Atlantis Online
June 19, 2021, 05:21:22 am
Welcome, Guest. Please login or register.

Login with username, password and session length
News: Hunt for Lost City of Atlantis
http://news.bbc.co.uk/1/hi/world/europe/3227295.stm
 
  Home Help Arcade Gallery Links Staff List Calendar Login Register  

Hipparchus' Celestial Globe

Pages: [1] 2 3   Go Down
  Print  
Author Topic: Hipparchus' Celestial Globe  (Read 2317 times)
Bianca
Superhero Member
******
Posts: 41646



« on: December 08, 2007, 08:00:12 am »






A guy vacationing in Naples has stumbled across one of the most desperately sought pieces of ancient scholarship, long thought lost forever when the great Library of Alexandria Egypt was destroyed around 400 AD.

Apparently, it had been right in front of millions of tourists for decades.

A statue of Atlas carrying the Universe on his shoulders turns out to have used the lost celestial globe of Hipparchus, the Greek astronomer who first discovered the precession of Earth’s axis, observed a nova, precisely calculated the length of the year, and invented the stellar brightness scale used today.

And he also made this newly-rediscovered, amazingly accurate star map, complete with celestial equator, ecliptic, and Tropics of Cancer and Capricorn.



April 04, 2005 | 

« Last Edit: December 08, 2007, 08:05:26 am by Bianca2001 » Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.

Share on Facebook Share on Twitter

Bianca
Superhero Member
******
Posts: 41646



« Reply #1 on: December 08, 2007, 08:07:57 am »











                                         Long Lost Star Catalog Found in Plain Sight




 
By Bjorn Carey
Staff Writer
24 January, 2005

The long lost star catalog of Hipparchus has been under our noses - or, more accurately, slightly above them - for more than 1,800 years.

Sitting atop the broad shoulders of a seven-foot statue known as the Farnese Atlas is a sky globe depicting the nighttime sky. Scientists have been able to match the constellations shown on the globe with descriptions from Hipparchus's only surviving work, Commentaries, and have concluded that this is a marble copy of his star catalog.

Hipparchus, who was Greek, was one of the greatest of the ancient astronomers and did his most important work between 140-125 BC. He calculated the length of the year to within six and a half minutes, developed a scale to rate the brightness of stars, was the first to record a nova, theorized on the motions of the Sun and Moon, provided high quality planetary observations and created the first ever catalog of 1,000 stars.

Perhaps his most important observation, and the one that provided the key to determining the Atlas held his catalog, was precession. Precession is the wobbling of Earth on its axis, like a spinning top as it slows down, over long periods of time. This wobbling is on a 26,000 year cycle, and causes the stars to appear to move across the sky. For example, Polaris, the North Star, is currently above the North Pole, but it has not always been so and will not be in the future.


Bradley Schafer of Louisiana State University, Baton Rouge combined data from the precession cycles with measurements he took of 70 positions on the globe and used a mathematical model to determine what point in time the Atlas's sky globe represents. Schafer determined that the best date for the original observations was 125 BC, with a normal margin of error of ± 55 years.

The date of 125 BC immediately suggests that this is the lost catalog of Hipparchus, who created his star catalog in 129 BC. The 125 BC date also eliminates all previously proposed candidates for this star catalog. The works of Aratus (275 BC), Eudoxus (366 BC), and the Assyrian observer (1130 BC), are all too early, while Ptolemy's work in 128 AD is too late to match up to this star catalog.

Providing more evidence that the constellation figures on the Farnese Atlas were based on a star catalog is that the accuracy is within 3.5 degrees - which would not be possible based on the simple verbal descriptions provided by Aratus or Eudoxus, which only have accuracy of about 8 degrees.

Additionally, the Atlas sky globe shares no differences and many unique similarities with the constellations Hipparchus described in Commentaries.

The Farnese Atlas, dating to 150 AD, is a well known Roman copy of a Greek statue, and depicts 41 constellations, the celestial equator, tropics, and ecliptic. It is currently in the Farnese Collection in the National Archaeological Museum in Naples, Italy. Atlas was sentenced by Zeus to hold up the sky - this Atlas holds the nighttime sky.

