Hipparchus

Greek astronomer

• Born: 190 b.c.e.
• Birthplace: Nicaea, Bithynia, Asia Minor (now İznik, Turkey)
• Died: After 127 b.c.e.
• Place of death: Possibly Rhodes, Greece

Hipparchus was the greatest astronomer of ancient times. He was the founder of trigonometry, which he used to determine the distances from Earth to the moon and sun, and the first to use consistently the idea of latitude and longitude to describe locations on Earth and in the sky.

Early Life

Very little is known about the life of Hipparchus (hih-PAHR-kuhs). He was born in Nicaea, a Greek-speaking city in Bithynia (modern İznik, Turkey), in the northwestern part of Asia Minor. Calculations in his works are based on the latitude of the city of Rhodes, on the island of the same name, so many historians believe that he spent a major portion of his life there. Rhodes was a merchant center, a convenient port from which to make voyages. At least one of Hipparchus’s observations was made in Alexandria, so it seems that he visited and perhaps spent time as a student or research scholar at that great nucleus of scientific inquiry. Because he was intensely interested in geography, it is likely that he traveled to other places in the Mediterranean basin and the Near East. He seems to have been familiar with Babylonian astronomy, including eclipse records, but it is impossible to say how he came to know these.

Life’s Work

Most of what is known of Hipparchus comes from the Mathēmatikē syntaxis (c. 150 c.e.; Almagest, 1948) of Ptolemy, whose work depends to a considerable extent on that of the earlier scientist, and from the Geōgraphica (c. 7 b.c.e.; Geography, 1917-1933) of Strabo. Of Hipparchus’s own writings, only the Tōn Araton kai Eudoxou phainomenon exigesis (commentary on the phenomena of Eudoxus and Aratus) survives, in three books. It criticizes the less accurate placement of stars and constellations by two famous predecessors. It is certainly not one of his most important works, but it contains some information on his observations of star positions, which were the basis of his lost star catalog. Other lost works of Hipparchus include Peri eviausiou megethous (on the length of the year) and Peri tes metabaseos tōn tropikon kai isemerinon semeion (on the displacement of the solstitial and equinoctial points). He is also credited with a trigonometrical table of chords in a circle, a work on gravitational phenomena called On Bodies Carried down by Their Weight, an attack on the geographical work of Eratosthenes, a compilation of weather signs, and some aids to computational astrology.

A number of achievements are attributed to Hipparchus by Ptolemy and other ancient writers. A new star appeared in the constellation Scorpio in July, 133 b.c.e. Hipparchus realized that without an accurate star catalog, it was impossible to demonstrate that the star was indeed new, so he set about producing a complete sky map with a table of the positions of the stars, including the angle north or south of the celestial equator (latitude) and the angle east or west of the vernal equinox point (one of the two intersections between the celestial equator and the sun’s path, or ecliptic).

In order to do this, he needed a means of measuring celestial angles, which led him to invent many of the sighting instruments, including the diopter and possibly the armillary astrolabe, used by astronomers before the invention of the telescope in the seventeenth century. He also knew how to calibrate water clocks. Hipparchus’s star catalog included about 850 stars, along with estimates of their brightness. He divided the stars into six categories, from the brightest to the dimmest, thus originating a system of stellar magnitude. He also made a celestial globe, showing the locations of the fixed stars on its surface.

In comparing his own measurements of positions of stars with those of earlier astronomers, Hipparchus discovered that there had been a systematic shift in the same direction in all of them. He noticed the phenomenon first in the case of the bright star Spica. In 283 b.c.e. Timocharis had observed the star to be eight degrees west of the autumnal equinoctial point, but Hipparchus found the figure to be six degrees. He found a displacement for every other star that he was able to check. These discrepancies, he established, were the result of a shift in the position of the equinoxes—and therefore of the celestial equator and poles. In modern astronomy, this shift is called the precession of the equinoxes and is known to be caused by a slow “wobble” in the orientation of Earth’s axis. The spot to which the north pole points in the sky (the north celestial pole) describes a circle in a period of more than twenty-six thousand years. Hipparchus was first to describe and to attempt to measure this phenomenon. He was, however, unable to explain its cause, since he held the geocentric theory, which postulates a motionless Earth at the center of a moving universe.

From the beginning of theoretical astronomy, the geocentric theory had been the accepted one. It assumed that the sun, moon, planets, and stars were carried on vast transparent spheres that revolved at different but constant speeds around Earth. Unfortunately, in order to explain the observed motions of the planets, which vary in speed and sometimes are retrograde relative to the stars, astronomers had to postulate the existence of additional spheres, invisible and bearing no celestial bodies but interconnected with the other spheres and affecting their motions. An Alexandrian astronomer, Aristarchus, had proposed the heliocentric theory, which holds that Earth, with its satellite, the moon, and all the other planets revolve around the central sun. The main appeal of this theory was its simplicity; it required fewer imaginary spheres to make it work.

Hipparchus rejected the heliocentric theory and instead adopted modifications of the geocentric theory to make it accord better with observations, perhaps following Apollonius of Perga. The main feature of the Hipparchan system is the epicycle, a smaller sphere bearing a planet, with its center on the surface of the larger, Earth-centered sphere and revolving at an independent speed. He also postulated eccentrics, that is, that the centers of the celestial spheres do not coincide with the center of Earth. The geocentric system with epicycles is often called “Ptolemaic,” as Ptolemy made observations to support the theory developed by Hipparchus. Aristarchus’s heliocentric theory is closer to the picture of the solar system provided by modern astronomy.

