Hipparchus.
'Hipparchus' (
Greek ; ca.
190 BC – ca.
120 BC) was a
Greek astronomer,
geographer, and
mathematician of the
Hellenistic period.
Hipparchus was born in Nicaea (now
Iznik,
Turkey), and probably died on the island of
Rhodes. He is known to have been a working astronomer at least from
147 BC to
127 BC. Hipparchus is considered the greatest astronomical observer and, by some, the greatest overall astronomer of
antiquity. He was the first Greek to develop quantitative and accurate models for the motion of the
Sun and
Moon. For this he made use of the observations and knowledge accumulated over centuries by the
Chaldeans from
Babylonia. He was also the first to compile a
trigonometric table, which allowed him to solve any triangle. With his solar and lunar theories and his numerical trigonometry, he was probably the first to develop a reliable method to predict
solar eclipses. His other achievements include the discovery of
precession, the compilation of the first
star catalogue of the western world, and, probably, the invention of the
astrolabe. It would be three centuries before
Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparchus; it is heavily dependent on it.
Life and work
Relatively little of Hipparchus' direct work survived into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by
Aratus was preserved by later copyists. Most of what is known about Hipparchus comes from
Ptolemy's (
2nd century) ''
Almagest'', with additional references to him by
Pappus of Alexandria and
Theon of Alexandria (
4th century) in their commentaries on the ''Almagest''; from
Strabo's ''Geographia'' ("Geography"), and from
Pliny the Elder's ''
Naturalis historia'' ("Natural history") (
1st century).
[1]
There is a strong tradition that Hipparchus was born in Nicaea (Greek ''Νικαία''), in the ancient district of
Bithynia (modern-day Iznik in province
Bursa), in what today is
Turkey.
The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him from
147 BC to
127 BC; earlier observations since
162 BC might also be made by him. The date of his birth (ca.
190 BC) was calculated by
Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his latest observations. Hipparchus obtained information from
Alexandria as well as
Babylon, but it is not known if and when he visited these places.
It is not known what Hipparchus' economic means were and how he supported his scientific activities. Also, his appearance is unknown: there are no contemporary portraits. In the 2nd and 3rd centuries
coins were made in his honour in Bithynia that bear his name and show him with a
globe; this supports the tradition that he was born there.
Hipparchus is believed to have died on the island of
Rhodes, where he spent most of his later life -- Ptolemy attributes observations made on Rhodes in the period from
147 BC to
127 BC to Hipparchus.
Hipparchus' only preserved work is ''Toon Aratou kai Eudoxou Fainomenoon exegesis'' ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a highly critical commentary in the form of two books on a popular
poem by
Aratus based on the work by
Eudoxus.
[2] Hipparchus also made a list of his major works, which apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalogue was incorporated into the one by Ptolemy, and may be almost perfectly reconstructed by subtraction of two and two thirds degrees from the longitudes of Ptolemy's stars.
We know Hipparchos made a
celestial globe; it has been proposed (1898 and 2005) that a copy of a copy may have been preserved in the only surviving large ancient celestial globe, which depicts the constellations with moderate accuracy: the globe carried by the
Farnese Atlas.
Very few specialists in the area have accepted this widely publicized speculation.
[3]
There is evidence, based on references in non-scientific writers such as Plutarch, that Hipparchus was aware of some physical ideas that we consider
Newtonian, and some claim that Newton knew this.
[4]
Babylonian sources
Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the
Metonic cycle and
Saros cycle may have come from Babylonian sources. Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically.
[5] He was the first Greek known to divide the circle in 360
degrees of 60
arc minutes (
Eratosthenes before him used a simpler
sexagesimal system dividing a circle into 60 parts). He also used the Babylonian unit ''pechus'' ("cubit") of about 2° or 2.5°.
Hipparchus probably compiled a list of Babylonian astronomical observations; G. Toomer, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the ''Almagest'' came from a list made by Hipparchus. Hipparchus' use of Babylonian sources has always been known in a general way, because of Ptolemy's statements. However,
Franz Xaver Kugler demonstrated that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian
ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to
Kidinnu).