"Perhaps the most fascinating part of the discovery is simply that we have recovered one of the most famous known examples of 'lost ancient wisdom,'" Schafer said.

This article is part of SPACE.com's weekly Mystery Monday series
« Last Edit: December 08, 2007, 08:15:45 am by Bianca2001 » Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #2 on: December 08, 2007, 08:09:41 am »











                           ANCIENT ASTRONOMER'S WORK FOUND ON ROMAN STATUE






From: http://www.swissinfo.org/sen/swissinfo.html?siteSect=143&sid=5461267

SAN DIEGO (Reuters) - A Roman statue of Atlas -- the mythical titan who carried the heavens on his shoulders -- holds clues to the long-lostwork of the ancient astronomer Hipparchus, an astronomical historian says.

The statue in question is known as the Farnese Atlas, a 2.1 metre tall marble work which resides in the Farnese Collection in the National Archeological Museum in Naples, Italy.

What makes it important to scientists is not the titan's muscular form but the globe he supports: carved constellations adorn its surface in exactly the locations Hipparchus would have seen in his day, suggesting that the sculptor based the globe on the ancient astronomer's star catalogue, which no modern eyes have seen.

"There are really very few instances where lost ancient secrets or wisdom are ever actually found," said Bradley Schaefer of LouisianaState University. "Here is a real case where rather well-known lost ancient wisdom has been discovered."

Hipparchus, who flourished around 140-125 BC, is believed to have been one of the world's first path-breaking astronomers. Among other innovations, he put together the first comprehensive list of the hundreds of stars he observed, known as a star catalogue.

This catalogue no longer exists, and previously the only evidence for it came from references made to it by astronomers who followed Hipparchus, Schaefer said.

Another Hipparchus invention -- the idea of precession, which is the slow movement of the stars and constellations across the sky in relation to the celestial equator -- led Schaefer to believe that Atlas's globe referred to Hipparchus's star catalogue.

An analysis of the positions of the constellation figures on Atlas's globe allowed Schaefer to date the work to 125 BC, plus or minus 55 years. This would have been within the range when Hipparchus would have been working.

Other theories about who wrote the star catalogue include observers who were either too early -- including a poet writing around 275 BC and an Assyrian observer around 1130 BC -- or too late. This includes the astronomer Ptolemy, writing in 128 AD.

Reuters
« Last Edit: December 08, 2007, 08:21:34 am by Bianca2001 » Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #3 on: December 08, 2007, 08:24:44 am »

Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #4 on: December 08, 2007, 08:33:24 am »








             THE EPOCH OF THE CONSTELLATIONS ON THE FARNESE ATLAS AND THEIR ORIGIN IN


                                                HIPPARCHUS’S LOST CATALOGUE





BRADLEY E. SCHAEFER, Louisiana State University, Baton Rouge

1. BACKGROUND

The Farnese Atlas is a Roman statue depicting the Titan Atlas holding up a celestial globe that displays an accurate representation of the ancient Greek constellations (see Figures 1 and 2). This is the oldest surviving depiction of this set of the original Western constellations, and as such can be a valuable resource for studying their early development. The globe places the celestial figures against a grid of circles (including the celestial equator, the tropics, the colures, the ecliptic, the Arctic Circle, and the Antarctic Circle) that allows for the accurate positioning of the constellations. The positions shift with time due to precession, so the observed positions on the Farnese Atlas correspond to some particular date. Also, the declination of the Arctic and Antarctic Circles will correspond to a particular latitude for the observer whose observations were adopted by the sculptor. Thus, a detailed analysis of the globe will reveal the latitude and epoch for the observations incorporated in the Atlas; and indeed these will specify enough information that we can identify the observer. Independently, a detailed comparison of the constellation symbols on the Atlas with those from the other surviving ancient material also uniquely points to the same origin for the fi gures.

