Astronomer and mathematician; b. ? (Nicaea, Bithynia), d. **after 127 BC** (Rhodes?)

Information about the life of Hipparchus is scant. It is known that he carried out astronomical observations in Bithynia on the island of Rhodes and in Alexandria. Analysis of his notes suggests strongly that he made observations on the star Eta Canis Majoris in 127 BC, so that year is conventionally used to estimate when Hipparchus lived.

Most information about Hipparchus' work comes from writings of Strabo of Amaseia, who worked about 21 AD, and from Ptolemy's *Almagest.* It is obvious from Ptolemy's references to Hipparchus that he held him in very high esteem.

Hipparchus was a brilliant observationalist and astute mathematician. He discovered the precession of the equinoxes, a gradual apparent shift of either of two points where the celestial equator crosses the ecliptic (see Lecture 7 for detail) against the stars, by comparing his own observations against records from Timocharis of Alexandria about 150 years earlier and observations made in Babylonian times. The movement is equivalent to a small change of the position of the north celestial pole relative to the stars in its vicinity.

Apparently Hipparchus described the effect in a work entitled "Precession of the Equinoxes." Today the effect is interpreted as a change in the Earth's rotational axis, which traces out a conical path around the axis of the orbital plane. Hipparchus' value of 45'' or 46'' (seconds of arc) per year is very close to the figure of 50.26'' accepted today and is much superior to the 36'' that Ptolemy obtained.

The discovery of precession enabled Hipparchus to determine the lengths of the tropical year and of the sidereal year (the period of the Sun's apparent revolution from a fixed star to the same fixed star) with great accuracy. His value for the tropical year was within 6.5 minutes of today's value.

In 134 BC Hipparchus noticed what he thought to be a new star. He decided to determine whether the number of stars was variable or not and began with the compilation of a star catalogue. Although such an undertaking was considered improper for religious reasons Hipparchus was not deterred. He measured the stellar positions with greater accuracy than any observer before him, and his star catalogue was used by Ptolemy, and 1800 years later by Edmond Halley (1656 - 1742) in his determination of the course of what became known as Halley's comet. Hipparchus' catalogue, completed in 129 BC, listed about 850 stars and included their apparent brightnesses on a scale of six magnitudes similar to that used today.

Hipparchus introduced the concept of the eccentric circle, ie a circle in which the Earth is not at the circle centre but at some point slightly eccentric from it, to explain some peculiarities of the motion of the Sun and the Moon. He realized and gave a geometrical proof that the eccentric circle is mathematically equivalent to the epicycle-deferent system used by Eudoxus. (There is evidence that Apollonius of Perga might have given the same proof a century earlier.)

The Greek belief that order in nature is beautiful worked against Hipparchus' eccentric circle idea. Most astronomers preferred the epicycle-deferent mechanism in which the Earth was in the centre of all movement. Ptolemy included both systems in his description of the geocentric system and acknowledged Hipparchus' method as equally accurate.

Hipparchus tried his own determination of the relative size of the Sun and the Moon, using the method devised by Aristarchus, which uses the Earth's shadow during a lunar eclipse. Eudoxus had obtained a value of 9:1, Phidias (the father of Archimedes) 12:1, Archimedes himself 30:1; Aristarchus believed 20:1 to be correct, although he was dissatisfied with the accuracy of his measurement. The present-day value is, approximately, 393:1.

Hipparchus introduced the same mathematical rigour to geography that he applied to celestial observations. He was very critical of the geographical work of Eratosthenes and tried to determine the location of places on the Earth's surface. He introduced the use of latitude and longitude (the method used today) and proposed methods to measure these.