[6]
Geometry, trigonometry, and other mathematical techniques
Hipparchus is recognised as the first mathematician who compiled a
trigonometry table, which he needed when computing the
eccentricity of the
orbits of the Moon and Sun. He tabulated values for the
chord function, which gives the length of the chord for each angle. He did this for a circle with a circumference of 21,600 and a radius (rounded) of 3438 units: this circle has a unit length of 1 arc minute along its perimeter. He tabulated the chords for angles with increments of 7.5°. In modern terms, the chord of an angle equals twice the
sine of half of the angle, i.e.:
:chord(''A'') = 2 sin(''A''/2).
He described the chord table in a work, now lost, called ''Toon en kuklooi eutheioon'' (''Of Lines Inside a Circle'') by
Theon of Alexandria (
4th century) in his commentary on the ''Almagest'' I.10; some claim his table may have survived in astronomical treatises in
India, for instance the ''
Surya Siddhanta''. This was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques.
[7]
For his chord table Hipparchus must have used a better approximation for
π than the one from
Archimedes of between 3 + 1/7 and 3 + 10/71; perhaps he had the one later used by Ptolemy: 3;8:30 (
sexagesimal) (''Almagest'' VI.7); but it is not known if he computed an improved value himself.
Hipparchus could construct his chord table using the
Pythagorean theorem and a
theorem known to Archimedes. He also might have developed and used the theorem in
plane geometry called
Ptolemy's theorem, because it was proved by Ptolemy in his ''Almagest'' (I.10) (later elaborated on by
Carnot).
Hipparchus was the first to show that the
stereographic projection is
conformal, and that it transforms circles on the
sphere that do not pass through the center of projection to circles on the
plane. This was the basis for the
astrolabe.
Besides geometry, Hipparchus also used
arithmetic techniques developed by the
Chaldeans. He was one of the first Greek mathematicians to do this, and in this way expanded the techniques available to astronomers and geographers.
There is no indication that Hipparchus knew
spherical trigonometry, which was first developed by
Menelaus of Alexandria in the
1st century. Ptolemy later used spherical trigonometry to compute things like the rising and setting points of the
ecliptic, or to take account of the lunar
parallax. Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans.
Lunar and solar theory
Motion of the Moon
Hipparchus also studied the motion of the
Moon and confirmed the accurate values for some periods of its motion that Chaldean astronomers had obtained before him. The traditional value (from Babylonian System B) for the mean
synodic month is 29 days;31,50,8,20 (sexagesimal) = 29.5305941... d. Expressed as 29 days + 12 hours + 793/1080 hours this value has been used later in the
Hebrew calendar (possibly from Babylonian sources). The Chaldeans also knew that 251
synodic months = 269
anomalistic months. Hipparchus extended this period by a factor of 17, because after that interval the Moon also would have a similar latitude, and it is close to an integer number of years (345). Therefore, eclipses would reappear under almost identical circumstances. The period is 126007 days 1 hour (rounded). Hipparchus could confirm his computations by comparing eclipses from his own time (presumably
27 January 141 BC and
26 November 139 BC according to [Toomer 1980]), with eclipses from Babylonian records 345 years earlier (''Almagest'' IV.2; [Jones 2001]). Already
al-Biruni (''Qanun'' VII.2.II) and
Copernicus (''de revolutionibus'' IV.4) noted that the period of 4,267 lunations is actually about 5 minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no less than 8 minutes [Stephenson & Fatoohi 1993; Steele ''et al.'' 1997]. Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than try to derive an improved value from his own observations. From modern ephemerides [Chapront ''et al.'' 2002] and taking account of the change in the length of the day (see
ΔT) we estimate that the error in the assumed length of the synodic month was less than 0.2 seconds in the
4th century BC and less than 0.1 seconds in Hipparchus' time.
Orbit of the Moon
It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its ''anomaly'', and it repeats with its own period; the
anomalistic month. The Chaldeans took account of this arithmetically, and used a table giving the daily motion of the Moon according to the date within a long period. The Greeks however preferred to think in geometrical models of the sky.
