Editing Hipparchus (section)

==Star catalog==
Late in his career (possibly about 135&nbsp;BC) Hipparchus compiled his star catalog. Scholars have been searching for it for centuries.{{r|swerdlow1992}} In 2022, it was announced that a part of it was discovered in a medieval parchment manuscript, [[Codex Climaci Rescriptus]], from [[Saint Catherine's Monastery]] in the [[Sinai Peninsula]], Egypt as hidden text ([[palimpsest]]).{{r|gwz2022}}<ref>{{cite journal|url=https://www.nature.com/articles/d41586-022-03296-1 |title=First known map of night sky found hidden in Medieval parchment |journal=Nature News |date=18 October 2022 |first=Jo |last=Marchant |volume=610 |issue=7933 |pages=613–614 |doi=10.1038/d41586-022-03296-1 |pmid=36258126 |bibcode=2022Natur.610..613M |s2cid=252994351 |access-date=22 October 2022}}</ref> This was proven wrong in 2024.<ref>{{Cite journal |last1=Grasshoff |first1=Gerd |last2=Hoffmann |first2=Susanne M. |date=2024-08-01 |title=An astronomical analysis of the data in the pseudo-Hipparchus palimpsest in the Codex Climaci Rescriptus |url=https://journals.sagepub.com/doi/10.1177/00218286241256345 |journal=Journal for the History of Astronomy |language=en |volume=55 |issue=3 |pages=332–349 |doi=10.1177/00218286241256345 |bibcode=2024JHA....55..332G |issn=0021-8286}}</ref>

[[File:School of Athens Raphael detail 03.jpg|thumb|The figure on the left may be Hipparchus, from [[Raphael]]’s fresco ''[[The School of Athens]]'']]
Hipparchus also constructed a celestial globe depicting the constellations, based on his observations. His interest in the [[fixed star]]s may have been inspired by the observation of a [[supernova]] (according to Pliny), or by his discovery of precession, according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by [[Timocharis]] and [[Aristillus]]. For more information see [[Discovery of precession]]. In [[Raphael]]'s painting ''[[The School of Athens]]'', Hipparchus may be depicted holding his celestial globe, as the representative figure for astronomy. It is not certain that the figure is meant to represent him.{{r|swerdlow1992}}

Previously, [[Eudoxus of Cnidus]] in the fourth century&nbsp;BC had described the stars and constellations in two books called ''Phaenomena'' and ''Entropon''. [[Aratus]] wrote a poem called ''Phaenomena'' or ''Arateia'' based on Eudoxus's work. Hipparchus wrote a commentary on the ''Arateia''—his only preserved work—which contains many stellar positions and times for rising, culmination, and setting of the constellations, and these are likely to have been based on his own measurements.

[[File:19th century Hipparchus engraving.jpg|thumb|A 19th century artist's impression of Hipparchus{{r|ks-engraving}}]]
According to Roman sources, Hipparchus made his measurements with a scientific instrument and he obtained the positions of roughly 850 stars. Pliny the Elder writes in book II, 24–26 of his Natural History:{{sfn|Hoffmann|2017}}

{{Blockquote|This same Hipparchus, who can never be sufficiently commended, ... discovered a new star that was produced in his own age, and, by observing its motions on the day in which it shone, he was led to doubt whether it does not often happen, that those stars have motion which we suppose to be fixed. And the same individual attempted, what might seem presumptuous even in a deity, viz. to number the stars for posterity and to express their relations by appropriate names; having previously devised instruments, by which he might mark the places and the magnitudes of each individual star. In this way it might be easily discovered, not only whether they were destroyed or produced, but whether they changed their relative positions, and likewise, whether they were increased or diminished; the heavens being thus left as an inheritance to any one, who might be found competent to complete his plan.}}

This passage reports that

* Hipparchus was inspired by a newly emerging star 
* he doubts on the stability of stellar brightnesses
* he observed with appropriate instruments (plural—it is not said that he observed everything with the same instrument) 
* he made a catalogue of stars

It is unknown what instrument he used. The [[armillary sphere]] was probably invented only later—maybe by Ptolemy 265 years after Hipparchus. The historian of science S. Hoffmann found clues that Hipparchus may have observed the longitudes and latitudes in different coordinate systems and, thus, with different instrumentation.{{r|hoffman-befunde}} Right ascensions, for instance, could have been observed with a clock, while angular separations could have been measured with another device.