The Farnese Atlas1 first came to modern attention in the early sixteenth century when it became part of the collection of antiquities in the Farnese Palace in Rome, hence its name. The statue was later transferred to the museum in Naples now called the Museo Archeologico Nazionale di Napoli. It is carved in white marble and depicts the bearded Atlas crouched down on one knee with a cloak over his shoulder and holding the celestial globe on his shoulder with both hands. The globe is 65cm in diameter. Its top has a substantial hole knocked into it and this has obliterated the constellations of Ursa Major and Ursa Minor. A total of 41 constellations2 are depicted, each drawn in positive relief as the classical figure, with no individual stars shown. Art historians conclude that the statue is a Roman copy from the second century A.D. of a Greek original dating to before the birth of Christ.3

What is the date of the observations used for depicting the constellation positions on the Farnese Atlas? A very wide range of plausible answers is possible. First, the Roman sculptor could have updated the constellation positions with his own observations (or those of a contemporary), hence suggesting a date of c. 150 A.D. Second, the Roman sculptor could have used the latest star catalogue to place the constellations accurately onto the coordinate grid of the sky, and this would be from the Almagest of Ptolemy,

0021-8286/05/3602-0167/$10.00 © 2005 Science History Publications Ltd
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #5 on: December 08, 2007, 08:34:31 am »



FiG. 1. The Atlas holds the celestial globe on his shoulders.

In this figure, we see the colure dividing the sky between Canis Major and Argo. This one observation immediately tells us that the constellations were placed to represent the sky as it was around the time of Hipparchus.

Photograph by Dr Gerry Picus, Griffith Observatory.

« Last Edit: December 08, 2007, 08:36:13 am by Bianca2001 » Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #6 on: December 08, 2007, 08:40:32 am »








FIG. 2. The rear side of the globe. We see the equator, the ecliptic, the equinoctial colure, and the two tropics. The edge of the horn of Aries is exactly on the colure, and this immediately tells us that the constellations were placed for around the time of Hipparchus.

Photograph by Dr Gerry Picus, Griffith Observatory.





Suggesting a date of c. 128 A.D. Third, art historians all point to the original Greek sculptor as using the constellations based in Aratus’s poem Phaenomena, which has a date of c. 275 B.C. An origin with Aratus was the dominant opinion amongst scholarly publications in the last century. Fourth, we know that Aratus’s work was substantially a copy of an earlier book of the same name by Eudoxus with a date of c. 366 B.C. Fifth, a precessional dating of 172 lore items derived from Eudoxus’s book proves that all of the lore actually dates from 1130 ± 80 B.C.4 So we are left with many candidates, all reasonable, for the date of the observations used to place the constellations: from 1130 B.C. to A.D. 150.

The possibility of deriving a date and latitude from the Farnese Atlas has not been lost on earlier researchers. E. L. Stevenson claims (purely on the basis of the positions of the solstices) that the constellations date “at least three hundred years before the Christian era”, while C. Gialanella and V. Valerio as well as M. Fiorini agree that the constellation positions suggest a date in the fourth century B.C., although Valerio later changed the date to A.D. 150. Thiele points to an origin by Hipparchus and Eudoxus based on stylistic considerations, and he also points to a latitude of 23° which he specifies as being greatly different from that of Rhodes. For the latitude of the observer, Fiorini gives 40° and points to Macedonia, Gialanella and Valerio give 32° and point to Alexandria, while Valerio later gives 33.5° and points to Middle Phoenicia. For the obliquity of the ecliptic, we hear values of 23° from Fiorini, 25.5° from Gialanella and Valerio, 25° from Valerio, and 24° from G. Aujac.

Throughout all the few sentences of discussions by the various authors, no evidence is ever presented, nor are methods of measurement ever discussed, nor is any indication of the accuracy of the claims ever made. With the total lack of these crucial details, we cannot take these off-hand claims seriously. In her appraisal of this situation, Aujac concludes: “A critical review of existing studies of the globe, together with detailed reproduction and careful analysis, is urgently needed to resolve these questions.”
« Last Edit: December 08, 2007, 08:43:48 am by Bianca2001 » Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #7 on: December 08, 2007, 08:45:46 am »








This paper will provide the requested analysis.

I start with a detailed analysis of the constellation symbols and descriptions on the Farnese Atlas as compared to all relevant surviving sources from Antiquity. In addition, I have taken detailed photographs of the Farnese Atlas under conditions for which photogrammetry can be performed. From these photographs, I have measured the positions of the constellations in the coordinate system of the globe. I have then performed a chi-square analysis to determine the best date (as well as the uncertainties in this value) for the constellation positions. In all, my results will point to the source of the observations with high confi dence.