Apollonius of Perga had at the end of the
3rd century BC proposed two models for lunar and planetary motion:
# In the first, the Moon would move uniformly along a circle, but the Earth would be eccentric, i.e., at some distance of the center of the circle. So the apparent angular speed of the Moon (and its distance) would vary.
# The Moon itself would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an ''epicycle'', that itself would move uniformly (with some mean motion in longitude) over the main circular orbit around the Earth, called ''deferent''; see
deferent and epicycle.
Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus was the first to attempt to determine the relative proportions and actual sizes of these
orbits.
Hipparchus devised a geometrical method to find the parameters from three positions of the Moon, at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the ''Almagest'' IV.11. Hipparchus used two sets of three lunar eclipse observations, which he carefully selected to satisfy the requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December
383 BC, 18/19 June
382 BC, and 12/13 December
382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at
22 September 201 BC,
19 March 200 BC, and
11 September 200 BC.
★ For the eccentric model, Hipparchus found for the ratio between the radius of the
eccenter and the distance between the center of the eccenter and the center of the ecliptic (i.e., the observer on Earth): 3144 : 327+2/3 ;
★ and for the epicycle model, the ratio between the radius of the deferent and the epicycle: 3122+1/2 : 247+1/2 .
The somewhat weird numbers are due to the cumbersome unit he used in his chord table. The results are distinctly different. This is partly due to some sloppy rounding and calculation errors, for which Ptolemy criticised him (he himself made rounding errors too). Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+1/2 : 247+1/2), which is too small (60 : 4;45 hexadecimal): Ptolemy established a ratio of 60 : 5+1/4.
[8].
Apparent motion of the Sun
Before Hipparchus,
Meton,
Euctemon, and their pupils at
Athens had made a solstice observation (i.e., timed the moment of the summer
solstice) on
June 27,
432 BC (
proleptic Julian calendar).
Aristarchus of Samos is said to have done so in
280 BC, and Hipparchus also had an observation by
Archimedes. Hipparchus himself observed the summer solstice in
135 BC, but he found observations of the moment of
equinox more accurate, and he made many during his lifetime. Ptolemy gives an extensive discussion of Hipparchus' work on the length of the year in the ''Almagest'' III.1, and quotes many observations that Hipparchus made or used, spanning
162 BC to
128 BC.
Ptolemy quotes an equinox timing by Hipparchus (at
24 March 146 BC at dawn) that differs from the observation made on that day in
Alexandria (at 5h after sunrise): Hipparchus may have visited Alexandria but he did not make his equinox observations there; presumably he was on Rhodes (at the same geographical longitude). He may have used his own armillary sphere or an equatorial ring for these observations. Hipparchus (and Ptolemy) knew that observations with these instruments are sensitive to a precise alignment with the
equator. The real problem however is that atmospheric
refraction lifts the Sun significantly above the horizon: so its apparent
declination is too high, which changes the observed time when the Sun crosses the equator. Worse, the refraction decreases as the Sun rises, so it may appear to move in the wrong direction with respect to the equator in the course of the day - as Ptolemy mentions; however, Ptolemy and Hipparchus apparently did not realize that refraction is the cause.
At the end of his career, Hipparchus wrote a book called ''Peri eniausíou megéthous'' ("On the Length of the Year") about his results. The established value for the
tropical year, introduced by
Callippus in or before
330 BC (possibly from Babylonian sources, see above), was 365 + 1/4 days. Hipparchus' equinox observations gave varying results, but he himself points out (quoted in ''Almagest'' III.1(H195)) that the observation errors by himself and his predecessors may have been as large as 1/4 day. So he used the old solstice observations, and determined a difference of about one day in about 300 years. So he set the length of the tropical year to 365 + 1/4 - 1/300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the actual value (modern estimate) of 365.24219... days = 365 days 5 hours 48 min 45 s by only about 6 min).
Between the solstice observation of Meton and his own, there were 297 years spanning 108,478 days. D.Rawlins noted that this implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14/60 + 44/60
2 + 51/60
3) and that this value has been found on a Babylonian clay tablet [A. Jones, 2001]. This is an indication that Hipparchus' work was known to Chaldeans.