===Stellar magnitude===
Hipparchus is conjectured to have ranked the [[apparent magnitude]]s of stars on a numerical scale from 1, the brightest, to 6, the faintest.{{sfn|Toomer|1984|loc=[https://archive.org/details/ptolemysalmagest0000ptol/page/16/ {{p.|16}}]: "The magnitudes range (according to a system which certainly precedes Ptolemy, but is only conjecturally attributed to Hipparchus) from 1 to 6.", {{pgs|341–399}}}} This hypothesis is based on the vague statement by Pliny the Elder but cannot be proven by the data in Hipparchus's commentary on Aratus's poem. In this only work by his hand that has survived until today, he does not use the magnitude scale but estimates brightnesses unsystematically. However, this does not prove or disprove anything because the commentary might be an early work while the magnitude scale could have been introduced later.{{r|hoffman-befunde}} Yet, it was proven that the error bars of magnitudes in ancient star catalogue is 1.5 mag which suggests that these numbers are not based on measurements.<ref>{{Cite journal |last1=Protte |first1=Philipp |last2=Hoffmann |first2=Susanne M. |date=2020 |title=Accuracy of magnitudes in pre-telescopic star catalogs |url=https://onlinelibrary.wiley.com/doi/10.1002/asna.202013803 |journal=Astronomische Nachrichten |language=en |volume=341 |issue=8 |pages=827–840 |doi=10.1002/asna.202013803 |issn=0004-6337|arxiv=2008.04967 |bibcode=2020AN....341..827P }}</ref> There were several suggestions on measurement methodologies and feasibility studies.<ref>Protte Ph. and Hoffmann S.M. (2021). Pre-Telescopic star catalogues – Accuracy in magnitudes and positions, in Wolfschmidt and Hoffmann [Hrsg.]: Applied and Computational History of Astronomy – Proceedings of the Splinter Meeting in the Astronomische Gesellschaft, Sept. 25. Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften; Vol. 55, tredition, Hamburg, 109-144</ref> In all cases, the error bars would be smaller. Hence, Hoffmann (2022) suggested that the magnitudes were not measured at all but mere estimates for globe makers to improve pattern recognition on globes as astronomer's computing machines.<ref>Hoffmann, S.M. (2022). Essay: On Ptolemy’s stellar magnitudes, in Hoffmann and Wolfschmidt (eds.). Astronomy in Culture – Cultures of Astronomy, tredition/ OpenScienceTechnology, Hamburg/ Berlin, 426-429</ref> 

Nevertheless, this system certainly precedes [[Ptolemy]], who used it extensively about AD 150.{{sfn|Toomer|1984|loc=[https://archive.org/details/ptolemysalmagest0000ptol/page/16/ {{p.|16}}]: "The magnitudes range (according to a system which certainly precedes Ptolemy, but is only conjecturally attributed to Hipparchus) from 1 to 6.", {{pgs|341–399}}}} This system was made more precise and extended by [[N. R. Pogson]] in 1856, who placed the magnitudes on a logarithmic scale, making magnitude 1 stars 100 times brighter than magnitude 6 stars, thus each magnitude is {{radic|100|5}} or 2.512 times brighter than the next faintest magnitude.<ref>{{cite journal|last=Pogson|first=N. R.|author-link=Norman Robert Pogson|date=1856|title=Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857|url=http://articles.adsabs.harvard.edu//full/seri/MNRAS/0017//0000012.000.html|journal=[[Monthly Notices of the Royal Astronomical Society|MNRAS]]|volume=17|page=12|bibcode=1856MNRAS..17...12P|doi=10.1093/mnras/17.1.12|doi-access=free}}</ref>

=== Coordinate System ===
It is disputed which coordinate system(s) he used. Ptolemy's catalog in the ''[[Almagest]]'', which is derived from Hipparchus's catalog, is given in [[ecliptic coordinate system|ecliptic coordinates]]. Although Hipparchus strictly distinguishes between "signs" (30° section of the zodiac) and "constellations" in the zodiac, it is highly questionable whether or not he had an instrument to directly observe / measure units on the ecliptic.{{r|hoffman-befunde}}{{sfn|Hoffmann|2017}} He probably marked them as a unit on his celestial globe but the instrumentation for his observations is unknown.{{r|hoffman-befunde}}

