Halley's Star Catalog

Introduction

Edmond Halley (1656–1742) was an English astronomer and mathematician born in East London. He showed an interest in mathematics and astronomy at an early age, and his father sent him to St. Paul's school and later to the Univerity of Oxford.

The task of improving on Tycho Brahe's catalog being already in the hands of Flamsteed and Hevelius, Halley resolved instead to complete Tycho's catalog by the addition of southern stars, an idea already suggested by Hevelius. This project received enthusiastic support, including from King Charles II, and an expedition was arranged by the East India Company to send him to the island of St. Helena with the proper equipment to conduct his observations. He reached the island in 1676 (he was only 20) and stayed there for two years. The expedition resulted in the star catalogue Catalogus Stellarum Australium [4] (1679).

In 1678, Halley was granted the M.A. degree from the University of Oxford and elected a fellow of the Royal Society. The episode where he visited Hevelius in Gdańsk to evaluate his methods takes place in 1679.

During the rest of his long career, Halley made numerous discoveries in various branches of science and philosophy and published abundantly. He was instrumental in the publication of Newton's Principia Mathematica in 1687. He was appointed Savilian professor of geometry at Oxford in 1704. In A Synopsis of the Astronomy of Comets [3] (1705), he determined the orbital elements of 24 comets from historical observations, based on Kepler's laws. He noticed that the comet of 1682, which now bears his name, was probably the same as the ones observed in 1607 and 1531, and successfully predicted its return in 1758.

In 1720, he succeeded Flamsteed as Astronomer Royal at Greenwich and held this position until his death in 1742.

The southern stars catalog

Halley's catalog contains 341 stars. It covers (at least in part) some of the Ptolemaic constellations of the southern hemisphere (Sco Sgr Eri CMa Nav Hya Cen Lup Ara CrA) as well as Columba and 11 of the 12 new southern constellations (Aps Cha Dor Gru Hyi Mus Pav Phe TrA Tuc Vol) introduced by Petrus Plancius. Indus and Piscis Austrinus are not covered, due to bad weather (except Fomalhaut, inserted between Canis Major and Columba). In honor of the king, Halley introduces the new constellation Robur Carolinum objected to by Lacaille (see the last paragraph of Lacaille's appendix to Table des Ascensions Droites) and now obsolete.

The catalog uses 2 to 4 lines to represent each catalog entry. Longitudes and latitudes use the same columns on two consecutive lines. Magnitude values occupy the last column and magnitude ranges are represented by two magnitude values on consecutive lines.

Reference stars

Halley determined star positions by trigonometrical computation from measured angular distances to reference stars. With few exceptions, the catalog entries mention the reference stars used (by a short description) and the measured distances. The positions of the reference stars are to be found in Tycho's catalog or in Halley's own catalog.

No distances to reference stars are mentioned for the last six stars of Lupus; the catalog explains that they were observed using an imprecise method while sailing.

Only one distance is given for five stars in Scorpius, for which it is indicated that the longitude or latitude is to be found in Tycho's catalog or Kepler's (secunda classis). Halley has precessed these longitudes by 1°04' to account for the difference between Tycho's equinox (1601-01-01 Julian) and his own (1678-01-01 Julian), which corresponds to a precession rate of about 49.87" per year.

Most entries mention two distances to reference stars, but sometimes three distances (3 cases) or even four (only 1 case, Nav 41, Canopus) are given.

The old catalog

Star positions E Catal. Vetusto (from the old catalog) or E Catal. Bartschii (from Bartsch's catalog) are also given for many stars. According to the introduction, the old catalog is the one found in Christophorus Clavius's commentary on Sacrobosco's De sphæra mundi [5, p. 151]. It is an adaptation of Ptolemy's catalog. Bartsch's catalog comes from Kepler's Tabulæ Rudolphinæ, the tertia classis section.

Clavius's longitudes are precessed by -6°40' with respect to Ptolemy's. Halley has precessed them by 28°41' to his own equinox. This suggests that Clavius uses an equinox far in the past (to be elucidated: I haven't looked very hard for the mention of an equinox in the Latin text).

Bartsch's longitudes have been precessed by 1°05' or 1°04' (why the variation ?) except in a few cases (Phe 4 by 55', Mus 4 by 1°02', Cha 8 by 1°20'), maybe typos.

Catalog data

Halley's catalog has already been put in machine-readable form by F. Verbunt and R. H. van Gent as part of their study of early southern star catalogs [1], and made available as part of VizieR catalog J/A+A/530/A93.

I digitized it independently, retaining all the data fields of the original, and added Baily's reprint of the catalog in [2], including his star identifications.

The following files contain catalog data and auxiliary information.

