaurus is absent, reducing the total number of entries to 777. Coma Berenices is listed here between Ericthonius and Ophiuchus. No star occurs twice in this shorter catalogue, and the number of stars in it equals the number of entries. The version we use is the reprint in Volume 2 of the complete works by Tycho Brahe edited by Dreyer (1915).
Kepler restores the order of constellations as used by Ptolemaios; it also restores most stars omitted in Progym. For some stars Kepler adds an alternative position, indicated with meus catalogus (``my catalogue'') or with Piferus or abbreviated versions of these indications. For this catalogue we use the orginal edition (Kepler 1627). Piferus refers to Francesco Pifferi whose translation with commentary of Sacrobosco's Tractatus de Sphaera was printed in Siena in 1604. In comments with some entries Kepler (1627) refers to Grünbergerus, i.e. Christoph Grünberger, who in 1612 brought out an edition of Brahe's star list.
Table 1: Constellations and numbers of stars in them.
The ordering of the constellations and the numbers of stars in each constellation is given for the two printed editions (1602 and 1627) in Table 1. Generally, Manuscript has the same stars in the same order within each constellation as Kepler. Exceptions are
- Kepler adds new stars in Cygnus
(Nova 1600 = P Cygni) and Cassiopeia (Nova
1572) at the end of these constellations. (Remarakbly,
the supernova of 1604, now named after Kepler, is not
in the catalogue
.)
- Manuscript lists thirteen stars denoted as Sequentes pertinent ad Ophiuchum et eius Serpentem (the following belong to Ophiuchus and his Snake) before the stars of Ophiuchus. Manuscript also erroneously gives the position of the Oph 14 as identical to that of Oph 12. Kepler places these thirteen stars in his catalogue as follows: the first one In dextra tibia Ophiuchi (in the right shinbone of Ophiuchus) is identified with Oph 14 In dextra tibia and gives it its correct position; the remaining twelve are listed at the end of Ophiuchus, as Oph 26 to Oph 37.
- Kepler omits Gem 30 of Manuscript. (As one of the stars additional to Gemini in Manuscript, this star is also absent from Progym.)
- In Kepler Com 15 is identical to Com 2. Com 15 is not in Manuscript and Com 2 is not in Progym.
- Manuscript contains a star which would have been between Eri 13 and Eri 14 in Kepler, but Kepler omits it. Its position is almost the same as that of Eri 8, and it certainly refers to the same star. Progym lists only 10 stars for Eridanus.
For each star a short description is followed by the ecliptic longitude
and latitude, and the magnitude. The longitude is given in degrees (G: integer),
minutes (M: integer or integer
plus 0.5), and zodiacal sign. The zodiacal sign is indicated
with its symbol in the original
catalogues, which we replace with an integer number Z
from 1 to 12 as shown in Table 2. The longitude in
decimal degrees follows as

The latitude is given in degrees (G: integer) and minutes (M: integer or integer plus 0.5), plus a B or A indicating north (Borealis) or south (Australis). In the 1627 edition the B or A is often omitted, assumed implicitly to be the same as for the previous star. The latitude in decimal degrees follows as

The equinox of the coordinates is given in all three versions of the catalogue as 1600 (MDC) annum completum, or in modern terms AD 1601.00.
The last number given for each star is the magnitude. This is given as an integer, occasionally followed in Progym by a colon (:) or decimal point (.). According to Dreyer (1890, p. 354) these qualifications indicate somewhat brighter (:) and fainter (.), respectively. Manuscript and Kepler omit the magnitude qualifications. In lieu of a magnitude the original catalogues occasionally refer to a star as ne, for nebulous.
Table 2: Numbers Z replacing the zodiacal signs in the machine-readable longitudes.
3 Identification procedure
To identify each star from the star catalogue of Brahe with a modern counterpart, we start with the selection from the Hipparcos Catalogue (ESA 1997) of all stars brighter than Johnson visual magnitude 6.0. We correct the equatorial Hipparcos star positions for proper motion, then precess the coordinates to equinox 1601.00 (old style, JD 2 305 824), and finally convert equatorial to ecliptic coordinates. For each entry in the old catalogue, we find the Hipparcos entry at the smallest angular distance.
3.1 Conversion of the coordinates
The Hipparcos coordinates are equatorial, for
epoch 1991.25 (JD 2 448 349.0625)
and equinox 2000.0. The proper motion thus has to be corrected
for -390.25 years. We apply linear corrections separately to
right ascension and declination, i.e. we ignore curvature in
the proper
motion. A major reason for using the Hipparcos
Catalogue is that it provides errors on the proper motion,
and that these errors are small. The typical accuracy of the proper
motions given in the Hipparcos Catalogue is
a few mas/yr, corresponding to less than an arcsec
over the 390.25 period. The best measurements by Brahe have an
accuracy of the order of an arcminute. The error in the Hipparcos
position computed for 1601 contributes less than one percent
to the error in the difference between the Brahe and Hipparcos
positions if the error in the proper motion is less than 0
1
in 390.25 yrs, i.e. less than 0
015/yr.
This is the case for all but eight of the stars with V<6.0.
The star with the largest error in proper motion among these eight is
Cen;
at
/yr,
this error is less than 1 percent of the proper motion itself,
and leads to a positional accuracy of 13
for epoch 1601. Note
that 3869 and 645 stars with V<6.0
have proper motions leading to displacements larger than 0
1 and 1
over 390.25 yr, respectively. We conclude that correction for
proper motion is important, but that the errors in this correction may
be neglected.
For precession of the equatorial coordinates from 2000.0 to 1601.0 we use Eqs. (3.211) and (3.212-2) of Seidelman (1992).
Finally, for conversion of equatorial to ecliptic coordinates we use the value for the obliquity in 1601, computed with Eq. (3.222-1) of Seidelman (1992).
3.2 Finding the nearest counterpart
The angle d between two stars with
position
and
is computed from
For small angles d, computations based on this equation suffer from round-off errors. Therefore, if Eq. (1) results in

3.3 Deciding on the identification
In many cases, the nearest Hipparcos match to the
star in the Brahe catalogue, as found with Eqs. (1) or (2),
is the obvious and unambiguous counterpart, as no
other star is nearby. This may be seen most directly in the figures we
provide in Sect. C,
in which filled circles indicate a star from the Brahe catalogue and
open circles stars from the Hipparcos Catalogue.
Bigger symbols indicate brighter stars. A filled circle within
an open circle is strongly indicative of a secure counterpart. Aries
and Gemini are examples of constellations in which all stars are thus
securely identified (Figs. C.30, C.31).
In some cases the offset between the positions is large and
indicates an error, but the identification is still secure with the
nearest counterpart. Examples are Aur
(near +5, +5 in Fig. C.17), and the
three northern stars in Corona Borealis (Fig. C.8).
In a number of cases we consider not the nearest but another
nearby Hipparcos match to the star in the Brahe
catalogue as a secure identification. There are two possible reasons
for this: first, the nearest Hipparcos
star is much fainter than another unidentified Hipparcos
star at a slightly larger angular distance; second,
the nearest Hipparcos star is more
plausibly identified with another star in Brahe's catalogue.
An example of the first reason is
K 101, near -1, +28 in Fig. C.4.
K 101 is 0
7 from HIP 80309 (V=5.7),
and 10
5 from HIP 80331 (
Dra,
V=2.7) and we consider HIP 80331 the secure
counterpart. Because we consider a pair of Hipparcos
stars to be one object when they are within 2
from one another, most identifications of Brahe entries with a
not-nearest Hipparcos star involve large positional
errors. For example, K 646 lies
about 61
from the
6.0 mag star HIP 65545 and about 78
from the 3.4 mag star HIP 66249
(near +4, +5 in Fig. C.37). We consider
HIP 66249 (=
Vir)
a secure identification even if
not the nearest Hipparcos star. An example of the second
reason may be seen in the constellation Centaurus: Fig. C.58 shows
convincingly that the position of the whole constellation is shifted to
lower longitude in the Brahe catalogue. This implies that the
counterpart of the middle star on the left is not HIP 67153
just south of it, but HIP 67669 almost a degree east
of it. Another example of the second reason is
UMa
which forms a pair with
UMa
just north of it (near -20, -7
in Fig. C.2).
UMa is
closest to HIP 44127, but so is
UMa,
and
UMa
may be securely identified with HIP 44471 just east
of it. A further example is illustrated in
Fig. C.5.
