Hipparchus (ca. 190 BC - ca. 120 BC) was a Greek astronomer, geographer, and mathematician. He was born in Nicaea (now Iznik, Turkey) and probably died on the island of Rhodes. He is known to have been active at least from 147 BC to 127 BC. Hipparchus is considered the greatest astronomical observer, and by some the greatest 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, and probably the invention of the astrolabe. Claudius Ptolemaeus, three centuries later depended much on Hipparchus. However, his synthesis of astronomy superseded Hipparchus's work: although Hipparchus wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus has been preserved by later copyists. As a consequence, we know comparatively little about Hipparchus.
Most of what is known about Hipparchus comes from Ptolemy's (2nd century) Almagest ("the great treatise" 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).
There is a strong tradition that Hipparchus was born in Nicaea, 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 honor in Bithynia that bear his name and show him with a globe; this confirms 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 to him from Rhodes in the period from 141 BC to 127 BC.
Hipparchus's main original works are lost. His only preserved work is Toon Aratou kai Eudoxou Fainomenoon exegesis ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a critical commentary in two books on a popular poem by Aratus based on the work by Eudoxus. It was published by Karl Manitius (In Arati et Eudoxi Phaenomena, Leipzig, 1894).
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 probably was incorporated into the one by Ptolemy, but cannot be reliably reconstructed.
We know he made a celestial globe; a copy of a copy may have been preserved in the oldest surviving celestial globe accurately depicting the constellations: the globe carried by the Farnese Atlas.
Hipparchus is recognized as the originator and father of scientific astronomy. He is believed to be the greatest Greek astronomical observer, and many regard him as the greatest astronomer of ancient times, although Cicero gave preferences to Aristarchus of Samos. Some put in this place also Ptolemy of Alexandria. Hipparchus' writings had been mostly superseded by those of Ptolemy, so later copyists have not preserved them for posterity.
Many of the works of Greek scientists - mathematicians, astronomers, geographers - have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by Middle Eastern civilizations, notably those in Babylonia, had been forgotten.
After the discovery of the archaeological sites in the 19th century, many writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by A. Sachs, and later published by Otto Neugebauer in "Astronomical Cuneiform Texts" (3 vol.; Princeton and London, 1955).
Since the rediscovery of the Babylonian civilization, it has become apparent that Greek astronomers, and in particular Hipparchus, borrowed a lot from the Chaldeans.
F.X. Kugler demonstrated in his book Die Babylonische Mondrechnung ("The Babylonian lunar computation", Freiburg im Breisgau, 1900) the following: Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself.
However Kugler found 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).
Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations.It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made.
Preserved examples date from 652 BC to AD 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar, i.e., 26 February 747 BC.
This raw material by itself must have been hard to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events.
The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year.Similarly various relations between the periods of the planets were known.
The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets.
All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BC). According to the late classical philosopher Simplicius (early 6th century AD), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle.
It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West.
It is striking that he mentions the title teresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing".
Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BC (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BC. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu.
Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it is said that later he founded a school of astrology on the Greek island of Kos.
Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC.In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans.
Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days; 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon.
This made it very tedious to compute the time interval between events.What Hipparchus may have done is transform these records to the Egyptian calendar, which uses a fixed year of always 365 days (consisting of 12 months of 30 days and 5 extra days): this makes computing time intervals much easier. Ptolemy dated all observations in this calendar.
He also writes that "All that he (=Hipparchus) did was to make a compilation of the planetary observations arranged in a more useful way" (Almagest IX.2).
Pliny states (Naturalis Historia II.IX(53)) on eclipse predictions: "After their time (=Thales) the courses of both stars (=Sun and Moon) for 600 years were prophecied by Hipparchus, ...". This seems to imply that Hipparchus predicted eclipses for a period of 600 years, but considering the enormous amount of computation required, this is very unlikely.
Rather, Hipparchus would have made a list of all eclipses from Nabonasser's time to his own.
Other traces of Babylonian practice in Hipparchus' work are:
He described it 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; his table seems to have survived in astronomical treatises in India, for instance the Surya Sidhanta. 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.
For his chord table Hipparchus must have used a better approximation for than the one from Archimedes (between 3 + 1/7 and 3 + 10/71); maybe 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 from 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 the new technique for computing 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 this (to read values off the coordinate grids drawn on it), as well as approximations from planar geometry, or arithmetical approximations developed by the Chaldeans.
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 best clocks and timing methods of the age had an accuracy of no better than 8 minutes.
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 and taking account of the change in the length of the day we estimate that the error in the assumed length of the synodic month was less than 0.2 s in the 4th century BC and less than 0.1 s in Hipparchus' time.
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.
2. 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.
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.
Apparent motion of the Sun
Before Hipparchus, Meton, Euktemon, 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 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 eniausou megthous ("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. This implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14/60 + 44/602 + 51/603), and this value has been found on a Babylonian clay tablet.
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.
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
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 "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 = 0ƒ33'14".
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 the Moon circles the
center of the Earth, but the
observer is at the surface - 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 for 4/5 by the Moon.
Alexandria and Nicaea are on the
same meridian. Alexandria is at
about 31ƒ North, and the region of
the Hellespont at about 41ƒ 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+‡ 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 minumum 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.
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 9/10 than
to the reported 4/5).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 book 2.
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 60‡ 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.
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 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 Prs tn 'Eratosthnous geografan ("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 7). 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 catalogue
After that, in 135 BC,
enthusiastic about a nova in the
constellation of Scorpius, he
measured with an equatorial
armillary sphere ecliptical
coordinates of about 1,000 stars
(the exact number is not known) for
his star catalogue.
He also knew the work
Phainomena (Phenomena). That poem,
known as Phaenomena or Arateia,
describes the constellations and
the stars that form them.