The plan of this paper is to start in Section 2 by making a detailed comparison of the symbols on the Farnese Atlas with those from all other ancient sources. This analysis will include detailed comparison of descriptions of each constellation as compared with the works of Aratus (from the Phaenomena, and hence also Eudoxus), Hipparchus (from his Commentary on the Phaenomena of Aratus and Eudoxus), Ptolemy (from the Almagest), and Psuedo-Eratosthenes (from the Catasterismi and hence also Eratosthenes). In Section 3, I will present the results of my extensive photogrammetry, such that I will derive a very confident date for the original observations used to place the constellations onto the globe. This section will also give the declination of the Arctic and Antarctic Circles on the globe and discuss the implications for the latitude of the observer. A third part of Section 3 will discuss the accuracy of the placement of the constellations and the implications for the source of the original observations. Section 4 will put all the results together and a strong case will be made for the identification of the original observer. Section 5 will discuss some implications and applications of this conclusion. Section 6 will summarize the conclusion.

This paper has an extensive Appendix, into which I have placed all the technical details relating to the photogrammetry. The goal is to provide complete details so that readers can test my results or perform their own analyses.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #8 on: December 08, 2007, 08:48:16 am »








              2. DETAILED COMPARISON OF CONSTELLATION FIGURES WITH ANCIENT SOURCES



 

The Atlas’s globe contains a wealth of information in the form of constellation fi gures. From a detailed comparison of these symbols with all known sources describing the ancient constellations, we might be able to select and/or eliminate possible sources for the sculptor. Here, I will make this comparison with the works of Aratus (and hence Eudoxus), Hipparchus, Pseudo-Eratosthenes (and presumably Eratosthenes), and Ptolemy.

As a preview, I will highlight several of the more distinct differences. First, the Farnese Atlas is completely missing the later Greek constellations of Equuleus, Coma Berenices, and Antinous. Second, Hercules is depicted as a kneeling man with no clothes and no objects in his hand instead of as the Greek hero. These two facts suggest that the source of the constellations was not in later Greek times. Third, the modern constellation of Libra is depicted as a separate balance, even though the claws of Scorpius extend up to the balance. Fourth, the summer solstice is depicted as being at the start of Cancer near the head of Pollux, in stark contrast to the tradition from Aratus and Eudoxus that the solstice is near the start of Leo. These last two items suggest that the source is after the time of Aratus.

Before I perform the detailed comparison with the individual books, I will give a list of the details that are different from all ancient sources. These details then cannot be useful evidence against any one source, but rather point to changes incorporated after the data left their source (e.g., by the sculptor). Here are the universal differences:

(1–2) The horn of the Bull does not touch the foot of the Charioteer, and the head of Andromeda does not overlay the navel of Pegasus, at odds with all ancient descriptions of these constellations. Likely, the sculptor avoided the overlap simply for artistic reasons and clarity.

(3) The curious rectangular feature above Cancer corresponds to nothing recorded in any of the ancient sources, and is undoubtedly a later addition by either the Greek or Roman sculptor.

(4–5) The globe does not depict Sagitta or Triangulum, whereas every ancient source explicitly discusses both. These are inconspicuous constellations in crowded areas, so perhaps their absence is just an artistic decision by the sculptor.

(6) The globe does not depict Ursa Minor, although this is attested by all ancient sources. But the Little Bear should be on the very edge of the hole in the top of the globe, so there is a small chance that the fi gure was in the hole and that there is some other error relating to the positioning near the north pole (cf. Section A.2.2).

(7) The ecliptic crosses the equator 5° west of the colure lines. This arrangement is wrong by definition, as precession moves the sky along the ecliptic, suggesting that the sculptor made the change because of his lack of astronomical knowledge.

(Cool The string attached to the northern fi sh of Pisces is missing, although the string is present in all ancient sources.

(9) Sagittarius appears to have a bare back, even though the Almagest and Commentaries talk about the cloak-strap. Since all nine differences are universal, they cannot be used to point towards or away from any one source. Instead, these differences indicate changes made after the information had left the astronomer, likely by the sculptor.