K 93 is closest to HIP 86219 and
K 94 to the very close (
)
pair HIP 86614+86620 (
Dra). From the
brightness of the stars, however, we prefer to identify K 93
with HIP 86614+86620 and K 94 with
HIP 87728. Dreyer (1916)
agrees in the identification of K 93, but identifies
K 94 with HIP 89937 (
Dra), relying more
on the description in Brahe's star catalogue of stars K 93-95
as a triangle. Rawlins (1993)
corrects the position of K 94, and validates
Dreyer's interpretation. All these examples illustrate the importance
of identifying stars in context, rather than individually.
In a number of cases we cannot find a secure counterpart. Some of these are illustrated in Fig. C.3. K 68, K 72 and K 74 may be identified with nearby Hipparcos stars, which we consider probable rather than secure. K 75 is at an equal distance of two Hipparcos stars, and might be identified with either of them. The remaining stars cannot be identified with any Hipparcos star, either because no nearby matches are found, or - in the case of K 67 - because the nearby star is identified with another star from the Brahe catalogue. Another constellation with stars we cannot confidently identify is Ophiuchus (the group near +10, -16 in Fig. C.19, see also Fig. C.20). We discuss uncertain identifications in Sect. B.
Finally, in three cases we find that two entries in the star catalogue are identical (K 10 = K 252; K 339 = M 701; K 483 = K 470), and in other cases almost identical and probably referring to the same star. In two cases three entries appear to refer to the same star. These multiple entries are listed in Table 3.
Table 3: Multiple entries in the Brahe catalogue.
We note that all three stars from Manuscript
omitted in Kepler are in Table 3,
i.e. they were presumably recognised by Kepler as double
entries. We already noted that one of the stars added in Kepler,
viz. K 483, is a repeat entry.
Thus, if we accept that all 15 entries in the second column of
Table 3
refer to the corresponding star in the first column, this implies that
the 1004 entries in the Manuscript
actually correspond to 990 stars; and that
the 1004 entries in Kepler
correspond to 992 stars. It may be argued that some
entries from the second column of Table 3 refer to a
hitherto unidentified star. This can be excluded in all cases where the
angular separation between the catalogue entries is less than 2,
the resolution of the human eye. On the
basis further of the absence of sufficiently bright candidate
counterparts, as illustrated in the figures mentioned in
Table 3,
we consider it most likely that all entries from the second
column are in fact repeat entries.
While looking for identifications we occasionally encountered cases where an emendation to the Brahe star catalogue appears to be warranted. We describe these in Appendix A.
Table 4: First lines from the machine-readable tables KeplerE and Variants.
3.4 Identifications by Dreyer and Rawlins
Unavoidably, deciding between secure and probable identifications or between probable and possible identifications is sometimes subjective. We therefore compare our identifications with those by Dreyer (1916) and Rawlins (1993) in their editions of the Manuscript version of the star catalogue by Brahe, thus obtaining independent opinions.
To compare the identifications by Dreyer with those
by us, we convert his identifications to a Hipparcos number.
In most cases, Dreyer provides a Flamsteed
number which is present in the
Bright Star Catalogue (Hoffleit & Warren 1991), allowing us
to obtain the Hipparcos identification from the
HR number via the HD number. In some cases a
Flamsteed number given by Dreyer is not listed in the Bright
Star Catalogue. For these we first
check the SIMBAD data base: for any
Flamsteed number in this data base the Hipparcos
number is provided. In seven cases we have not found the
Flamsteed number in the Bright Star Catalogue or in
the SIMBAD database. For these
(54 And, 51 Lib, 31 Mon, 2,4,9 Crt
and 35 Cam) we consulted the Flamsteed catalogue (Flamsteed 1725).
To find the corresponding Hipparcos
numbers we convert the positions of all Hipparcos
entries brighter than V=6.0 to the equinox of the
Flamsteed catalogue 1690.0 (old style) =
JD 2 338 331 by first correcting for proper
motion and then precessing the coordinates. We then find the Hipparcos
entry with the closest coordinates to each of the seven Flamsteed
stars. (In the constellation Camelopardalis some entries only
provide a latitude, omitting the longitude; in counting
entries to find number 35, we ignore these entries.) This
leads to an unambiguous identification in all cases, with positional
differences ranging from 0
3 to 1
0.
In seventeen cases Dreyer gives an
identification consisting of the letter P followed by a roman
and an arabic number. This refers to the catalogue of Piazzi (1803; we use the
1814 reprint). To find the corresponding Hipparcos
numbers we convert the positions of all Hipparcos
entries brighter than V=6.0 to the equinox of the
Piazzi catalogue 1800.0 =
JD 2 378 497 and find the nearest Hipparcos
entry to each of the 17 Piazzi stars. This
leads to an unambiguous identification in all 17 cases with
positional differences ranging from 0
06 to 0
19.
In two instances Dreyer gives an
identification consisting of a letter G followed by a number
(and in both cases by a question mark). This refers to the catalogue by
Groombridge (1838),
which uses an equinox 1810.0 =
JD 2 382 149. G 3887 is 107
from HIP 112519 (corrected for proper motion and precession);
however, G 3928 is only 0
03 from HIP 112519.
G 2807 has no Hipparcos counterpart with V<6,
but HIP 90182 (V = 6.2)
lies at 11
7 from it.
Some emendations to Dreyer's identifications that we consider probable are discussed in Sect. A.3.
To compare the identifications by Rawlins (1993) with those by us we convert his Bright Star Catalogue (HR) number for each of his identifications to an HD number using the Bright Star Catalogue (Hoffleit & Warren 1991), and use the HD number to find the corresponding Hipparcos number.
4 The machine-readable catalogues
A large majority of the entries is identical in the three catalogues. To save unnecessary duplication we produce the basic machine-readable catalogue from Kepler to which we add the three stars from Manuscript that Kepler omits. This basic catalogue is referred to in the following as KeplerE. A second catalogue, referred to below as Variants, collects variants to the entries in KeplerE. A third catalogue, Names, contains the descriptions of the stars from Manuscript.
4.1 The basic catalogue
Kepler (1627) gives alternative positions for some stars, indicated with meus catalogus or with Piferus or abbreviated versions of these; these are omitted from KeplerE (and given in Variants). In KeplerE the emendations discussed in Sect. A.1 have been implemented.
The columns in KeplerE give the following information.
Columns 1-3 give the sequence numbers of the stars in the three versions of the catalogue viz. M for the manuscript version (Brahe 1598), B for the printed edition of Brahe (1602), and K for the Kepler (1627) edition. KeplerE follows the sequence of entries in Kepler (1627); three stars from Manuscript omitted by Kepler (1627) are listed at the end of KeplerE. Thus KeplerE contains 1007 entries. To obtain the ordering of the stars/entries in the Manuscript (1598) or Brahe (1603) edition, one simply orders the table on Cols. 1 or 2, respectively. A sequence number zero indicates that the entry is absent in the corresponding catalogue.
Columns 4 and 5 indicate the constellation in which the star is listed in Kepler (1627). For convenience the constellation is indicated both with its sequence number C in Kepler (1627; see Table 1) and with the modern abbreviation (preceded by the equal sign =). We use Atn and Arg as abbreviations for Antinous and Argo, respectively, constellations which are no longer in use. Column 6 gives the sequence number of the star within the constellation in KeplerE.
Columns 7-14 copy the information of the original catalogue: Cols. 7-9 give the longitude (Z, G and M), Cols. 10-12 the latitude (G, M and A or B), and Cols. 13, 14 the magnitude VB and its qualifier (blank, . or :). The meaning of these numbers and qualifiers is explained in Sect. 2. Kepler (1627) often omits the B or A for the latitude, implicitly setting it equal to the value of the previous entry; KeplerE always gives B or A explicitly. A magnitude indicated as ``ne'' in the original catalogue is denoted 9 in KeplerE.
Columns 15-22 provide additional information from our analysis. Columns 15 and 16 give the number of the star in the Hipparcos Catalogue with which we identify the entry, and a flag I giving the quality of the identification, as explained in Sect. 3. The meanings of the identification flags are given in Table 5.
Table 5: Meaning of flags I classifying our identifications.
It should be noted that in general we limit our search for counterparts to Hipparcos stars with V<6.0, and the term nearest in our identification flag ignores stars fainter than this limit. In the case of double entries it is not clear whether the star listed in the first or that in the second column of Table 3 should be considered the repeat entry. In general we have the entry closest to the Hipparcos star a flag 1 or 3, and the other doubles entries a flag 6.