File name	Explanation
ReadMe	File descriptions
halley.dat	Halley's full catalog
halley_h.dat	Halley's simplified catalog
halley_b.dat	Halley's catalog according to Baily
corrs.dat	Corrections to the full catalog
corrs_h.dat	Corrections to the simplified catalog
corrs_b.dat	Corrections to Baily's version
notes.dat	Notes on Halley's catalog
notes_cla.dat	Mapping Halley - Ptolemy based on positions
notes_bar.dat	Mapping Halley - Bartsch based on positions
notes_dist.dat	Notes on distance computations
ref_stars.dat	List of reference stars

The ReadMe file describes the file formats, following the conventions for catalog descriptions of the VizieR service.

The file halley.dat contains the full catalog. The multi-line entries in the original have been flattened to fit on a single line, at the expense of some sparsely populated columns. The files halley_h.dat and halley_b.dat contain the catalog versions according to Halley (a selection of fields from the full catalog) and Baily, with the same layout for easy comparison.

In the original, the first value of a magnitude range is lower than the second except in one case (Nav 30, magnitude range 3-2). Baily represents ranges by half integers (for instance, the range 2-3 is represented by the decimal value 2.5) and halley_h.dat follows the same convention for consistency.

Corrections

There are a few obvious errors in the catalog: the zodiac sign is wrong for Sco 14 and Sco 15, the longitude is wrong for Hya 3, the distances to reference stars have been swapped for Sgr 11 and Cha 7. Baily has corrected the zodiac signs. Verbunt & van Gent [1, p. 12] document all of them. Also, the ancient catalog zodiac sign is wrong for Sgr 12 and there may be other errors in the ancient catalog positions, as mentioned in notes_cla.dat and notes_bar.dat

The files corrs.dat, corrs_h.dat, and corrs_b.dat contain the corrections to apply to the corresponding versions, in the form of overlays to the affected records.

The corrections have been applied before drawing the maps on the next page.

Notes

The file notes.dat collect various observations about the originals, including details about the five stars in Scorpius whose latitude or longitude is to be taken from Tycho or Kepler.

Halley's catalog is sufficiently accurate that most of its stars can be easily identified. Its references to Clavius's and Bartsch's catalogs may therefore provide a useful insight into the identification of their stars, at least according to Halley. The file notes_cla.dat shows the mapping between Halley's stars with a position E Catal. Vetusto and the corresponding Ptolemy star (through Clavius's catalog). Similarly, the file notes_bar.dat show the mapping between Halley's stars and Kepler's tertia classis stars implied by positions E Catal. Bartschii.

Computing the coordinates of a star given angular distances from two reference stars known by their coordinates is a tricky trigonometry problem. I don't know which method Halley used to solve it, let alone the algorithms he used to perform the computations by hand. I haven't even found a description of a "standard" solution to this problem so far. I attempted to reconstruct Halley's positions from the reference stars' using a custom method (which I would be happy to share). The result is shown in the notes_dist.dat file.

Reference stars are represented by a unique key in the catalog file halley.dat. For each of these keys, the file ref_stars.dat mentions the longer names used by Halley in the catalog (sometimes more than one per reference star) and the designations and positions from Tycho's catalog, or the designation from Halley's catalog itself. Reference stars from Tycho's catalog are present in all the versions (Progymnasmata, Manuscript, Kepler) with the same coordinates, except Ser 8 which has a different latitude in Kepler's version. The latitude from the Progymnasmata and Manuscript versions results in a better match with Halley's positions and that's the one I retained.

Star identifications

VizieR catalog J/A+A/530/A93 provides identifications of Halley stars in terms of HIP numbers, and more in the corresponding article [1]. Baily assigns Bayer or Lacaille designations and sometimes, in the notes, a Flamsteed designation.

I gathered Baily's identifications in their raw form in the file cross_b.dat described in ReadMe. Bayer designations are the pre-Lacaille ones.

File name	Explanation
cross_b.dat	Star identifications according to Baily [2]

References

[1] F. Verbunt & R. H. van Gent, Early star catalogues of the southern sky, De Houtman, Kepler (second and third classes), and Halley, Astronomy & Astrophysics 530, A93 (2011).

[2] Francis Baily, The Catalogues of Ptolemy, Ulugh Beigh, Tycho Brahe, Halley, Halley, Deduced from the Best Authorities. With Various Notes and Corrections, and a Preface to Each Catalogue. To Which is Added the Synonym of each Star, in the Catalogues of Flamsteed or Lacaille, as far as the same can be ascertained. Memoirs of the Royal Astronomical Society, Vol. 13, London, 1843. Also available here.

[3] Edmond Halley, A synopsis of the astronomy of comets. London: John Senex, 1705.

[4] Edmond Halley, Catalogus Stellarum Australium sive Supplementum Catalogi Tychonici. London: Thomas James, 1679.

[5] Christophorus Clavius (1538–1612) In Sphæram Ioannis De Scacro Bosco Commentarius. Rome, 1581.