Similarly, the universal similarities between the globe and all ancient sources (e.g., that only the stern of Argo is depicted) cannot be used to distinguish the origin of the fi gures. Thus, the only data relevant for determining the origin of the figures are the differences between the globe and sources, which vary with the source.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #9 on: December 08, 2007, 08:50:51 am »








The Phaenomena of Aratus was a popular description of the constellations; it dates to around 275 B.C, and is the earliest surviving discussion of the ancient Greek constellations.5 Its popularity served to freeze the development of the constellations as well as to define the basic properties of the group. The text is largely a version of an earlier (now lost) book of the same name by Eudoxus from around 366 B.C., with substantial further fragments from the work by Eudoxus appearing in the only surviving work of Hipparchus (his Commentary). The Phaenomena gives descriptions of the constellation figures and also tells how these figures relate to the various circles on the sky.




A detailed comparison with the Farnese Atlas shows many differences:

(1) Aratus stated the summer solstice to be at the start of Leo, whereas the statue shows it to be near the head of Pollux with the entire constellation of Cancer between.

(2) The human part of the Centaur is said to be under Scorpius, whereas the statue places it under Virgo, with the entire constellation of Libra between.

(3) Eridanus is said to stop at the neck of Cetus while the stars under Lepus are said to be nameless, whereas the Farnese Atlas shows Eridanus as extending all the way through Columba over to the feet of Canis Major.

(4) Aratus says that Auriga has the Goat and Kids, whereas the globe in Naples shows the Charioteer instead to be holding a whip.

(5) Serpens is said to encircle the waist of Ophiucus, contrary to what is seen on the statue.

(6) The constellation of Libra is depicted as a balance on the globe, but Aratus simply calls it “The Claws”.

(7) The knees of the Charioteer are said to be on the Tropic of Cancer, whereas the globe shows even his feet to be north of the tropic.

(Cool The left shoulder and shin of Perseus are said to be on the Tropic of Cancer, whereas on the statue all of Perseus is north of the tropic.

(9) The head and neck of Cygnus are said to be on the Tropic of Cancer, whereas the sculptor depicts the constellation with the beak tip touching the tropic.

(10) Ophiucus’s shoulders are said to be along the tropic, whereas the globe shows the top of his head to be there.

(11) The knees of Ophiucus are not on the equator as in Aratus, but are depicted as being substantially south of the equator.

(12) The belt of Cepheus is said by Aratus to be on the Arctic Circle, whereas the Atlas has the neck of Cepheus so drawn. There are many further discrepancies for which the case is less clear, for example Aratus says that the head of Draco is on the Arctic Circle and that Crater and Corvus are on the equator, while the globe shows the head only as being near the Arctic Circle and the raven and cup as only tangent to the equator.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #10 on: December 08, 2007, 08:54:08 am »








Hipparchus was perhaps the greatest astronomer of Antiquity, his outstanding discovery being the precession of the equinoxes. He is said to have compiled a large star catalogue with at least hundreds of stars, although this catalogue has not survived. Indeed, only one of Hipparchus’s works has survived, the Commentary, which gives extensive quotes from both Eudoxus and Aratus.6 The thrust of the Commentary is to correct perceived errors in the Phaenomena by quoting the author’s own data and interpretation of the constellation figures. As a result, we can make a detailed comparison of Hipparchus’s personal descriptions with the Farnese Atlas. First the differences between Hipparchus and the globe:

(1) The head of Pollux is close to the Tropic of Cancer (and might even lie upon it), whereas Hipparchus says that the heads of both Twins are north of the Tropic and he even says that Pollux is north of the Tropic by 6°. But that is all: I can find only one non-universal difference between the globe and the Commentary. This difference is only quantitative, and it is only 1.7-σ in error (cf. Section A.2.1), which is not adequate grounds to claim a significant discrepancy. That is, the small shift of Gemini is typical of the scatter in the placement of the constellations, and so this is not grounds for considering the misplacement to be indicative. Another potential difference is that the globe depicts the modern Libra as a balance with the scorpion’s claws extending into it, while Hipparchus usually calls the constellation “The Claws”; however, in one place Hipparchus does recognize the constellation as “The Balance” (Commentary 3.1.5), so this cannot be regarded as being a true difference.