Columns 17 and 18 give flags D and R that compare our identification with those by Dreyer (1916) and Rawlins (1993), respectively. The meanings of these flags are given in Table 6.
Table 6: Meaning of flags D and R for identifications by Dreyer (1916) and Rawlins (1993).
Column 19 gives the visual (Johnson)
magnitude V of the Hipparcos
object given in Col. 15. Columns 20, 21 give
the differences in longitude
and latitude
between the correct position
(based on information from the Hipparcos
Catalogue) and the catalogue entry in tabulated
Minutes M. If the catalogue entry
for minutes as computed from the position
and proper motion in Hipparcos Catalogue
is
,
and M is the value actually given
in the Brahe catalogue, then Cols. 20 and 21
give
.
Column 22 gives the difference
between correct and tabulated position in
.
4.2 Catalogue with variants
The second catalogue Variants collects five types of variants. First, it gives the original entries of Kepler (1627) for all entries which are emended in KeplerE to allow the reader to judge the validity of our emendations and if required to restore the original Kepler (1627) edition. Next, Variants gives entries from the 1598 manuscript version of the catalogue and from the 1602 edition when these are different from the corresponding entry in KeplerE. Finally we give the alternative positions given by Kepler (1627) as originating from meus catalogus or Piferus.
Each entry in Variants starts with the variant of an entry in KeplerE, and ends with a 4-character string indicating the origin of the variant. If the first character in this string is K the entry gives the original values of the Kepler (1627) edition (for which KeplerE gives emended values). If the second character is P the entry gives values from Brahe (1602) that differ from KeplerE. If the third character is M the entry gives the values for the Manuscript version of Brahe (1598) that differ from KeplerE. This notation allows us to give variants which are common between different versions of the star catalogue in a single line. If the fourth character of the string is C or P the entry gives a variant given by Kepler (1627) with the characterization meus catalogus or Piferus, respectively.
Note that the identification procedure is done independently for all variant positions; when the variant position differs much from the KeplerE position, this may lead to a different identification.
4.3 Catalogue with descriptions
The third catalogue Names gives the descriptions of the stars as given in the manuscript version of the star catalogue (Brahe 1598). For convenience we add to this the sequence numbers M, B and K of each entry in the various editions of the catalogue.
5 Analysis and discussion
It is beyond the purpose of this paper to provide a full analysis of the star catalogue by Brahe and it different editions, but a few general remarks may be made.
5.1 Identifications, emendations and the three versions
In Table 7, in the columns labelled all, we list the numbers of our identifications of the entries in KeplerE and in Progym. It is seen that only 14 entries remain unidentified in KeplerE, and 5 in Progym. A large majority of stars is securely identified.
Table 7: Frequency of flags D of Dreyer (1916) identifications as a function of the flags I of our identifications.
The sixteen emendations that we apply to Kepler
affect the number of identifications. In particular, eight
lead to secure identifications (all with
)
of previously unidentified stars. One other emendation leaves an
unidentified star (K 67) unidentified,
one gives a probable identification of a previously
unidentified star (K 68), one improves the
positional correspondence with its Hipparcos
counterpart (K 801), and five lead to different
identifications with better positions. Note that with one
exception (K 801) all the emendations that we make to
Kepler are taken from Progym
and/or Manuscript. In Fig. 1 we show the
change in position caused by our emendations to Kepler,
and by different positions in Progym or Manuscript
with respect to KeplerE. Not surprisingly,
all emendations lead to better
positions. Figure 1
shows that most differences between Progym and KeplerE
are small, as are most differences between Manuscript
and KeplerE. Remarkably, the figure also
shows
that in all cases where the positions differ strongly between Kepler
and Progym and/or Manuscript,
the positions in the older catalogues are better. 25 of the
26 entries from Progym that differ from
the corresponding entries in KeplerE have the same
identification in both versions, but K 547 is identified in KeplerE
but unidentified in Progym. Similarly,
39 of 42 entries from Manuscript
that differ from the corresponding entries in KeplerE
have the same identification in both versions,
one (K 251) is identified in KeplerE
but not in Manuscript, and two
(K 64 and K 300) have a different
identification in KeplerE than in Manuscript.
![]() |
Figure 1:
Comparison of the accuracies of positions that are different in
different versions of the star catalogue of Brahe.
|
Open with DEXTER |
5.2 Comparison with Dreyer (1916) and Rawlins (1993)
In Table 7 we compare the identifications as found by us with those given by Dreyer (1916). For both the Brahe (1602) and the emended Kepler (1627) versions, we find that our identifications agree with the earlier ones by Dreyer in most cases. We have identified a number of stars not identified by Dreyer, in some cases prefer another one from several plausible possibilities, and in some cases reject an identification by Dreyer.
The numbers in Table 7 should be read as indicative rather than exact, due to unavoidable arbitrariness in some classifications. The pair K 146/K 147 is an example (see Sect. B): we flagged our identifications as secure (I = 1) and Dreyer's as wrong (D = 3), but could have chosen ours as one of several possibilites (I = 4) and Dreyer's as an alternative to our choice (D = 2). Another example is the case of K 218 in Cygnus. We have assigned HIP 106062 as its counterpart, because the closer and brighter counterpart has been assigned to K 440, a star in Pegasus. This is a reasonable choice if we assume that Kepler was aware of the proximity of K 440 to K 218. If such was not the case, we could follow Dreyer and consider K 218 as a repeated entry for K 440, and our identification flag would be I = 6 rather than I = 2; and the flag for Dreyer's identification D = 1 rather than D = 3.
The sixteen emendations that we apply to Kepler also affect the numbers in Table 7.
Comparison of our identifications with those by Rawlins (1993) must be made with some care, because his identifications refer to an ideal version of the catalogue, that Brahe might have produced given the time, whereas our identifications refer to the catalogue in the versions edited by Brahe and Kepler. Thus Rawlins identifies the stars that Brahe actually observed, whereas we identify the stars closest to the catalogue positions.
In Table 8
we compare the identifications as found by us with those given by
Rawlins for the emended Kepler edition. The three entries in KeplerE
that do not occur in Manuscript are not discussed
by Rawlins; all other entries are identified.
In 937 cases our identification agrees with the one
by Rawlins. We include in this four identifications
(of K 583, K 718, K 120,
and K 411) given by Rawlins (1993) that refer to
one of a close pair of stars, whereas our identification refers to the
other star of the pair. In each of these cases the pair is not
separable with the naked eye, with a separation <2,
and our identification refers to the star that is brighter in the Hipparcos
Catalogue. In 911 cases the identifications
given by Dreyer (1916),
Rawlins (1993)
and us all agree. In one case the identification given by
Rawlins refers to one of two possibilities considered by us.
In 53 cases Rawlins finds a
different identification because he has corrected the catalogue
position. For 4 entries, all in Ophiuchus,
Rawlins concludes that Brahe invented positions without having observed
them: they are ``utter fakes'' (see Fig. C.20).
Table 8: Frequency of flags R of Rawlins (1993) identifications as a function of the flags I of our identifications for KeplerE.
This leaves 6 entries where our identification is different
from that given by Rawlins. Five of these concern pairs of
stars, with separations varying from 3
8 to 10
5, in which our
suggested counterpart is closer to the catalogue position than the
counterpart given by Rawlins. An example is shown in
Fig. C.48.
In four cases (K 183, K 209,
K 671, K 870) our counterpart is the brighter star of
the pair, in one case (K 804) only slightly
fainter than the other star. In some cases,
e.g. K 175, K 183 and K 209,
Rawlins combines two stars separated by 8-11
into one counterpart; in such cases we may choose the brighter
and/or closer star as the counterpart, or leave the entry
unidentified.
The corrections applied by Rawlins (1993) also affect the number of repeated entries, as indicated in Table 3.
5.3 Accuracy
Table 7
shows that 14 stars remain unidentified in our emended Kepler
catalogue. Two entries in KeplerE have a
secure identification, but no counterpart from the Hipparcos
Catalogue: K 267 is SN 1572
and K 577 is Praesepe. To identify the
fourteen unidentified stars would require that one accepts either a
fainter counterpart, or a larger positional offset.
It is necessary to note that such acceptance increases the
probability of chance coincidences, i.e. of spurious
identifications. That this is a serious problem may be concluded from
the fact that we classified as ``secure'' four identifications
of entries in Kepler (1627)
that were identified with other counterparts after
our emendation was applied. Thirteen of our unidentified entries are
corrected by Rawlins (1993)
to new positions, that allow him to identify them. One of our
unidentified entries (K 175) is identified by Rawlins
as the combined light of HIP 87045 (V = 6.47)
and HIP 87119 (V = 6.83)
two stars separated by 8
8.