[[File:Alm signs+consts.jpg|thumb|upright=1.8|Ptolemy's constellation areas (blue polygons) and "signs" of the zodiac had different sizes and extends; it is highly likely Hipparchus considered these units the same. Reconstruction from the Almagest{{sfn|Hoffmann|2017}}]]

Delambre in his {{lang|fr|Histoire de l'Astronomie Ancienne}} (1817) concluded that Hipparchus knew and used the [[equatorial coordinate system]], a conclusion challenged by [[Otto Neugebauer]] in his ''History of Ancient Mathematical Astronomy'' (1975). Hipparchus seems to have used a mix of [[ecliptic coordinate system|ecliptic coordinates]] and [[equatorial coordinate system|equatorial coordinates]]: in his commentary on Eudoxus he provides stars' polar distance (equivalent to the [[declination]] in the equatorial system), right ascension (equatorial), longitude (ecliptic), polar longitude (hybrid), but not celestial latitude. This opinion was confirmed by the careful investigation of Hoffmann{{sfn|Hoffmann|2017}} who independently studied the material, potential sources, techniques and results of Hipparchus and reconstructed his celestial globe and its making.

As with most of his work, Hipparchus's star catalog was adopted and perhaps expanded by Ptolemy, who has (since Brahe in 1598) been accused by some<ref>{{cite book |last1=Newton |first1=Robert Russell |title=The Crime of Claudius Ptolemy |date=1977 |publisher=Johns Hopkins University Press |location=Baltimore, MD |isbn=978-0-8018-1990-2 |url=https://archive.org/details/crime-of-cladius-ptolemy |via=[[Internet Archive]]}}</ref> of fraud for stating (''Syntaxis'', book 7, chapter 4) that he observed all 1025 stars—critics claim that, for almost every star, he used Hipparchus's data and precessed it to his own epoch {{fraction|2|2|3}} centuries later by adding 2°40' to the longitude, using an erroneously small precession constant of 1° per century. This claim is highly exaggerated because it applies modern standards of citation to an ancient author. True is only that "the ancient star catalogue" that was initiated by Hipparchus in the second century BC, was reworked and improved multiple times in the 265 years to the Almagest (which is good scientific practise even today).{{r|hoffmann2018}} Although the Almagest star catalogue is based upon Hipparchus's, it is not only a blind copy but enriched, enhanced, and thus (at least partially) re-observed.{{r|hoffman-befunde}}

=== Celestial globe ===
[[File:HipparchsGlobus smh2017.png|thumb|Reconstruction of Hipparchus's celestial globe according to ancient descriptions and the data in manuscripts by his hand (excellence cluster TOPOI, Berlin, 2015 - published in Hoffmann (2017){{sfn|Hoffmann|2017}}).]]
Hipparchus's celestial globe was an instrument similar to modern electronic computers.{{sfn|Hoffmann|2017}} He used it to determine risings, settings and culminations (cf. also Almagest, book VIII, chapter 3). Therefore, his globe was mounted in a horizontal plane and had a meridian ring with a scale. In combination with a grid that divided the celestial equator into 24 hour lines (longitudes equalling our right ascension hours) the instrument allowed him to determine the hours. The ecliptic was marked and divided in 12 sections of equal length (the "signs", which he called {{lang|grc-Latn|zodion}} or {{lang|grc-Latn|dodekatemoria}} in order to distinguish them from constellations ({{lang|grc-Latn|astron}}). The globe was virtually reconstructed by a historian of science.

=== Arguments for and against Hipparchus's star catalog in the Almagest ===

For:
* common errors in the reconstructed Hipparchian star catalogue and the Almagest suggest a direct transfer without re-observation within 265 years. There are 18 stars with common errors - for the other ~800 stars, the errors are not extant or within the error ellipse. That means, no further statement is allowed on these hundreds of stars. 
* further statistical arguments

Against:
* Unlike Ptolemy, Hipparchus did not use ecliptic coordinates to describe stellar positions. 
* Hipparchus's catalogue is reported in Roman times to have enlisted about 850 stars but Ptolemy's catalogue has 1025 stars. Thus, somebody has added further entries. 
* There are stars cited in the Almagest from Hipparchus that are missing in the Almagest star catalogue. Thus, by all the reworking within scientific progress in 265 years, not all of Hipparchus's stars made it into the Almagest version of the star catalogue.

Conclusion: Hipparchus's star catalogue is one of the sources of the Almagest star catalogue but not the only source.{{r|hoffmann2018}}