Hipparchus

gigatos | January 10, 2023

Summary

Hipparchus of Nicaea (Greek Ἳππαρχος) was an ancient Greek astronomer, mechanic, geographer, and mathematician of the second century BCE, often called the greatest astronomer of antiquity. Hipparchus is credited with bringing the predictive accuracy of Ancient Babylonian astronomy to Greek geometric models of the motion of celestial bodies. He is known as the probable “father of trigonometry.

Hipparchus was born in Nicaea (now Iznik, Turkey). He worked most of his life on the island of Rhodes, where he probably died. His first and last astronomical observations date from 162 and 127 B.C., respectively. He is believed to have been in contact with astronomers in Alexandria and Babylon, but it is not known whether he personally visited these scientific centers. The main sources of information about his writings are Pappus”s Mathematical Collection, Strabo”s Geography, and Ptolemy”s Almagest; the latter left the following characterization of Hipparchus: “a hardworking man and an admirer of truth.” Of Hipparchus” own works only one has come down to us, the Commentary on the Phenomena of Eudoxus and Aratus (“Περὶ τῶν Ἀράτου καὶ Εὐδόξου φαινομένων”) in three books. The treatise contains a critical commentary on the descriptions of the positions of the stars and constellations in the sky in Aratus” popular astronomical poem based on Eudoxus” observations. In addition, the work provides many numerical data on the rising and setting of many stars and their individual coordinates. A study of this information shows their close connection with the star catalog in Ptolemy”s Almagest. He may have participated in the creation of the Antikythera mechanism, built in Rhodes in the II century BC.

The most important achievement of Hipparchus is considered to be the discovery of the advance of the equinoxes, or astronomical precession, which consists in the fact that the equinoxes gradually move among the stars, so that each year the equinox occurs earlier than in the preceding years. According to Ptolemy, Hipparchus made this discovery by comparing the coordinates of Spica determined by himself with the measurements of the Alexandrian astronomer Timocharis. A more detailed study allowed Hipparchus to reject the assumption that this change in coordinates was caused by the stars” own movements, because only the longitudes of the stars (their angular distances from the vernal equinox, counted along the ecliptic), but not their latitudes (angular distances from the ecliptic) changed. According to Hipparchus, the rate of precession is 1˚ per century (actually, 1˚ per 72 years).

According to the American historian of science Knowle Sverdlov, the measurements of the stellar coordinates available to Hipparchus are not accurate enough to judge the rate of precession. Sverdlov suggests that Hipparchus measured the rate of precession based on the difference between the tropical and sideric (stellar) years. Recently, there are reasons to believe that the difference between these two types of year was known to Aristarchus of Samos, who lived a century and a half before Hipparchus. If this is true, the merit of Hipparchus is not so much in the discovery of precession, as in a detailed study of this phenomenon on the basis of data on the coordinates of the stars.

Hipparchus compiled the first star catalog in Europe, which included the exact coordinates of about a thousand stars (the work to determine the coordinates of the stars was begun in the first half of the III century BC by Timocharis and Aristilus in Alexandria). Pliny the Elder wrote that the direct reason for compiling the catalog was a new star in Scorpio, which flashed in 134 BC and suggested to Hipparchus the idea that the “supralunar world” is just as subject to changes as the earthly world: “He determined the places and brightness of many stars, so that he could make out whether they disappear, whether they reappear, whether they move, whether they change in brightness. He has left a legacy of the sky to posterity, if there is anyone who will accept this legacy.” From this we see that Hipparchus himself at least admitted the possibility of his own movements of the stars. With the intention of leaving to later observers data for the easiest determination of changes in the positions of the stars, he recorded several cases where three or more stars lie approximately on one line (the great circle of the celestial sphere). Note that the presence of proper motions is incompatible with the view of the stars as bodies fixed on one sphere; the view of the immobility of the Earth requires that the stars be rigidly fixed on the celestial sphere, for in this case the daily rotation of the sky is considered real and not apparent, as in the case of a rotating Earth. Although most astronomers consider Hipparchus a supporter of the view of the immobility of the Earth, it may be assumed that he at least did not rule out the possibility of a rotating Earth.