![]() |
Figure 2: Distribution of the magnitudes in Progym (above) and KeplerE (below). In the large frames the histograms indicate the magnitudes according to Brahe for stars which we have securely identified (red; flags 1-2 in Table 5) or not securely identified (blue, flags 3-5), and the magnitudes from the Hipparcos catalogue for securely identified stars (black). The numbers of securely and not-securely identified stars are indicated. The small frames give the Hipparcos magnitude distributions for securely identified stars for each magnitude according to Brahe separately. The number of securely identified stars at each (Brahe) magnitude is indicated. |
Open with DEXTER |
In Fig. 2 we compare the magnitude distributions of the stars in KeplerE to those of their securely identified counterparts. In our opinion, a difference between an Hipparcos magnitude and the magnitude assigned by Brahe cannot be called an error, since the magnitudes for Brahe correspond to a classification rather than a measurement. It is striking that Brahe's classification in general correlates well with the modern magnitude; only his magnitude 6 corresponds to mostly brighter stars in Hipparcos. The number of securely identified stars peaks at modern magnitudes 4 and 5, and rapidly drops for magnitude 6. This lends support to our hesitance in accepting stars with modern magnitudes V>6 as feasible counterparts.
![]() |
Figure 3:
Above: correlations of the differences in longitude
|
Open with DEXTER |
In Fig. 3
we show the offsets between the position in KeplerE
and the position derived from the Hipparcos data,
for longitudes and latitudes separately. We showed in Sect. 3.1 that
errors in conversion of the modern data to the positions in 1601 are
negligible, so that the offsets describe the errors in the
position as given by Brahe (or Kepler). If the errors
were fully random, we might expect their distributions to be Gaussian,
but this is not the case: Gaussians that fit the peak of the
distribution (
,
say) have a width
and predict much smaller numbers at
than observed. The excess in the wings of the distributions with
respect to a Gaussian description is presumably due to the correlations
and buildup of errors when the position of a star is determined by
measurement with respect to another star which already has a positional
error. However, for large errors,
say,
the possibility of a copying error must be considered,
as illustrated by the differences between the different
versions of the catalogue (see Fig. 1), and as
proven for many cases by Rawlins (1993).
The average offsets
and
are not zero, but for Gaussian fits to the central part of the
distributions are both around
.
Together with the small but systematic dependence of the average
offsets on longitude, also shown in Fig. 3, this
suggests that a small part of the errors may be due to small errors in
the position of the zero point in longitude and in the value of the
obliquity that Brahe used. Brahe used an obliquity
=
23
525 (Brahe 1602,
p. 18 and p. 208) whereas the correct value
for
1601 according to modern determinations
(see Sect. 3.1)
was
=
23
491. For small
declinations
,
the resulting error in latitude
due to the error
after converting equatorial to ecliptic coordinates may be written
This dependence on right ascension is clearly seen in Brahe's data, as illustrated in Fig. 4.
![]() |
Figure 4:
Above: latitude errors |
Open with DEXTER |
Brahe also assumed that refraction at altitudes above 20
is negligible, whereas a modern estimate would give 0
7 at the altitude of the
equatorial pole for Hven (latitude almost 56
;
the actual refraction depends somewhat on weather
circumstances). Declination measurements with respect to this pole
would thus all be offset by -0
7, and this would lead to a
systematic offset in
.
Even though the real situation would be more complicated, involving
differences in refraction errors between stars measured at different
altitudes (see Fig. 4), we think that
this offset largely explains the overall offset in
seen in Figs. 3
and 4,
which averages -0
5, and is already
present in the positions of Brahe's nine standard stars (Fig. 4; see also
Dreyer 1890,
p. 387).
![]() |
Figure 5:
Distribution of the position errors |
Open with DEXTER |
If
and
were distributed as Gaussians centered on zero,
the distribution of the total position errors
could
be written
The maximum of this function is at






Using Kolmogorow-Smirnov tests to compute the probability that
the distributions of the errors
in the range
for V=n is the same as for V=n+1
we find no significant differences. However, the distribution
of
for
is significantly different from that for
(probability for being identical is 0.003). Comparing the
differences between the distributions of
over the full range of
,
i.e. including large offsets, we find a significant difference
between V=5 and V=6
(probability for being identical is 0.001). We conclude that
the positions of stars with Brahe magnitudes 1 and 2
are
better than those of fainter stars; and that a larger fraction
of the positions of stars with magnitude 6 is wrong by more
than 10
than for positions of fainter stars.
We thank Dr. Gertie Geertsema for help in photographing Kepler. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and was supported by The Netherlands Organisation for Scientific Research under grant 614.000.425.
References
- Baily, F. 1843, MNRAS, 5, 279 [NASA ADS] [Google Scholar]
- Brahe, T. 1598, Stellarum octavi orbis inerrantium accurata restitutio (manuscript), ed. A. Dreyer, 1916, 333 [Google Scholar]
- Brahe, T. 1602, Astronomiae Instauratae Progymnasmata, ed. Dreyer, 1915, 258 [Google Scholar]
- Dreyer, J. L. E. 1890, Tycho Brahe. A picture of scientific life and work in the sixteenth century (Edinburgh: Adam and Charles Black) [Google Scholar]
- Dreyer, J. L. E. 1915, Tychonis Brahe Dani Scripta Astronomica, Vol. II (Kopenhagen: Gyldendal) [Google Scholar]
- Dreyer, J. L. E. 1916, Tychonis Brahe Dani Opera Omnia, Vol. III (Kopenhagen: Gyldendal) [Google Scholar]
- ESA 1997, The Hipparcos and Tycho Catalogues (Noordwijk: ESA Publications Division), SP-1200 [Google Scholar]
- Flamsteed, J. 1725, Historia Coelestis Brittanicae (London: H. Meere), 3 [Google Scholar]
- Groombridge, S. 1838, A catalogue of circumpolar stars, ed. G. B. Airy (London: Murray) [Google Scholar]
- Hoffleit, D., & Warren, W. H. 1991, Bright Star Catalogue, 5th Revised Ed., Astronomical Data Center, NSSDC/ADC, http://cdsarc.u-strasbg.fr/viz-bin/Cat?V/50 [Google Scholar]
- Kepler, J. 1627, Tabulae Rudolphinae (Ulm: Jonas Saur) [Google Scholar]
- Meeus, J. 1998, Astronomical Algorithms2 (Richmond: Willmann-Bell) [Google Scholar]
- Piazzi, G. 1803, Praecipuarum stellarum inerrantium positiones mediae (Palermo: Typis Regiis), reprinted 1814 [Google Scholar]
- Rawlins, D. 1993, DIO, 3, 1 [Google Scholar]
- Saemundsson, T. 1986, Sky & Telescope, July, 72, 70 [Google Scholar]
- Seidelman, P. K. 1992, Explanatory supplement to the astronomical almanac (Sausalito, California: University Science Books) [Google Scholar]
- Wesley, W. G. 1978, JHA ix, 42 [Google Scholar]
Appendix A: Emendations
We have emended some obvious errors in Kepler (1627). Positional errors are obvious if they place a star well outside the constellation; in general we emend them only if the correct version appears in the Brahe (1603) version. In the following, we abbreviate Meus Cat for an alternative position labelled Meus Catalogus in Kepler (1627). In this section reference to Dreyer is short for Dreyer (1916) and reference to Rawlins for Rawlins (1993).
A.1 Applied emendations
We list errors in Kepler (1627) that we emended.
K 67, 68 have
and
for their longitudes in Kepler, and
and
,
respectively, in Manuscript. Because the
description Tertia (the third) for
K 69 couples it to that of K 68 Secunda
earundem (the second of the same [sc. stars]) we
apply the correction. Whether or not we apply the emendation, we don't
find close counterparts for these stars.
K 145 has
in Kepler, but
in Manuscript. Because K 145 is described
as following K 144 (hanc sequens), we
follow Manuscript.
K 238 has
in Kepler for the longitude, but
in Progym and Manuscript.
Because the star is described together with K 237 and
K 239 as in the bench (scabellum) of the throne on which
Cassiopeia sits, it should be near these two stars.
K 378 has 29
in the latitude in Kepler, too far from the other
stars of Sagitta. We emend to the value 39
of Progym and Manuscript.