Now let us examine items in which the globe matches details particular to Hipparchus:

(A) Hipparchus explicitly corrects Aratus’s claim about the position of the Centaur (see item 2 above), and Hipparchus’s claim is matched by the depiction on the globe.

(B–G) Hipparchus also explicitly corrects Aratus’s items 7–12 above, and these corrections are entered onto the globe.

(H–J) Hipparchus explicitly corrects the Phaenomena by saying that the head of Draco is only close to the Arctic Circle, and that Crater and Corvus are south of the equator; all these items are as represented on the globe.

(K) Hipparchus states that the Arctic Circle is 37° from the north pole (i.e., at a declination of 53°), and this is reasonably consistent with my measured declination of 51.7° ± 0.9° for the Farnese Atlas.

(L) Item 3 (from the penultimate paragraph) is apparently corrected to agreement with the Atlas, as Hipparchus states that Eridanus has a second westward segment.

In all, the one difference is statistically insignificant while the dozen agreements between Hipparchus’s personal observations and the globe are close, many, and detailed. With this, we see that the comparison between the Atlas and Hipparchus is arguably perfect (other than the 9 itemized differences that are true for all ancient sources).
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #11 on: December 08, 2007, 08:57:14 am »








The Catasterismi that survives to today is an epitome from c. A.D. 100 (by an author known as Pseudo-Eratosthenes) of an original work of the same name by the famous Eratosthenes from c. 245 B.C.7 It is unclear what fraction of the surviving text is from Eratosthenes’s composition. The Catasterismi contains a verbal description of the myths and constellations, these being for the most part simply the usual descriptions such as are from Aratus. The Catasterismi does give some non-traditional details that match with the statue, in particular that

(A) the Arctic Circle is along the neck of Cepheus,

(B) the upheld wrist of Bootes is also along the Arctic Circle, and

(C) Eridanus appears above Canopus (hence it must extend through Columba). The Catasterismi differs in many details from those visible on the Farnese Atlas:



(1) Auriga is not shown on the Atlas with either the Goat or the Kids.

(2) The Asses are not shown on the west side of Cancer.

(3) Hercules is not shown on the Atlas as standing.

(4) Hercules is not shown as holding a lion skin. (5) Hercules is not shown as holding a club.

(6) Pegasus is shown as having wings, despite the explicit denial in the Catasterismi.

(7) The constellation Corona Australis is depicted on the globe but never mentioned by the Catasterismi.

(9) The modern constellation of Libra is not separated out and is described as simply the claws of Scorpius, unlike what we find on the statue.





Ptolemy’s Almagest dates from c. A.D. 128 and contains a long catalogue of stars individually labelled by their positions in the constellations.8 These labels allow us to visualize the constellation figure for comparison with the Farnese Atlas. There are many differences between the Almagest and the Atlas:

(1) Auriga is not shown on the statue as carrying the Kids.

(2–4) The constellations of Equuleus, Coma Berenices, and Antinous are not depicted on the globe.

(5) The Almagest identifi es the Asses near the middle of Cancer, while these are not displayed on the globe.

(6) The modern constellation of Libra is called “The Claws” by the Almagest but is drawn as a balance on the Farnese Atlas.

(7) Sagittarius does not have a cloak over the shoulders as stated in the Almagest.

(Cool In the Almagest Aquarius in not said to have a water jar, although this is clearly depicted on the statue.

(9) Canis Major does not have a crown, as shown on the globe, although the crown may simply be a depiction of light rays from Sirius.

(10) In the Almagest Eridanus turns south along the modern track near υ Eri, rather than extending to near the feet of Canis Major as shown on the Farnese Atlas.

(11) Ptolemy explicitly assigns two legs to Cygnus, whereas the Atlas shows only one.

From this detailed analysis, we see that the Farnese Atlas is virtually identical to the constellation description by Hipparchus, yet is greatly different from the descriptions from all other ancient sources. This obviously strongly suggests that the ultimate source of the position information used by the original Greek sculptor was Hipparchus’s data, which must be closely related to his (now lost) star catalogue.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #12 on: December 08, 2007, 08:59:15 am »








                                                     3. EPOCH AND LATITUDE





The constellations in the sky move slowly with respect to the declination circles and the colures, as a result of precession. The epoch for the observations that were incorporated into the Farnese Atlas is near that year for which the constellation positions on the globe most closely match those in the sky.