Another of Hipparchus” innovations in compiling the catalog was the system of stellar magnitudes: the first magnitude stars are the brightest and the sixth is the weakest. This system in an improved form is used today.

The catalog of Hipparchus itself has not come down to us. Many astronomers (beginning with Tycho Brahe), however, believe that the star catalog given in Ptolemy”s Almagest is in fact an altered catalog of Hipparchus, contrary to the statement of Ptolemy that all the stars in his catalog were observed by him himself. There is a very heated debate on this issue, but recently the opinion that Hipparchus was the author has begun to prevail. In particular, A. K. Dambis and Yu. N. Efremov came to such a conclusion in 2000, having determined the age of the catalog according to the data on the proper motions of the stars.

In 1898 Georg Thiele suggested that the star globe, which is a part of the Hellenistic sculpture “Farnese Atlantus” (sometimes called “Atlas Farnese”), was made on the basis of the Hipparchus catalog. In 2005 this hypothesis was proposed again by B. Schaefer. Experts note that on closer examination the images on the Farnese globe have much more differences than similarities with the Hipparchus data, which does not allow to accept this hypothesis.

Hipparchus made a significant contribution to the improvement of the calendar. He determined the duration of the tropical year to be 365+(1

The difference between the tropical and sideric years is determined by precession; according to Galen, the hipparchal value of the sideric year is 365+(1

Based on his definition of the length of the tropical year, Hipparchus made another improvement in the lunar-solar calendar cycle: 1 cycle of Hipparchus is 4 cycles of Callippus (304 years) without one day, that is 111,035 days, or 3,760 synodic months.

Another definition of the length of the tropical year, 365.24579 days, or 365+(1

Ptolemy also reports that Hipparchus made a connection between the various species of the month:

4,267 synodic months = 4,573 anomalistic months = 4,612 sideric months = 126007 days + 1 hour = 345 years – 7˚30”.

In addition, according to Hipparchus, 5458 synodic months correspond to 5,923 draconic months.

All the theories of the movement of celestial bodies created by Babylonian astronomers considered only their movements across the sky, moreover, only in projection on the ecliptic (which was quite sufficient, from the point of view of astrology, for the needs of which these theories were created). On the contrary, astronomers of Ancient Greece sought to establish the orbits of celestial bodies in space. Beginning with Apollonius of Perga, 3rd century B.C. (and according to the outstanding mathematician and historian of science Barthel van der Varden, since the Pythagoreans in the Preplatonic era), they constructed orbits based on a combination of large and small circles – deferents and epicycles. It was on the basis of this principle that Hipparchus created the first extant theories of the motion of the Sun and the Moon.

If the Sun (in the geocentric system) were moving uniformly in a circle centered on the Earth, its angular velocity across the sky would be constant and the astronomical seasons would have an equal duration. However, even Euktemon and later Callippus established that the duration of the seasons was not the same: according to Hipparchus” own measurements, more accurate than those of his predecessors, the interval between the spring equinox and the summer solstice was 94.5 days, between the summer solstice and the autumn equinox – 92.5 days. Therefore, according to the theory of Hipparchus, the daytime luminary moves uniformly along the epicycle, the center of which, in turn, rotates uniformly along the deferent. Periods of both rotations are the same and equal to one year, their directions are opposite, as a result, the Sun uniformly describes in space a circle (eccentre), the center of which does not coincide with the center of the Earth. Van der Varden believes that similar theories of the Sun were created even earlier, in particular by Callippus in the 4th century BC.

From the observations it was necessary to determine the eccentricity of the orbit (that is, the ratio of the distances between the centers of the Earth and the eccentric) and the direction of the line of apices (the line passing through the centers of the Earth and the eccentric). Knowing the duration of the seasons, Hipparchus solved this problem: the eccentricity of the Sun”s orbit is 1

Since, unlike the Sun, the periods of the Moon”s fastest or slowest motion across the sky each month fall in a new constellation, to create a theory of the Moon”s motion Hipparchus had to assume that the speeds of the Moon”s motion along the deferent and epicycle do not coincide. To obtain the orbital parameters, Hipparchus used a beautiful method based on the use of three lunar eclipses, his own theory of the Sun, and data from earlier ancient Greek astronomers. Hipparchus created two theories with slightly different parameters. Because of the complexity of the motion of our natural satellite, Hipparchus” lunar theory was not as successful as his theory of the Sun, but it nevertheless allowed him to make eclipse predictions with an accuracy not available to earlier astronomers, including Babylonian astronomers.