K 499, 500 have southern latitude A in Kepler, but northern latitude B in Progym and Manuscript.
K 530 has southern latitude A in Kepler,
both Manuscript and Progym
give B.
Kepler gives Z of K 539
as ;
both Manuscript and Progym
give
.
The magnitudes of K 535-545 are erroneously replaced in Kepler
with those of K 536-546, and the magnitude of K 546
is left empty. This is due to an erroneous shift by one line of the
magnitude column, starting with a meus cat
alternative position for K 535.
K 547. Manuscript has B for the latitude
of K 547, whereas Progym and Kepler
give A. B is clearly correct, as it fits the
description of the star Quae est inter binas praec.
in colli
(which is between the two leading stars in the square at the
neck) and lies within 0
3 of HIP 19171.
K 685, 686 are A(ustralis) in Kepler but
B(orealis) in Manuscript. The southern positions
give no near counterparts, whereas the northern positions do.
The descriptions for K 685 Superior et Orientalior
(North and East, sc. of K 684) and K 686 Quae
hanc sequitur (Which follows this one) imply positions north
of K 685, and thus B.
K 801. Manuscript, Progym
and Kepler all have B for the latitude of this
star, close to K 802, and with no near counterpart.
A latitude A gives an excellent match both to the
otherwise unidentified o Psc, and to the description In lineo
boreo a connexu praecedens (in the northern line
leading the connection).
K 934. Manuscript and Progym
have G = 11 in the longitude, Kepler
has G = 19. The descripton Quae
in fronte ad dextram aurem (Which is in the forehead
at the right ear) is not compatible with the position in Kepler.
K 972, K 973. Manuscript and Progym
have
for longitude, Kepler has
.
A.2 Not-applied emendations
We list errors in Kepler (1627) which we decided not to emend.
K 59-61 all three have magnitude 5 in Manuscript,
and 3 in Kepler. Their counterparts
indicate that the Manuscript magnitudes are
correct.
K 534 has the same position in Manuscript,
Progym, and Meus Cat which
differs from that in Kepler. The Manuscript
position give a better match to Electra (see Fig. C.34).
K 581. Manuscript has B for the latitude
of K 581, whereas Progym and Kepler
give A. The manuscript position gives a better match with
HIP 42911 (= Cnc)
at 0
9.
A.3 Emendations to Dreyer
In a number of cases the Flamsteed number is accompanied by an
(extended) Bayer identification that is different from the one given in
the 5th edition of the Bright Star Catalogue (Hoffleit
& Warren
1991). For
example 35 Lib (K 679 = HIP 76126)
is listed as
by Dreyer and as
Lib
in the Bright Star Catalogue. Similarly with
Ori (K 860-865). Since we use
only Flamsteed numbers to identify the counterpart we do not emend such
differences.
K 580 Dreyer gives Flamsteed No. 41 for Cnc;
correct is 43.
K 646. Dreyer gives Flamsteed No. 70 for Vir;
correct is 79.
K 990. Dreyer gives Flamsteed No. 23 for Crt.
Correct is 21.
K 263 and K 264. Dreyer gives no identification for
K 263 and P.IX.37 = HIP 47193 for
K 264. From the position HIP 47193 is a better match
for K 263, which when accepted leaves K 264
unidentified by Dreyer.
Appendix B: Notes on individual identifications
In this section reference to Dreyer is short for Dreyer (1916) and reference to Rawlins for Rawlins (1993).
K 10-13 lie in a straight line in Fig. C.1 (lower
right corner), without close counterparts. All four identifications we
choose lie to the northwest. K 12 lies rather closer
to HIP 24914, 63
4 to the southeast,
and this star is an alternative identification. The counterpart
suggested for K 12 by Dreyer, HIP 24348 is too faint
and still not very close (V=6.5,
).
K 14, near +5.5, +1.5 in Fig. C.1,
is very close (14)
to K 64 in Ursa Maior, and refers to the same star.
K 15, near -6, +15 in Fig. C.1,
is tentatively identified by Dreyer with
Groombridge 2708, possibly identical to HIP 90182
at 11
7 from the Groombridge
position. We
consider HIP 90182 too faint, at V=6.2.
K 18, near -12, +14 in Fig. C.1,
is tentatively identified by Dreyer with
Groombridge 3887; however, HIP 112519, our
counterpart for K 18, corresponds to
Groombridge 3928.
K 26, near -16, +16 in Fig. C.2,
has no near counterpart. It lies between two faint
stars HIP 50685 (V=5.9, =
111
East)
and HIP 47594 (V=5.7,
=
102
West),
but we prefer the brighter star slightly further West.
Dreyer agrees.
K 29, near -15, +10 in Fig. C.2,
is not identified by us. We consider HIP 47911,
the counterpart given by Dreyer, too faint (V=6.6)
and far ( = 46
7)
to be viable.
K 93,94. We identify K 93 with the close pair
HIP 86614/86620 ( Dra) and
K 94 with HIP 87728. For K 94
Dreyer prefers HIP 89937 (
Dra)
as counterpart. See Fig. C.5
K 101, near -1, +28 in Fig. C.4, lies very
close to HIP 80309 (V=5.7, = 0
7),
but its much brighter neighbour is our preferred counterpart.
K 146 and K 147, near -0.5, +17.5 in Fig. C.7.
Our identification for K 146 is that of
K 147 in Dreyer, and vice versa, because we
identify with the nearest object,
whereas Dreyer follows order in longitude.
K 175, near +7, +18 in Fig. C.9, is listed
in the catalogue as nebulous, and is identified by Dreyer with
HIP 87280, a Be star. Although variable,
HIP 87280 is too faint
(V=6.8) and too far ( = 50
)
to be a viable counterpart. Rawlins identifies K 175 with the
combined light of HIP 87045 (V=6.47) and
HIP 87119 (V=6.83) two stars separated
by 8
8. We leave K 175
unidentified.
K 183, near -16, +6 in Fig. C.9,
is identified by Dreyer with HIP 86534, but this star
is at a distance = 77
,
whereas our identification, which corresponds
to 53 Boo, lies at 1
2 from K 183.
Rawlins identifies this entry with the combined light of
52 Boo (=HIP 75973, V=5.0)
and 53 Boo, separated by 10
5.
K 191, near -2.5, -3 in Fig. C.10,
is identified by Dreyer with HIP 92398 (= Lyr),
which is both fainter and further (V=5.9,
= 14
)
as our identification HIP 92405 (=
Lyr).
K 209, near +4.5, +14 in Fig. C.11,
is identified by Dreyer with HIP 99639, both fainter
and further (V=4.8, = 9
5) than our suggested
counterpart HIP 99675. Rawlins identifies this entry with the
combined light of these two stars.
K 216 is at 7
8 from K 201;
K 220 is at 1
0 from K 201
(Fig. C.12).
We think that these three entries refer to the same star,
HIP 96441. Dreyer identifies K 201 as we do, but
identifies K 216 and K 220 both with
HIP 96895, but this star is 54
from K 220.
K 218, near +13, -12 in Fig. C.11.
HIP 106140, the counterpart suggested by Dreyer,
is brighter and closer than our suggested counterpart,
but it is already taken by K 440.
K 220: see K 216.
K 237-239. Notwithstanding implied position errors
of 224,
161
,
68
,
it is tempting to agree with Hevelius, Dreyer and Rawlins and
identify these three stars with
HIP 9598, HIP 9480 and HIP 9009,
respectively, since these counterparts are not matched by other entries
in Brahe's catalogue, even though rather brighter than the
counterparts we choose because of
their positional matches, HIP 5926, HIP 7078 and
HIP 7965. See Figs. C.13, C.14. Rawlins
indeed corrects the positions. Note that the Brahe catalogue give
magnitudes 6 to K 237-239.
K 249 lies very close to K 300 (Fig. C.14), but we
do not consider this to be a double entry:
see K 297-300.
K 254, near +20, -9 in Fig. C.13, lies
between HIP 33449 and HIP 32489. We choose the
HIP 33449 as a counterpart as it is brighter; Dreyer chooses
HIP 32489, which is fainter but closer (V=5.3,
)
K 264, 265, near +14, +18.5 in Fig. C.13, form a
pair close to the pair HIP 51384 and HIP 51502.
If we follow Dreyer and identify K 265 with
HIP 51502 (at 6
0), K 264 is without
counterpart. We have chosen to identify the pair, accepting the larger
offsets. Neither solution is very satisfactory.