The latitude of the observer is related to the declination of the Ant/Arctic Circles as presented on the globe. Both of these calculations require that we get the positions of the constellations in the reference frame of the globe’s coordinate system. In principle this could be performed by taking a tape measure to the globe, but in practice an equivalent method is to take pictures of the globe and then carefully measure the pictures.

I took 49 pictures of the Farnese Atlas in Naples on 1 June 2004. I used a digital camera that allowed for good recording of the details without special lighting. For photogrammetry, it is important to know the distance between the camera and the near surface of the globe, as this is required to transform positions on the photograph to spherical coordinates on the globe. (All previous published photographs were taken at unknown distances, and that is why a new set of photographs was required.)

My photographs were all taken with the camera at a distance of either 6 or 20 feet from the surface
of the globe. There was substantial duplication and some pictures were not useable for various
reasons, so I ended up doing photogrammetry on twelve pictures. Detailed explanations and examples
for my photogrammetry techniques are presented in Appendix 1. Detailed results and analysis of the constellation positions and the declinations of the tropics and Ant/Arctic Circles are presented in Appendix 2.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #13 on: December 08, 2007, 09:01:04 am »








3.1. Epoch





At a simple level, the date of the Farnese Atlas’s astronomical information can be determined by looking at the position of the vernal equinox. For example, Ptolemy gives the position of the westernmost edge of the horns of Aries (γ Ari) as having an ecliptic longitude of 6ş for the year c. A.D. 128, while this same star will have a right ascension of zero (i.e., it will lie exactly on the colure) in the year 166 B.C. The Farnese Atlas shows the westernmost edge of the Ram’s horn to lie exactly on the colure, so we already know that the constellation position falls some time around the second century B.C. In particular, this one position argues against the Almagest or any late Greek or Roman source for the constellations on the Atlas.

Similarly, we can look at the position of the summer solstice point. According to Aratus (and hence Eudoxus) the summer solstice point is at the beginning of Leo (a statement that was true around 1250 B.C.9), while the position of the summer solstice is at the beginning of Cancer (just below the head of Pollux) around 1 B.C. The Farnese Atlas shows the summer solstice point to be at the start of Cancer and just beside the head of Pollux. This is a huge and critical difference of an entire constellation in the position of the summer solstice. This argues against any early Greek origin as well as Aratus’s or Eudoxus’s being the source for the constellations on the globe.

The two positions discussed in the previous paragraphs are indicative, but the uncertainties associated with any one position are likely to be a few centuries. However, by combining a similar analysis for many points on the Farnese Atlas, these uncertainties can be greatly reduced. The reduction of errors scales as a factor of the inverse square root of the number of points included in the analysis. My analysis in Appendix 2 uses 70 points on the globe, and so my formal (one-sigma) error bar is 55 years. That is, by combining 70 points, I can substantially reduce the various random and happenstance problems, such that I can pin the origin of the Farnese Atlas’s constellations to the nearest half-century. This accuracy is good enough for me to be able to specify the historical setting as well as to eliminate all but one of the candidates for the source.

My analysis (see Appendix 2) yields 125 B.C. for the date when some observer made the astronomical observations of the positions of the constellations that ultimately got incorporated into the Farnese Atlas. The one-sigma error bar is ±55 years, which means that there is a 68% probability that the date is between 180 B.C and 70 B.C. The two-sigma error bar gives a 95% probability that the date is between 245 B.C. and 10

B.C. Within these quoted uncertainties, my result is very strong and solid.