It is interesting that according to one of the Hipparchus lunar theories, the ratio of the radii of the epicycle and the deferent is 327+2

Ptolemy reports that Hipparchus did not engage in the development of similar theories of planetary motions, limiting himself to criticizing the theories that existed at his time. The main defect that Hipparchus identified in these theories was that the planetary motions they gave were always of the same duration and length.

The first person to attempt to measure these magnitudes was Aristarchus of Samosky. According to his estimates, the Moon is about 3 times smaller than the Earth in diameter, and the Sun is 6.5 times larger; the Sun is 19 times farther from us than the Moon. In the book devoted to this question Aristarchus does not give the value of the distance to the Moon, but it can be reconstructed: it turns out 80 times the radius of the Earth. According to S. V. Zhitomirsky, Archimedes, who obtained the distance to the Moon of about 62 Earth radii, also did this.

According to Ptolemy and the mathematician Pappus of Alexandria, Hipparchus wrote two books “On Dimensions and Distances” (περὶ μεγεθῶν καὶ ἀποστημάτων) devoted to measuring distances to the Moon and the Sun. Reconstructions of Hipparchus” attempts to determine these parameters were undertaken by F. Gulch, N. Sverdlov.

In the first book, Hipparchus used observations of the solar eclipse, which was observed in full phase in Hellespont and in phase 4 in Alexandria

Apparently, Hipparchus repeatedly returned to this subject. Theon of Smyrna and Chalcidius state that he obtained the volume of the Sun 1880 times the volume of the Earth, and the volume of the Moon 27 times the volume of the Earth. These numbers do not coincide with those given by Papp of Alexandria. Knowing the angular radius of the Moon (1

Hipparchus wrote the book “On Bodies Moving Downward under the Influence of their Gravity,” the main ideas of which we are familiar with in Simplicus” paraphrase. Hipparchus did not share Aristotle”s conception of natural and violent motion, according to which “heavy” earthly bodies move downward toward the center of the world, and “light” bodies (such as fire) move upward away from the center. According to Simplicus, “Hipparchus writes that if you throw a piece of earth straight up, the cause of upward motion will be the throwing force as long as it exceeds the gravity of the thrown body; and the greater the throwing force, the faster the object moves upward. Then, as the force decreases, the upward movement will proceed with decreasing speed, until at last the body begins to move downward by its own attraction-though to some extent the throwing force will still be present in it; as it is exhausted, the body will move downward faster and faster, reaching its maximum speed when the force will finally disappear. In fact, here we have before us the first formulation of the concept of the impetus, widespread among medieval scholars (e.g., John Philoponus, Jean Buridan). Simplicus continues: Hipparchus “attributes the same cause to bodies falling from a height. Namely, there is also a force in these bodies which held them at height, and the action of this force explains the slower motion of the body at the beginning of its fall”. This concept of Hipparchus resembles the modern concept of potential energy. Unfortunately, the above ideas of Hipparchus were not developed in antiquity.

The mathematician and historian of science Lucio Russo believes that Hipparchus was familiar with the concept of inertia and gave a qualitative description of the action of gravity. He thus interprets some passages in Plutarch”s On the Face Visible on the Disk of the Moon. According to Rousseau, Hipparchus was actually a heliocentrist, but his relevant writings did not reach Ptolemy.

Mathematics. In developing the theories of the Moon and Sun, Hipparchus used an ancient version of trigonometry. He may have been the first to compile a table of chords, an analogue of modern tables of trigonometric functions.