K 267 is SN 1572. The positional error is rather
large, about 15,
mainly in longitude.
K 294. Rawlins makes a large correction to its position and
identifies it with HIP 19949 (V=5.2).
K 297-300 are the four additional stars (indicated blue) top
left in Fig. C.15.
K 297 and K 300 are close to HIP 15520 (
)
and HIP 14862 (
),
respectively, whereas K 298, 299 have no nearby counterparts.
This is the choice made by Dreyer. Looking at the figure we have the
distinct impression that the correct position of this group of four
stars is about 10
(mainly towards the south) from the catalogued positions. We give our
identifications accordingly. Rawlins identifies K 297 with
HIP 15520 and corrects the positions of K 298-300 to
identify K 298 with HIP 16281, K 299 with
HIP 16292 and K 300 with HIP 16228.
K 317. The Kepler position is closest to
the counterpart of K 316, so that we choose
HIP 27673 as counterpart (near +3, -1 in
Fig. C.17,
the two entries of the Brahe catalogue - in
blue - are merged). For the position of Meus Cat
HIP 27673 is in fact the star closest
to K 317.
K 319, near -2, -5 in Fig. C.17, lies between
HIP 25471 (V=5.9,
)
and our preferred counterpart HIP 24879, brighter and at the
same distance
(V=5.1,
).
Dreyer takes HIP 25541 as counterpart (V=5.1,
).
K 336, K 347 and K 364 have virtually the
same position, and all correspond to HIP 86284 (= Oph).
See Fig. C.21.
K 341: see K 353.
K 344-347. We agree wih Dreyer in considering K 361
to K 364 as repeat entries for K 344 to
K 347. Alternatively, one may identify the pair
K 345/K 362 with the pair
HIP 86263/HIP 86266. See Fig. C.21.
K 347: see K 336.
K 353-364. Kepler annotates these entries with: Desunt
in meo seqq. ad finem. Vide Classem secund. (The
following until the end are absent in mine, see Second Class). Kepler
refers to the stars in the catalogue of Ptolemaios that Brahe omitted
in his catalogue as the Second Class, and lists these separately,
on pages following his edition of the Brahe catalogue.
K 353-357 are illustrated in Fig. C.20. Our
interpretation has K 353 as a repeat entry for K 341;
and identifies K 354 with HIP 85207 and
K 355-357 with HIP 84970, HIP 85340 and
HIP 86755, respectively. An alternative possiblity would be to
identify K 341 with HIP 85207 and K 354 with
HIP 84626, but we consider this less likely. Dreyer gives no
identifications for K 353-357. Rawlins argues that
K 354-357 are utter fakes.
K 360-364 are all repeat entries (see Table 3) K 360
is near -6, +6 in Fig. C.19. For
K 361-364 see Fig. C.21. One may
consider the pair K 362-K 345 to correspond to the
pair HIP 86266-HIP 86263, but we consider this less
likely, because the orientation is not right and because the two
entries preceding K 362 and the two following are all repeat
entries.
K 470 is a rather confusing entry. It is repeated
exactly as K 483, apparently unnoticed by Kepler; Manuscript
gives it at the location of K 470 only, and Progym
gives it at the location of K 483 only. It has no
nearby identification. Kepler annotates
K 470 Meus solus. Forte eadem (Mine only.
Accidentally in the same place). This may refer to its absence at this
location in Progym and suggests that Kepler thought
it as almost at the same coordinates as K 469. Did he
consider 28 for M in longitude as
an error for 18?
K 471-473. From the positions in the catalogue, K 471
and K 472 both lie closest to HIP 60697
(near -4.2, -0.7 in Fig. C.28) and
K 473 is close to HIP 60746, leaving
HIP 60904 (near -3.2, -1.6) without
catalogue counterpart. The catalogue describes K 471-473 as
following one another, hence we prefer to identify K 472 with
HIP 60746 and K 473 with HIP 60904. Dreyer
agrees.
K 484 = HIP 8832 corresponds to HR 545+546 (
Ari).
K 517 is identified with the northern of the pair
(HIP 20885 and
HIP 20894) by Dreyer, but actually is
closer to the southern star. See Fig. C.33.
K 534 is Electra in the Pleiades, as shown by its
position in Manuscript (see Fig. C.34).
K 543 lies between HIP 21683 and HIP 21673,
somewhat closer to the latter (Fig. C.33). We list
the brighter star as the counterpart. HIP 21673 is fainter (V=5.1)
but closer (2
4), and is listed by Dreyer as
the counterpart.
K 547. The position in Manuscript gives
excellent agreement with HIP 19171 (at 0
3), which is the identification
also given by Dreyer. The position given in Progym
and
Kepler does not lead to a good identification.
See Fig. C.32.
K 556, near +5.5, +5.5 in Fig. C.31, lies between
HIP 36393 (at 8
9) and HIP 36492.
Dreyer gives HIP 36393 as identification, we choose the closer
star.
K 577 is the open star cluster Praesepe; Dreyer identifies it
with the brightest star (at V=6.3) in
Praesepe, Cnc = HIP 42556
K 607, near -7, -3 in Fig. C.36,
is identified with HIP 51585 (46 Leo,
near -0.5, -0.5) by Dreyer; too far to be believable.
HIP 50333, near -4, -2, is closer.
K 625, near -3.0, +12 in Fig. C.36, is identified
with 7.3 mag star HIP 52240 (39 LMi) by
Dreyer, too faint to be believable. We think our
identification with HIP 52422 is secure, as this is
the only sufficiently bright star near K 625.
K 646, near +4, +5 in Fig. C.37,
is securely identified with HIP 66249 ( Vir)
even though the rather fainter HIP 65545 is somewhat closer
at 61
2.
K 650, near +13.5, -1.0 in Fig. C.37,
is possibly identified with HIP 68940, as no other
sufficiently bright star is nearer. Dreyer gives no identification.
K 676, near -2, +1 in Fig. C.38. We accept a
counterpart with V=6.1 as no brighter stars are
nearby; the identification by Dreyer, HIP 75294, is
fainter and further (V=6.5, d=33').
K 687,688, near -2.5, -9 and -2.5, -3.5 in Fig. C.38, have better
positions in Manuscript, i.e. closer to
the counterparts, than in Kepler.
K 713 is closer to ,
the brighter and southern star of the pair
,
Cap (Fig. C.42).
Dreyer gives
as identification.
K 717, 718 and 720 are listed ``ne'', but are well identified
with stars (see Fig. C.41).
K 737, near +9.5, +3 in Fig. C.41,
is rather far from its identification, but no star with V
< 6 is closer.
K 738, near +11.5, +0.5 in Fig. C.41,
is identified (by us and Dreyer) with HIP 108036,
which leaves K 739, right next to it, without counterpart,
unless we are willing to accept a V
=6.3 star.
K 759, near +4, -3 in Fig. C.43) is
tentatively identified by us with HIP 112542
(near +7, -3) and by Dreyer with HIP 110778
(near +1, -4).
K 772, near +17, -12 in Fig. C.43).
Our identication is both brighter and closer than the
identification given by Dreyer HIP 116889 ( = 14
2).
K 804, near +17, +3 in Fig. C.44). Our
identification is closer than, but slightly fainter than the
identification given by Dreyer and Rawlins, Psc = HIP 6706
(
= 5
6).
K 808, near +13, +12 in Fig. C.44). Our
counterpart has V = 6.1.
K 870 (Fig. C.48)
is identified with HIP 26268 by Dreyer (V=5.2,
= 5
1).
Our identification HIP 26237 is brighter and closer; note that
the angle between HIP 26268 and HIP 26237 is
just 4
2.
K 871 is identified by Dreyer with HIP 26235 (= Ori,
V=5.0,
= 1
7).
Our identification
Ori is equally
bright and marginally closer
(Fig. C.48).
Note that
Ori
corresponds to HIP 26220 and HIP 26221
(separation 13
). HIP 26224
(at 21
,
V=6.7) is also part of
,
but much fainter.
K 893, near +6, -10 in Fig. C.47,
is identified by Dreyer with HIP 30700 (V=6.5,
= 29
5).
Our identification is much closer and brighter.
K 938, near -4.5, +1 in Fig. C.50) is
identified by Dreyer with HIP 31700 (= CMa; V=4.4,
= 52
7)
almost a degree north of it. Our identification
CMa
is brighter and much nearer.