Another value for the year that is attributed to Hipparchus (by the astrologer
Vettius Valens in the
1st century) is 365 + 1/4 + 1/288 days (= 365.25347... days = 365 days 6 hours 5 min), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1/4 + 1/144 days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear if this would be a value for the
sidereal year (actual value at his time (modern estimate) ca. 365.2565 days), but the difference with Hipparchus' value for the tropical year is consistent with his rate of
precession (see below).
Orbit of the Sun
Before Hipparchus the Chaldean astronomers knew that the lengths of the
seasons are not equal. Hipparchus made equinox and solstice observations, and according to Ptolemy (''Almagest'' III.4) determined that spring (from spring equinox to summer solstice) lasted 94 + 1/2 days, and summer (from summer solstice to autumn equinox) 92 + 1/2 days. This is an unexpected result given a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus' solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well (of course today we know that the
planets like the Earth move in
ellipses around the Sun, but this was not discovered until
Johannes Kepler published his first two laws of planetary motion in
1609). The value for the
eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1/24 of the radius of the orbit (which is too large), and the direction of the
apogee would be at longitude 65.5° from the
vernal equinox. Hipparchus may also have used another set of observations (94 + 1/4 and 92 + 3/4 days), which would lead to different values. The question remains if Hipparchus is really the author of the values provided by Ptolemy, who found no change three centuries later, and added lengths for the autumn and winter seasons.
Distance, parallax, size of the Moon and Sun
Main articles: Hipparchus On Sizes and Distances
Hipparchus also undertook to find the distances and sizes of the Sun and the Moon. He published his results in a work of two books called ''Peri megethoon kai 'apostèmátoon'' ("On Sizes and Distances") by Pappus in his commentary on the ''Almagest'' V.11;
Theon of Smyrna (
2nd century) mentions the work with the addition "of the Sun and Moon".
Hipparchus measured the apparent diameters of the Sun and Moon with his ''diopter''. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the '
mean' distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are 360/650 = 0°33'14".
Like others before and after him, he also noticed that the Moon has a noticeable
parallax, i.e., that it appears displaced from its calculated position (compared to the Sun or
stars), and the difference is greater when closer to the horizon. He knew that this is because in the then-current models the Moon circles the center of the Earth, but the observer is at the surface -- the Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth
radii can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", more than ten times smaller than the resolution of the unaided eye).
In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, presumably that of
14 March 190 BC. It was total in the region of the
Hellespont (and in fact in his birth place Nicaea); at the time the Romans were preparing for war with
Antiochus III in the area, and the eclipse is mentioned by
Livy in his ''
Ab Urbe Condita'' VIII.2. It was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont at about 41° North; authors like Strabo and Ptolemy had fairly decent values for these geographical positions, and presumably Hipparchus knew them too. So Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the
meridian, and as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 81 Earth radii.
In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 470 Earth radii. This would correspond to a parallax of 7', which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2';
Tycho Brahe made naked eye observation with an accuracy down to 1'). In this case, the shadow of the Earth is a
cone rather than a
cylinder as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2+½ lunar diameters. That apparent diameter is, as he had observed, 360/650 degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of 67+1/3, and consequently a greatest distance of 72+2/3 Earth radii. With this method, as the parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radii - exactly the mean distance that Ptolemy later derived.
Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters (in fact, modern calculations show that the size of the solar eclipse at Alexandria must have been closer to 9/10ths and not the 4/5ths reported to Hipparchus).
Ptolemy later measured the lunar parallax directly (''Almagest'' V.13), and used the second method of Hipparchus' with lunar eclipses to compute the distance of the Sun (''Almagest'' V.15). He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results (''Almagest'' V.11): but apparently he failed to understand Hipparchus' strategy to establish limits consistent with the observations, rather than a single value for the distance. His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from Hipparchus' second book.
Theon of Smyrna wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to
volumes, not
diameters. From the geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is 60½ radii. Similarly,
Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses.
See [Toomer 1974] for a more detailed discussion.