With a very high confidence in the derived epoch of 125 ± 55 B.C., we can immediately test the many possible origins. The common conclusion that the constellations are from Aratus (c. 275 B.C.) is greatly inconsistent with this, even if we ignore the fact that the data in Aratus really date to 1130 ± 80 B.C. Similarly, the proposal that constellations are from Eudoxus (c. 366 B.C.) or the original Assyrian observer (1130 ± 80 B.C.) are surely to be rejected. The reasonable possibility that the Roman sculptor (presumably

c. A.D. 175 and around 40.9° latitude) is near the origin of the constellation information is also surely to be rejected. Finally, the possibility that the constellations depicted are based on Ptolemy’s Almagest (c. A.D. 128) is eliminated. In all, we have confidently ruled out all published proposals for the origin of the constellation figure data on the Farnese Atlas. The only remaining reasonable possibility is that the Farnese Atlas is based on Hipparchus’s star catalogue (c. 129 B.C.). Here we have a perfect match in date with what is seen on the Farnese Atlas. So for the second time, with completely independent reasoning, we confidently eliminate all known possibilities except Hipparchus and we find a perfect match with Hipparchus.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Bianca
Superhero Member
******
Posts: 41646



« Reply #14 on: December 08, 2007, 09:02:48 am »








3.2. Latitude





Appendix 2 presents an analysis that derives the declination of the Ant/Arctic Circles to be ±51.7° ± 0.9°. This datum must be related in some sense to the latitude of the observer. There are three reasonable interpretations.

The obvious interpretation is that this value is 90° minus the observer’s latitude. This case is where a mathematically-inclined observer measured his own latitude and derived the position of the Ant/Arctic Circles as being that angle from both poles. Thus, the observer (whose report was used ultimately by the sculptor) was at a latitude of 38.3° ± 0.9°. This parallel cuts through the Straits of Messina, Athens, and central Turkey. This would likely rule out that the observer was in Mesopotamia (30°–36°), Alexandria (31.2°), or near Rome (41.9°). This latitude is consistent with an origin in classical Greece (36°–40°) as well as being not greatly inconsistent with Hipparchus in Rhodes (36.4°).

The second interpretation is that the depicted circles might be intended to match actual observations of the lowest declination where the stars never set and of the most southerly limits of visibility. For the Arctic Circle, the observer might have a northern horizon that is higher up than an ideal horizon or he might have adopted a visibility definition such that a star is circumpolar only if it is actually visible at its lower meridian passage. In the latter case, the adopted declination would be closer to the pole and lead to our deriving a latitude that is too far north, and hence the latitude of the observer might be closer to 34°. For the Antarctic Circle, the effects of normal extinction in the atmosphere results in a significant difference between the ideal southern horizon and the actual southernmost visible star depicted. This difference is roughly 4° for the bright southern stars of relevance.10 Hence, the visibility conditions would suggest an observer farther south, perhaps at a latitude of 34°. Other interpretations are possible as an intermediary between the ‘obvious’ value (38.3°) and the visibility value (~34°). For example, perhaps the placement of the circles on the globes was made by the mathematical calculation based on the known latitude while the actual visible constellation figures were stretched to reach these circles (causing the distortion in declination noted in the Appendix). With this interpretation, the latitude of the observer could be from roughly 34° to 38°. With this extension, the latitude of Hipparchus in Rhodes (36.4°) becomes easily acceptable.

James Evans has suggested a reasonable third interpretation. He points out that Geminus implies that there was something like a standard latitude for the manufacture of celestial globes when he says “all the spheres are inscribed for the horizon of Greece”, and he explicitly remarks in this context that the Arctic Circle is 6/60 of a full circle (i.e., 36°) from the pole.11 That is, apparently the Arctic Circle on globes are standardized to be at 54° in declination, although the universality of this convention is not complete. For example, Hipparchus’s Commentary gives a value of 53°. The existence of such conventions is common, for example in the placement of α = 0° at the vernal equinox for some standard epoch even for mapmakers at other epochs, as well as the placement of the prime meridian
at Greenwich even for mapmakers far from England. The Farnese Atlas might either have its Arctic Circle slightly misplaced as a standard or have adopted some alternative standard. In such a case,
the observer could have been anywhere in the Greco-Roman world.

In all, the declinations of the Ant/Arctic Circles (±51.7° ± 0.9°) has an unknown relation to the latitude of the observer who provided the constellation positions. Any observer in the Greco-Roman world is consistent with this constraint.
Report Spam   Logged

Your mind understands what you have been taught; your heart what is true.
Pages: [1] 2 3   Go Up
  Print  
 
Jump to:  

Powered by EzPortal
Bookmark this site! | Upgrade This Forum
SMF For Free - Create your own Forum
Powered by SMF | SMF © 2016, Simple Machines
Privacy Policy