K 959-961. Kepler annotates Has
tres trajecit Grünbergerus ad finem Hydrae (Grünberger moves
these three to the end of Hydra). Figure C.53 shows the
area near
K 959 and K 960, which includes K 975 and
K 976 (in Hydra). Our preferred
identification for each of these is with the nearest HIPPARCOS star in
the figure. One problem with this is that we couple the fainter of the
pair K 960/K 976 to the brighter of the pair
HIP 49809/HIP 49841. Another problem is the
description of K 960 as Sequens earundem
(the following of the same two [sc. K 959 and
K 960]) which appears inapt for a faint star between two
brighter
ones. Dreyer identifies both K 960 and K 976 with
HIP 49841, but this has the problem that these two stars have
significantly different coordinates and magnitudes in the catalogue.
The same problem arises with the identification by Dreyer of both
K 961 and K 982 with 9 Crt =
HIP 54204 (see Fig. C.54). We
prefer to identify K 961 with HIP 54204, and the
fainter K 982 with the fainter HIP 54255. Hevelius
and Rawlins correct the longitude of K 961, to
(by replacing
Z=6 with Z = 4)
which gives a close (0
5) match to HIP 37447
(=
Mon;
see Fig. C.52).
K 975, K 976: see K 959, K 960.
K 982: see K 961.
K 1003, K 1004 both are closest to
HIP 67153, near 0, 0 in Fig. C.58, but from
the pattern of the whole constellation it is seen that K 1004
is HIP 67669.
M 94 is almost identical to M 102 = K 584.
M 703 is an exact repeat of M 701 = K 339.
M 915 is an almost identical repeat of M 908 =
K 908.
Appendix C: Figures
To illustrate and clarify our identifications we provide figures for each constellation. It should be noted that the following equations are used only for the figures, i.e. for illustrative purposes: to compute the angles between positions, e.g. to find the nearest counterpart, we always use Eqs. (1) and (2).
In these figures the stars listed with the constellation in Progym are shown red, those added in Kepler in blue, and other stars listed in Progym and Kepler are shown light-red and light-blue, respectively. For all stars we use positions from KeplerE. In yellow we indicate stars from Secunda Classis (which are discussed in Verbunt & Van Gent, Paper III, in preparation).
To minimize deformation of the constellations, we determine
the center of the constellation
from
the extremes in
and
,
compute the rotation matrix
![]() |
(C.1) |
which moves this center to (x,y,z)=(1,0,0), and then apply this rotation to each of the stellar positions

![]() |
(C.2) |
The resulting y,z values correspond roughly to differences in longitude and latitude, exact at the center






Where necessary we show enlarged detail figures; for easy comparison with the figures showing the whole constellation, these detail figures use the same rotation center (and thus rotation matrix).
![]() |
Figure C.1: Ursa Minor. The stars additional to the 7 stars given in Progym include four stars in Camelopardalis (below right) with no close counterparts, and one star (near +5.5, 1.5) also listed in Ursa Maior. We agree with Dreyer in not finding a suitable identification for K 15 (near -6, 14.5). |
Open with DEXTER |
![]() |
Figure C.2:
Ursa Maior. K 67 and K 88 at the positions given in
Kepler are
indicated |
Open with DEXTER |
![]() |
Figure C.3: Ursa Maior detail. No good counterparts are found for K 67-75 even if the search is extended down to V=6.5. Rawlins (1993) notes that Brahe's positions in this area are in ``extreme confusion''. Compare with Fig. C.2. |
Open with DEXTER |
![]() |
Figure C.4: Draco. |
Open with DEXTER |
![]() |
Figure C.5:
Draco detail. K 93,94. We identify K 93 with the
close pair
HIP 86614/86620 ( |
Open with DEXTER |
![]() |
Figure C.6: Cepheus. |
Open with DEXTER |
![]() |
Figure C.7:
Bootes. The position of K 145 in Kepler
is indicated |
Open with DEXTER |
![]() |
Figure C.8: Corona Borealis. |
Open with DEXTER |
![]() |
Figure C.9: Hercules. The star from Secunda Classis near -1.4, 3.2 may be identified with M 13. |
Open with DEXTER |
![]() |
Figure C.10: Lyra. |
Open with DEXTER |
![]() |
Figure C.11:
Cygnus. Nova 1600 aka P Cygni =
HIP 100044 is indicated with |
Open with DEXTER |
![]() |
Figure C.12: Detail of Cygnus illustrating that K 201, K 216 and K 220 are repeated entries for the same star. |
Open with DEXTER |
![]() |
Figure C.13:
Cassiopeia. The blue |
Open with DEXTER |
![]() |
Figure C.14: Cassiopeia detail, illustrating the identifications by Dreyer (1916) and Rawlins (1993) of K 237-239 with HIP 9598, HIP 9480 and HIP 9009. |
Open with DEXTER |
![]() |
Figure C.15:
Perseus. The additional stars (in blue) appear shifted from a
better match about 10 |
Open with DEXTER |
![]() |
Figure C.16: Serpens. |
Open with DEXTER |
![]() |
Figure C.17: Auriga. |
Open with DEXTER |
![]() |
Figure C.18: Sagitta. |
Open with DEXTER |
![]() |
Figure C.19: Ophiuchus. |
Open with DEXTER |
![]() |
Figure C.20: Ophiuchus detail. |
Open with DEXTER |
![]() |
Figure C.21: Ophiuchus detail. |
Open with DEXTER |
![]() |
Figure C.22: Aquila. |
Open with DEXTER |
![]() |
Figure C.23: Antinous. |
Open with DEXTER |
![]() |
Figure C.24: Pegasus. |
Open with DEXTER |
![]() |
Figure C.25: Delphinus. |
Open with DEXTER |
![]() |
Figure C.26: Equuleus. |
Open with DEXTER |
![]() |
Figure C.27: Andromeda. |
Open with DEXTER |
![]() |
Figure C.28: Coma Berenices. |
Open with DEXTER |
![]() |
Figure C.29: Triangulum. |
Open with DEXTER |
![]() |
Figure C.30: Aries. |
Open with DEXTER |
![]() |
Figure C.31: Gemini. |
Open with DEXTER |
![]() |
Figure C.32:
Taurus. The Kepler position of K 547,
indicated |
Open with DEXTER |
![]() |
Figure C.33:
Taurus: enlarged detail of the head, showing K 517 to be best
identified with |
Open with DEXTER |
![]() |
Figure C.34:
Taurus: enlarged detail of the Pleiades. The position of K 534
in Manuscript and Progym is
indicated with a blue |
Open with DEXTER |
![]() |
Figure C.35: Cancer. The red square indicates K 577, Praesepe. |
Open with DEXTER |
![]() |
Figure C.36: Leo. |
Open with DEXTER |
![]() |
Figure C.37: Virgo. |
Open with DEXTER |
![]() |
Figure C.38:
Libra. The position as given in Kepler for
K 685,686 are indicated with |
Open with DEXTER |
![]() |
Figure C.39: Scorpius. Only the northern stars are in Brahe's catalogue. |
Open with DEXTER |
![]() |
Figure C.40: Sagittarius. |
Open with DEXTER |
![]() |
Figure C.41:
Capricornus. Three stars listed as nebulous by Brahe, indicated
with |
Open with DEXTER |
![]() |
Figure C.42:
Capricornus detail, showing identification of K 713
with |
Open with DEXTER |
![]() |
Figure C.43: Aquarius. |
Open with DEXTER |
![]() |
Figure C.44:
Pisces. The blue |
Open with DEXTER |
![]() |
Figure C.45: Cetus. |
Open with DEXTER |
![]() |
Figure C.46: Lepus. |
Open with DEXTER |
![]() |
Figure C.47: Orion. |
Open with DEXTER |
![]() |
Figure C.48: The sword of Orion. |
Open with DEXTER |
![]() |
Figure C.49: Eridanus. |
Open with DEXTER |
![]() |
Figure C.50:
Canis Maior. The blue |
Open with DEXTER |
![]() |
Figure C.51: Canis Minor. |
Open with DEXTER |
![]() |
Figure C.52:
Argo. K 961 is near 23, 1 (see also Fig. C.54),
its position as emended by Hevelius is indicated with the
blue |
Open with DEXTER |
![]() |
Figure C.53: Argo detail. |
Open with DEXTER |
![]() |
Figure C.54: Argo detail. |
Open with DEXTER |
![]() |
Figure C.55: Crater. |
Open with DEXTER |
![]() |
Figure C.56: Corvus. |
Open with DEXTER |
![]() |
Figure C.57: Hydra. |
Open with DEXTER |
![]() |
Figure C.58: Centaurus. The catalogue longitudes appear shifted by about a degree. |
Open with DEXTER |
Footnotes
- ... Catalogue
- The full tables KeplerE and Variants (see Table 4) and the table with the latin descriptions of the stars are available in electronic form only at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/516/A28
- ... catalogue
- It is however in the Secunda Classis, a list which immediately follows the star catalogue of Brahe in Kepler's (1627) edition, and which contains stars not in the Brahe catalogue
All Tables
Table 1: Constellations and numbers of stars in them.