Eclipses
Pliny (''Naturalis Historia'' II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy discussed this a century later at length in ''Almagest'' VI.6. The geometry, and the limits of the positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in ''Almagest'' VI.5. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere - as Pliny indicates -, and the latter was inaccessible to the Greek.
Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Hipparchus must have been the first to be able to do this. A rigorous treatment requires
spherical trigonometry, but Hipparchus may have made do with planar approximations. He may have discussed these things in ''Peri tes kata platos meniaias tes selenes kineseoos'' ("On the monthly motion of the Moon in latitude"), a work mentioned in the ''
Suda''.
Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the moon was eclipsed in the west while both luminaries were visible above the earth." (translation H. Rackham (1938),
Loeb Classical Library 330 p.207). Toomer (1980) argued that this must refer to the large total lunar eclipse of
26 November 139 BC, when over a clean sea horizon as seen from the citadel of Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus' lunar theory. We do not know what "exact reason" Hipparchus found for seeing the Moon eclipsed while apparently it was not in exact
opposition to the Sun. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered.
Astronomical instruments and astrometry
Hipparchus and his predecessors mostly used simple instruments for astronomical calculations and observations, such as the
gnomon, the
astrolabe, and the
armillary sphere.
Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for
naked-eye observations. According to
Synesius of Ptolemais (
4th century) he made the first ''astrolabion'': this may have been an
armillary sphere (which Ptolemy however says he constructed, in ''Almagest'' V.1); or the predecessor of the planar instrument called
astrolabe (also mentioned by
Theon of Alexandria). With an astrolabe Hipparchus was the first to be able to measure the geographical
latitude and
time by observing stars. Previously this was done at daytime by measuring the shadow cast by a ''
gnomon'', or with the portable instrument known as ''
scaphion''.
Ptolemy mentions (''Almagest'' V.14) that he used a similar instrument as Hipparchus, called ''
dioptra'', to measure the apparent diameter of the Sun and Moon.
Pappus of Alexandria described it (in his commentary on the ''Almagest'' of that chapter), as did
Proclus (''Hypotyposis'' IV). It was a 4-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon.
Hipparchus also observed solar
equinoxes, which may be done with an
equatorial ring: its shadow falls on itself when the Sun is on the
equator (i.e., in one of the equinoctial points on the
ecliptic), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in ''Almagest'' III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time.
Geography
Hipparchus applied his knowledge of spherical angles to the problem of denoting locations on the Earth's surface. Before him a grid system had been used by
Dicaearchus of
Messana, but Hipparchus was the first to apply mathematical rigor to the determination of the
latitude and
longitude of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer
Eratosthenes of Cyrene (
3rd century BC), called ''Pròs tèn 'Eratosthénous geografían'' ("Against the Geography of Eratosthenes"). It is known to us from
Strabo of Amaseia, who in his turn criticised Hipparchus in his own ''Geografia''. Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the
geographical longitudes of different
cities at
lunar eclipses (Strabo ''Geografia'' 1.1.12). A lunar eclipse is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical.
Star catalog
Late in his career (possibly about
135 BC) Hipparchus compiled his star catalog. He also constructed a celestial globe depicting the constellations, based on his observations. His interest in the
fixed stars 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
Aristyllos; for more information see
Discovery of precession).
Previously,
Eudoxus of Cnidus in the 4th century 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' 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.
Hipparchus made his measurements with an
armillary sphere, and obtained the positions of at least 850 stars. It is disputed which coordinate system he used. Ptolemy's catalog in the ''
Almagest'', which is derived from Hipparchus' catalog, is given in
ecliptic coordinates. However Delambre in his ''Histoire de l'Astronomie Ancienne'' (1817) concluded that Hipparchus knew and used the
equatorial coordinate system, a conclusion challenged by
Otto Neugebauer in his ''A History of Ancient Mathematical Astronomy'' (1975). Hipparchus seems to have used a mix of
ecliptic coordinates and
equatorial coordinates: in his commentary on Eudoxos he provides the polar distance (equivalent to the
declination in the equatorial system) and the ecliptic longitude.
Hipparchus' original catalog has not been preserved today. However, an analysis of an ancient statue of
Atlas (the so-called
Farnese Atlas) published in
2005 shows stars at positions that appear to have been determined using Hipparchus' data.