Geography. Hipparchus” treatise “Against the Geography of Eratosthenes” in three books has not reached us. Its content is known mainly from Strabo”s reports. Hipparchus subjected Eratosthenes” work to a detailed and partly unfair criticism, criticizing it mainly for internal contradictions and insufficient rigor in determining the position of geographic points. According to Hipparchus, the basis for the construction of a geographical map should only be accurate astronomical measurements of latitude and longitude and triangulation to calculate the unknown distances. Hipparchus himself was not able to meet these strict requirements, and real opportunities for their implementation did not appear until the XV-XVI centuries.

Hipparchus had three important innovations in the field of geographical theory. He was the first to use a grid of degrees, the first to suggest that latitude be determined not only by the sun, as it had been done long before him, but also by the stars, and to determine longitude he suggested using observations of lunar eclipses. In the practical part of his work, the so-called “table of climates,” Hipparchus indicated the latitudes of several dozen cities and localities. In particular, he gave more accurate estimates of the latitudes of Athens, Sicily and the southern tip of India than those of Eratosthenes. When calculating geographic latitudes based on the duration of the longest day in the light, Hipparchus used the corrected value of the angle of inclination of the ecliptic – 23°40′ (the true value in the second half of the 2nd century BC was about 23°43′), whereas other ancient authors knew only a rounded value of 24°, and Claudius Ptolemy used a less precise 23°51′. Moreover, Hipparchus argued against the view accepted in his time that the Atlantic and Indian Oceans and the Caspian Sea were parts of a single world ocean, and suggested that the oikumene, that is, the inhabited part of the land, occupied the entire space from the equator to the northern polar circle. This idea of Hipparchus was reflected in Ptolemy”s Geography. In fact, the whole work of Ptolemy is an attempt to implement Hipparchus” ideas of what geography should be.

Astrology. Perhaps the great astronomer was no stranger to astrology, which had penetrated into the Hellenistic world from Babylon. As Pliny the Elder writes, “this Hipparchus, who cannot but deserve sufficient praise… more than anyone else proved man”s kinship with the stars and that our souls are part of the sky. Hipparchus was one of the first astronomers of antiquity to engage in astrology, and is sometimes mentioned in ancient lists of famous astrologers.

The lunar crater, the asteroid (4000) Hipparchus, and the Hipparcos orbiting telescope of the European Space Agency, designed for astrometric measurements, are named after Hipparchus.

Sources

1. Гиппарх
2. Hipparchus
3. ^ These figures use modern dynamical time, not the solar time of Hipparchus”s era. E.g., the true 4267-month interval was nearer 126,007 days plus a little over half an hour.
4. Graßhoff G. The History of Ptolemy”s Star Catalogue. — Springer Verlag, 1990. — ISBN 0-387-97181-5.
5. Duke D. W. (2002). «Associations between the ancient star catalogs» Архивная копия от 2 июня 2020 на Wayback Machine. Archive for the History of Exact Sciences 56 (5): 435—450.
6. Ксенофон Мусас. Древнегреческий компьютер. «Редкие земли» № 1 (8), 2017, стр.112-117.
7. a b Gerd Graßhoff: The Analysis of the Star Catalogue. In: The History of Ptolemy’s Star Catalogue. Band 14. Springer New York, New York, NY 1990, ISBN 978-1-4612-8788-9, S. 92–128, doi:10.1007/978-1-4612-4468-4_5.
8. Gerd Graßhoff: The Stars of the Almagest. In: The History of Ptolemy’s Star Catalogue. Band 14. Springer New York, New York, NY 1990, ISBN 978-1-4612-8788-9, S. 6–22, doi:10.1007/978-1-4612-4468-4_2.
9. a b c Susanne M. Hoffmann: Sternbilder und Koordinatensysteme: die Positionssysteme des Himmels. In: Hipparchs Himmelsglobus. Springer Fachmedien Wiesbaden, Wiesbaden 2017, ISBN 978-3-658-18682-1, S. 1–52, doi:10.1007/978-3-658-18683-8_1.
10. C. M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy[νεκρός σύνδεσμος], σελ. 52, Cambridge University Press (2004) ISBN 0-521-82750-7