In developing his astronomical system, Hipparchus observed the period of revolution of the celestial objects that move against the background of the stars. That of the sun, which is the year, he found to be 365¼ days, less 1/300 of a day, a figure that was closer to the true one than that of any previous astronomer. He noticed the inequality in the lengths of the seasons, which he correctly attributed to the varying distance between Earth and the sun but incorrectly explained by assuming that the center of the sun’s sphere of revolution was eccentric to the center of Earth. These conclusions were, perhaps, a step in the direction of recognizing that the relative motion of the two bodies describes an ellipse. He also achieved a measurement of the length of the lunar month, with an error of less than one second in comparison with the figure now accepted. The Roman scholar Pliny the Elder wrote that Hipparchus countered the popular fear of eclipses by publishing a list that demonstrated their regularity over the preceding six hundred years.

Hipparchus attempted to measure the distances of the moon and sun from Earth by observing eclipses and the phenomenon of parallax (the shift in the apparent position of the moon against the background of the stars under changing conditions). His figure for the distance of the moon (60.5 times the radius of Earth) was reasonably accurate, but his estimate of the sun’s distance (2,550 times Earth’s radius) was far too small. (The true ratio is about 23,452 to 1.) In fairness to Hipparchus, it should be noted that he regarded his solution to the problem of the sun’s distance as open to question.

In order to make the mathematical computations required by these problems, it was necessary for Hipparchus to know the ratios of the sides of a right triangle for the various angles the sides make with the hypotenuse—in other words, the values of trigonometrical functions. He worked out tables of the sine function, thus becoming, in effect, the founder of trigonometry.

Geography also occupied Hipparchus’s attention. He began the systematic use of longitude and latitude, which he had also employed in his star catalog, as a means of establishing locations on Earth’s surface. Previous geographers show evidence of knowing such a method, but they did not employ it consistently. Hipparchus was able to calculate latitudes of various places on Earth’s surface by learning the lengths of the days and nights recorded for different seasons of the year, although the figures given by him were often in error. As the base of longitude, he used the meridian passing through Alexandria. He was especially critical, probably too much so, of the descriptive and mathematical errors in the work of Eratosthenes. He even had some quibbles with the famous measurement of the spherical Earth, which is the latter’s most brilliant achievement. It may be Hipparchus, rather than Eratosthenes, who first described climatic zones, bounded by parallels of latitude north and south of the equator.

Significance

Hipparchus was a careful and original astronomer whose discoveries, particularly that of precession, were of the greatest importance in the early history of the science. He was a meticulous observer who produced the first dependable star catalog and who determined the apparent periods of revolution of the moon and the sun with an exactitude never before achieved. As a mathematician, he originated the study of trigonometry, compiling a sine table and using it in an attempt to measure distances in space beyond Earth that was, at least in the case of the moon, successful. Both as astronomer and as geographer, he pioneered the systematic use of the coordinates of latitude and longitude. He devised instruments for use in these observations and measurements.

Unfortunately, almost all Hipparchus’s writings have disappeared, so modern assessments of his work must depend on ancient writers who happened to mention him. His influence was important enough to cause several later scientists whose works survive to refer to and summarize him. Most notable among these were Ptolemy and Strabo. It is sometimes hard to tell when these authors, particularly Ptolemy, are following Hipparchus and when they are going beyond him to present their own conclusions. Ptolemy’s work became the standard textbook on astronomy until the time of Nicolaus Copernicus in the sixteenth century; thus Hipparchus’s name was deservedly remembered. One of Hipparchus’s most important mathematical successors was Menelaus of Alexandria (fl. c. 100 c.e.), who developed the study of spherical trigonometry.

Bibliography

Dicks, D. R. Early Greek Astronomy to Aristotle. Ithaca, N.Y.: Cornell University Press, 1985. Hipparchus is not given major treatment, although he does appear as an important figure in the history of astronomy. The discussion of his criticisms of Eudoxus and Aratus is particularly good.

Dreyer, John L. E. A History of Astronomy from Thales to Kepler. 2d ed. New York: Dover, 1953. This fine, accessible study places Hipparchus clearly in the context of the development of astronomy. Dreyer differs from common interpretation in crediting Ptolemy, not Hipparchus, with the theory of epicycles.

Heath, Thomas. A History of Greek Mathematics. 2 vols. Reprint. New York: Dover, 1981. Includes a section on Hipparchus in the second volume, emphasizing his probable contributions to the origin of trigonometry and establishing his place in the history of mathematics.

Lloyd, G. E. R. Greek Science After Aristotle. New York: W. W. Norton, 1973. Rather than giving a separate treatment to the subject, this work discusses the contributions of Hipparchus as they arise in a general study of ancient science from the fourth century b.c.e. to the end of the second century c.e. The attention given to Hipparchus is appropriate and appreciative.

Neugebauer, Otto. A History of Ancient Mathematical Astronomy. 3 vols. New York: Springer-Verlag, 1975. This work contains a section on Hipparchus in volume 1, briefly discussing what little is known about his life and chronology and devoting the rest of its space to a careful consideration of his astronomical work. There are some mathematical and astronomical symbols and formulas that the layperson may find difficult.

Ptolemy. Ptolemy’s “Almagest.” Translated by G. J. Toomer. Princeton, N.J.: Princeton University Press, 1998. Much of what is known about Hipparchus is based on Ptolemy’s words. This fine translation has complete notes and a useful bibliography.