[1].
As with most of his work, Hipparchus' star catalog was adopted and expanded by Ptolemy. Although it has been strongly disputed how much of the star catalog in the ''
Almagest'' is due to Hipparchus, statistical and spatial analysis (by
R. R. Newton,
Dennis Rawlins,
Keith Pickering,
Gerd Grasshoff, and
Dennis Duke) have shown conclusively that the ''
Almagest'' star catalog is almost entirely Hipparchan. Ptolemy has even (since Brahe, 1598) been accused by astronomers of fraud for stating (''Syntaxis'' book 7 chapter 4) that he observed all 1025 stars: in most cases he used Hipparchus' data and precessed them to his own epoch three centuries later, but using an erroneous (too small) precession constant.
In any case the work started by Hipparchus has had a lasting heritage, and has been worked on much later by
Al Sufi (
964), and by
Ulugh Beg as late as
1437. It was superseded only by more accurate observations after invention of the
telescope.
Stellar magnitude
Hipparchus ranked stars in six
magnitude classes according to their brightness: he assigned the value of one to the twenty brightest stars, to weaker ones a value of two, and so forth to the stars with a class of six, which can be barely seen with the naked eye. A similar system is still used today.
Precession of the equinoxes (146 BC-130 BC)
:''See also
Discovery of precession''
Hipparchus is perhaps most famous for having discovered the
precession of the
equinoxes. His two books on precession, ''On the Displacement of the Solsticial and Equinoctial Points'' and ''On the Length of the Year'', are both mentioned in the ''
Almagest'' of Claudius
Ptolemy. According to Ptolemy, Hipparchus measured the longitude of
Spica and other bright stars. Comparing his measurements with data from his predecessors,
Timocharis and
Aristillus, he realized that Spica had moved 2° relative to the
autumnal equinox. He also compared the lengths of the
tropical year (the time it takes the Sun to return to an equinox) and the
sidereal year (the time it takes the Sun to return to a fixed star), and found a slight discrepancy. Hipparchus concluded that the equinoxes were moving ("precessing") through the zodiac, and that the rate of precession was not less than 1° in a century.
Ptolemy followed up on Hipparchus' work in the 2nd century. He confirmed that precession affected the entire sphere of fixed stars (Hipparchus had speculated that only the stars near the zodiac were affected), and concluded that 1° in 100 years was the correct rate of precession. The modern value is 1° in 72 years.
Hipparchus and astrology
As far as is known, Hipparchus never wrote about
astrology, ''i.e.'' the application of astronomy to the practice of
divination. Nevertheless the work of Hipparchus dealing with the calculation and prediction of celestial positions would have been very useful to those engaged in astrology. Astrology developed in the
Greco-Roman world during the
Hellenistic period, borrowing many elements from
Babylonian astronomy; some historians have suggested that Hipparchus played a key role in this. Remarks made by
Pliny the Elder in his ''Natural History'' Book 2.24, suggest that some
ancient authors did regard Hipparchus as an important figure in the
history of astrology. Pliny claimed that Hipparchus "can never be sufficiently praised, no one having done more to prove that man is related to the stars and that our souls are a part of heaven."
Named after Hipparchus
The
ESA's
Hipparcos Space Astrometry Mission was named after him, as are the
Hipparchus lunar crater and the
asteroid 4000 Hipparchus.
See also
★
Antikythera mechanism
★
Apparent magnitude
★
Astrometry
★
History of astrology
★
Geminus (of Rhodes) (
10 BC - circa
60)
★
Mira
★
Mithraism
★
Star catalogues
Notes
1. For general information on Hipparchus see the following biographical articles: G. J. Toomer, "Hipparchus" (1978); and A. Jones, "Hipparchus."
2. Modern edition: Karl Manitius (''In Arati et Eudoxi Phaenomena'', Leipzig, 1894).
3. B. E. Schaefer, "Epoch of the Constellations on the Farnese Atlas."
D.Duke ''Journal for the History of Astronomy'', February, 2006.