Hipparchus' commentary contains
many measurements of stellar
position and times for rising,
culmination, and setting of the
constellations treated in the
Phaenomena, and these are likely to
have been based on measurements of
stellar positions - and he knew the
Enoptron (Mirror of Nature) of
Eudoxus of Cnidus, who had his
school near Cyzicus on the southern
coast of the Sea of Marmara and
through the Phenomena Eudoxus'
sphere, which was made from metal
or stone and where there were
marked constellations, brightest
stars, the tropic of Cancer and the
tropic of Capricorn.
These comparisons embarrassed
him because he could not put
together Eudoxus' detailed
statements with his own
observations and observations of
that time. From all this he found
that coordinates of the stars and
the Sun had systematically changed.
Their ecliptic latitudes - remained
unchanged, but their ecliptic
longitudes had increased, at a
rate which he estimated to be at
least one degree per century.
This catalog served him to find
any changes on the sky but
unfortunately it is not preserved
today. However, a 2005 analysis of
an ancient statue of Atlas shows
stars at positions that appear to
have been determined using
Hipparchus' data.
His star map was thoroughly
modified as late as 1,000 years
later in 964 by Al Sufi and 1,500
years later (1437) by Ulugh Beg.
Later, Halley would use his star
catalogue to discover proper
motions as well.The system of
celestial coordinates used in
Hipparchus's star catalog is not
known. Since Ptolemy's copy in the
Almagest is given in ecliptical
coordinates, that system would seem
the most likely; although there is
evidence that both ecliptic
coordinates and equatorial
coordinates were used in the
original observations.
Brightness of stars
Hipparchus had in 134 BC ranked stars in six magnitude classes
according to their brightness: he assigned the value of 1 to the twenty
brightest stars, to weaker ones a value of 2, and so forth to the stars
with a class of 6, which can be barely seen with the naked eye. This
scheme was later adopted by Ptolemy and a similar system is still in
use today.
Precession of the equinoxes (146 BC-130 BC)
Hipparchus is perhaps most famous
for having been the first to
measure the precession of the
equinoxes. There is some suggestion
that the Babylonians may have known
about precession, but it appears
that Hipparchus was the first to
really understand it and measure
it. According to al-Battani,
Chaldean astronomers had
distinguished the tropical and
sidereal year. He stated that they
had, around 330 BC, an estimation
for the length of the sidereal year
to be SK = 365 days 6 hours 11 min
(= 365.258 days) with an error of
(about) 2 min. This phenomenon was
probably also known to Kidinnu
around 314 BC. Yu Xi (fourth
century) was the first Chinese
astronomer to mention precession.
Hipparchus and his predecessors
mostly used simple instruments for
astronomical calculations, such as
the gnomon, astrolabe, armillary
sphere, etc.
.Additionally, as the first in
history to correctly explain this
with retrogradical movement of
vernal point „ over the ecliptic
for about 45", 46" or 47" (36" or
3/4' according to Ptolemy) per
annum (today's value is 50.29"), he
showed the Earth's axis is not
fixed in space. By comparing his
own measurements of the position of
the equinoxes to the star Spica
during a lunar eclipse at the time
of equinox with those of Euclid's
contemporaries (Timocharis of
Alexandria (ca. 320 BC - 260 BC),
Aristyllus 150 years earlier, the
records of Chaldean astronomers
(especially Kidinnu's records), and
observations of a temple in Thebes,
Egypt, that was built around 2000
BC) he still later observed that
the equinox had moved 2ƒ relative
to Spica. He also noticed this
motion in other stars. He obtained
a value of not less than 1ƒ in a
century. The modern value is 1ƒ in
72 years.
After him many Greek and Arab
astronomers had confirmed this
phenomenon. Ptolemy compared his
catalogue with those of Aristyllus,
Timocharis, Hipparchus and the
observations of Agrippa and
Menelaus of Alexandria from the
early 1st century and he finally
confirmed Hipparchus' empirical
fact that the poles of the
celestial equator in one Platonic
year (approximately 25,777 sidereal
years) encircle the ecliptical
pole. The diameter of this circle
is equal to the inclination of
ecliptic relative to the celestial
equator. The equinoctial points in
this time traverse the whole
ecliptic and they move 1ƒ in a
century. This velocity is equal to
that calculated by Hipparchus.
Because of these accordances,
Delambre, P. Tannery and other
French historians of astronomy had
wrongly jumped to conclusions that
Ptolemy recorded his star catalogue
from Hipparchus' with an ordinary
extrapolation. It was not known
until 1898 when Marcel Boll and
others had found that Ptolemy's
catalogue differs from Hipparchus'
not only in the number of stars but
in other respects.
This phenomenon was named by
Ptolemy just because the vernal
point „ leads the Sun. In Latin
praecesse means "to overtake" or
"to outpass", and today also means
to twist or to turn. Its own name
shows this phenomenon was
discovered before its theoretical
explanation, otherwise it would
have been given a better term. Many
later astronomers, physicists and
mathematicians had occupied
themselves with this problem,
practically and theoretically. The
phenomenon itself had opened many
new promising solutions in several
branches of celestial mechanics:
Thabit ibn Qurra's theory of
trepidation and oscillation of
equinoctial points, Isaac Newton's
general gravitational law (which
had explained it in full), Leonhard
Euler's kinematic equations and
Joseph Lagrange's equations of
motion, Jean d'Alembert's dynamical
theory of the movement of a rigid
body, some algebraic solutions for
special cases of precession, John
Flamsteed's and James Bradley's
difficulties in the making of
precise telescopic star catalogues,
Friedrich Bessel's and Simon
Newcomb's measurements of
precession, and finally the
precession of perihelion in Albert
Einstein's general theory of
relativity. Hipparchus