Table 2: Numbers Z replacing the zodiacal signs in the machine-readable longitudes.
Table 3: Multiple entries in the Brahe catalogue.
Table 4: First lines from the machine-readable tables KeplerE and Variants.
Table 5: Meaning of flags I classifying our identifications.
Table 6: Meaning of flags D and R for identifications by Dreyer (1916) and Rawlins (1993).
Table 7: Frequency of flags D of Dreyer (1916) identifications as a function of the flags I of our identifications.
Table 8: Frequency of flags R of Rawlins (1993) identifications as a function of the flags I of our identifications for KeplerE.
All Figures
![]() |
Figure 1:
Comparison of the accuracies of positions that are different in
different versions of the star catalogue of Brahe.
|
Open with DEXTER | |
In the text |
![]() |
Figure 2: Distribution of the magnitudes in Progym (above) and KeplerE (below). In the large frames the histograms indicate the magnitudes according to Brahe for stars which we have securely identified (red; flags 1-2 in Table 5) or not securely identified (blue, flags 3-5), and the magnitudes from the Hipparcos catalogue for securely identified stars (black). The numbers of securely and not-securely identified stars are indicated. The small frames give the Hipparcos magnitude distributions for securely identified stars for each magnitude according to Brahe separately. The number of securely identified stars at each (Brahe) magnitude is indicated. |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Above: correlations of the differences in longitude
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Above: latitude errors |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Distribution of the position errors |
Open with DEXTER | |
In the text |
![]() |
Figure C.1: Ursa Minor. The stars additional to the 7 stars given in Progym include four stars in Camelopardalis (below right) with no close counterparts, and one star (near +5.5, 1.5) also listed in Ursa Maior. We agree with Dreyer in not finding a suitable identification for K 15 (near -6, 14.5). |
Open with DEXTER | |
In the text |
![]() |
Figure C.2:
Ursa Maior. K 67 and K 88 at the positions given in
Kepler are
indicated |
Open with DEXTER | |
In the text |
![]() |
Figure C.3: Ursa Maior detail. No good counterparts are found for K 67-75 even if the search is extended down to V=6.5. Rawlins (1993) notes that Brahe's positions in this area are in ``extreme confusion''. Compare with Fig. C.2. |
Open with DEXTER | |
In the text |
![]() |
Figure C.4: Draco. |
Open with DEXTER | |
In the text |
![]() |
Figure C.5:
Draco detail. K 93,94. We identify K 93 with the
close pair
HIP 86614/86620 ( |
Open with DEXTER | |
In the text |
![]() |
Figure C.6: Cepheus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.7:
Bootes. The position of K 145 in Kepler
is indicated |
Open with DEXTER | |
In the text |
![]() |
Figure C.8: Corona Borealis. |
Open with DEXTER | |
In the text |
![]() |
Figure C.9: Hercules. The star from Secunda Classis near -1.4, 3.2 may be identified with M 13. |
Open with DEXTER | |
In the text |
![]() |
Figure C.10: Lyra. |
Open with DEXTER | |
In the text |
![]() |
Figure C.11:
Cygnus. Nova 1600 aka P Cygni =
HIP 100044 is indicated with |
Open with DEXTER | |
In the text |
![]() |
Figure C.12: Detail of Cygnus illustrating that K 201, K 216 and K 220 are repeated entries for the same star. |
Open with DEXTER | |
In the text |
![]() |
Figure C.13:
Cassiopeia. The blue |
Open with DEXTER | |
In the text |
![]() |
Figure C.14: Cassiopeia detail, illustrating the identifications by Dreyer (1916) and Rawlins (1993) of K 237-239 with HIP 9598, HIP 9480 and HIP 9009. |
Open with DEXTER | |
In the text |
![]() |
Figure C.15:
Perseus. The additional stars (in blue) appear shifted from a
better match about 10 |
Open with DEXTER | |
In the text |
![]() |
Figure C.16: Serpens. |
Open with DEXTER | |
In the text |
![]() |
Figure C.17: Auriga. |
Open with DEXTER | |
In the text |
![]() |
Figure C.18: Sagitta. |
Open with DEXTER | |
In the text |
![]() |
Figure C.19: Ophiuchus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.20: Ophiuchus detail. |
Open with DEXTER | |
In the text |
![]() |
Figure C.21: Ophiuchus detail. |
Open with DEXTER | |
In the text |
![]() |
Figure C.22: Aquila. |
Open with DEXTER | |
In the text |
![]() |
Figure C.23: Antinous. |
Open with DEXTER | |
In the text |
![]() |
Figure C.24: Pegasus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.25: Delphinus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.26: Equuleus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.27: Andromeda. |
Open with DEXTER | |
In the text |
![]() |
Figure C.28: Coma Berenices. |
Open with DEXTER | |
In the text |
![]() |
Figure C.29: Triangulum. |
Open with DEXTER | |
In the text |
![]() |
Figure C.30: Aries. |
Open with DEXTER | |
In the text |
![]() |
Figure C.31: Gemini. |
Open with DEXTER | |
In the text |
![]() |
Figure C.32:
Taurus. The Kepler position of K 547,
indicated |
Open with DEXTER | |
In the text |
![]() |
Figure C.33:
Taurus: enlarged detail of the head, showing K 517 to be best
identified with |
Open with DEXTER | |
In the text |
![]() |
Figure C.34:
Taurus: enlarged detail of the Pleiades. The position of K 534
in Manuscript and Progym is
indicated with a blue |
Open with DEXTER | |
In the text |
![]() |
Figure C.35: Cancer. The red square indicates K 577, Praesepe. |
Open with DEXTER | |
In the text |
![]() |
Figure C.36: Leo. |
Open with DEXTER | |
In the text |
![]() |
Figure C.37: Virgo. |
Open with DEXTER | |
In the text |
![]() |
Figure C.38:
Libra. The position as given in Kepler for
K 685,686 are indicated with |
Open with DEXTER | |
In the text |
![]() |
Figure C.39: Scorpius. Only the northern stars are in Brahe's catalogue. |
Open with DEXTER | |
In the text |
![]() |
Figure C.40: Sagittarius. |
Open with DEXTER | |
In the text |
![]() |
Figure C.41:
Capricornus. Three stars listed as nebulous by Brahe, indicated
with |
Open with DEXTER | |
In the text |
![]() |
Figure C.42:
Capricornus detail, showing identification of K 713
with |
Open with DEXTER | |
In the text |
![]() |
Figure C.43: Aquarius. |
Open with DEXTER | |
In the text |
![]() |
Figure C.44:
Pisces. The blue |
Open with DEXTER | |
In the text |
![]() |
Figure C.45: Cetus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.46: Lepus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.47: Orion. |
Open with DEXTER | |
In the text |
![]() |
Figure C.48: The sword of Orion. |
Open with DEXTER | |
In the text |
![]() |
Figure C.49: Eridanus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.50:
Canis Maior. The blue |
Open with DEXTER | |
In the text |
![]() |
Figure C.51: Canis Minor. |
Open with DEXTER | |
In the text |
![]() |
Figure C.52:
Argo. K 961 is near 23, 1 (see also Fig. C.54),
its position as emended by Hevelius is indicated with the
blue |
Open with DEXTER | |
In the text |
![]() |
Figure C.53: Argo detail. |
Open with DEXTER | |
In the text |
![]() |
Figure C.54: Argo detail. |
Open with DEXTER | |
In the text |
![]() |
Figure C.55: Crater. |
Open with DEXTER | |
In the text |
![]() |
Figure C.56: Corvus. |
Open with DEXTER | |
In the text |
![]() |
Figure C.57: Hydra. |
Open with DEXTER | |
In the text |
![]() |
Figure C.58: Centaurus. The catalogue longitudes appear shifted by about a degree. |
Open with DEXTER | |
In the text |
Copyright ESO 2010
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