4. Lucio Russo, ''The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had To Be Reborn'', (Berlin: Springer, 2004). ISBN 3-540-20396-6.
5. For more information see G. J. Toomer, "Hipparchus and Babylonian astronomy."
6. Franz Xaver Kugler, ''Die Babylonische Mondrechnung'' ("The Babylonian lunar computation"), Freiburg im Breisgau, 1900.
7. Toomer, "The Chord Table of Hipparchus" (1973).
8. Toomer, 1967
References
★ Edition and translation: Karl Manitius: ''In Arati et Eudoxi Phaenomena'', Leipzig, 1894.
★ J. Chapront, M. Chapront Touze, G. Francou (2002): "A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements". ''Astronomy and Astrophysics'' '387', 700-709.
★ Duke, Dennis W. (2002). Associations between the ancient star catalogues. ''Archive for the History of Exact Sciences'' 56(5):435-450.
★ A. Jones: "Hipparchus." In ''Encyclopedia of Astronomy and Astrophysics''. Nature Publishing Group, 2001.
★ Patrick Moore (1994): ''Atlas of the Universe'', Octopus Publishing Group LTD (Slovene translation and completion by Tomaž Zwitter and Savina Zwitter (1999): ''Atlas vesolja''), 225.
★ Newton, R.R. (1977). ''The Crime of Claudius Ptolemy.'' Baltimore: Johns Hopkins University Press.
★ Rawlins, Dennis (1982). An Investigation of the Ancient Star Catalog. ''Proceedings of the Astronomical Society of the Pacific'' 94, 359-373.
★ B.E. Schaefer (2005): "The Epoch of the Constellations on the Farnese Atlas and their Origin in Hipparchus's Lost Catalogue". ''Journal for the History of Astronomy'' 'xxxvi', 1..29.
★ J.M.Steele, F.R.Stephenson, L.V.Morrison (1997): "The accuracy of eclipse times measured by the Babylonians". ''Journal for the History of Astronomy'' 'xxviii', 337..345
★ F.R. Stephenson, L.J.Fatoohi (1993): "Lunar Eclipse Times Recorded in Babylonian History". ''Journal for the History of Astronomy'' 'xxiv', 255..267
★ N.M. Swerdlow (1969): "Hipparchus on the distance of the sun." ''Centaurus'' '14', 287-305.
★ G.J. Toomer (1967): "The Size of the Lunar Epicycle According to Hipparchus." ''Centaurus'' '12', 145-150.
★ G.J. Toomer (1973): "The Chord Table of Hipparchus and the Early History of Greek Trigonometry." ''Centaurus'' '18', 6-28.
★ G.J. Toomer (1974): "Hipparchus on the Distances of the Sun and Moon." ''Archives for the History of the Exact Sciences'' '14', 126-142.
★ G.J. Toomer (1978): "Hipparchus." In ''Dictionary of Scientific Biography'' '15': 207-224.
★ G.J. Toomer (1980): "Hipparchus' Empirical Basis for his Lunar Mean Motions," ''Centaurus'' '24', 97-109.
★ G.J. Toomer (1988): "Hipparchus and Babylonian Astronomy." In ''A Scientific Humanist: Studies in Memory of Abraham Sachs'', ed. Erle Leichty, Maria deJ. Ellis, and Pamel Gerardi. Philadelphia: Occasional Publications of the Samuel Noah Kramer Fund, 9.
External links
General
★
★
Biographical page at the University of Cambridge
★
University of Cambridge's Page about Hipparchus' sole surviving work
★
Biographical page at the University of Oregon
★
Biography of Hipparchus on Fermat's Last Theorem Blog
★
Pastore, Giovanni, ''ANTIKYTHERA E I REGOLI CALCOLATORI'', Rome, 2006, privately published
★
The Antikythera Calculator (Italian and English versions)
Precession
★
David Ulansey about Hipparchus's understanding of the precession
Celestial bodies
★ M44 Praesepe at SEDS (
University of Arizona): http://www.seds.org/messier/m/m044.html
Star catalogue
★
A brief view by Carmen Rush on Hipparchus' stellar catalogue
★
Schaefer's site on the Farnese Atlas
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