Hipparchus

Hipparchus (born, Nicaea, Bithynia [now Iznik, Turkey]—died after 127 bce, Rhodes?) was a Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. Although he is commonly ranked among the greatest scientists of antiquity, very little is known about his life, and only one of his many writings is still in existence. Knowledge of the rest of his work relies on second-hand reports, especially in the great astronomical compendium the Almagest, written by Ptolemy in the 2nd century ce.

Lover of truth

As a young man in Bithynia, Hipparchus compiled records of local weather patterns throughout the year. Such weather calendars (parapēgmata), which synchronized the onset of winds, rains, and storms with the astronomical seasons and the risings and settings of the constellations, were produced by many Greek astronomers from at least as early as the 4th century bce.

Most of Hipparchus’s adult life, however, seems to have been spent carrying out a program of astronomical observation and research on the island of Rhodes. Ptolemy cites more than 20 observations made there by Hipparchus on specific dates from 147 to 127, as well as three earlier observations from 162 to 158 that may be attributed to him. These must have been only a tiny fraction of Hipparchus’s recorded observations. In fact, his astronomical writings were numerous enough that he published an annotated list of them.

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Hipparchus also wrote critical commentaries on some of his predecessors and contemporaries. In Tōn Aratou kai Eudoxou Phainomenōn exēgēseōs biblia tria (“Commentary on the Phaenomena of Aratus and Eudoxus”), his only surviving book, he ruthlessly exposed errors in Phaenomena, a popular poem written by Aratus and based on a now-lost treatise of Eudoxus of Cnidus that named and described the constellations. Apparently his commentary Against the Geography of Eratosthenes was similarly unforgiving of loose and inconsistent reasoning. Ptolemy characterized him as a “lover of truth” (philalēthēs)—a trait that was more amiably manifested in Hipparchus’s readiness to revise his own beliefs in the light of new evidence. He communicated with observers at Alexandria in Egypt, who provided him with some times of equinoxes, and probably also with astronomers at Babylon.

Solar and lunar theory

Hipparchus’s most important astronomical work concerned the orbits of the Sun and Moon, a determination of their sizes and distances from Earth, and the study of eclipses. Like most of his predecessors—Aristarchus of Samos was an exception—Hipparchus assumed a spherical, stationary Earth at the centre of the universe (the geocentric cosmology). From this perspective, the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn (all of the solar system bodies visible to the naked eye), as well as the stars (whose realm was known as the celestial sphere), revolved around Earth each day.

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Every year the Sun traces out a circular path in a west-to-east direction relative to the stars (this is in addition to the apparent daily east-to-west rotation of the celestial sphere around Earth). Hipparchus had good reasons for believing that the Sun’s path, known as the ecliptic, is a great circle, i.e., that the plane of the ecliptic passes through Earth’s centre. The two points at which the ecliptic and the equatorial plane intersect, known as the vernal and autumnal equinoxes, and the two points of the ecliptic farthest north and south from the equatorial plane, known as the summer and winter solstices, divide the ecliptic into four equal parts. However, the Sun’s passage through each section of the ecliptic, or season, is not symmetrical. Hipparchus attempted to explain how the Sun could travel with uniform speed along a regular circular path and yet produce seasons of unequal length.

Hipparchus knew of two possible explanations for the Sun’s apparent motion, the eccenter and the epicyclic models (see Ptolemaic system). These models, which assumed that the apparent irregular motion was produced by compounding two or more uniform circular motions, were probably familiar to Greek astronomers well before Hipparchus. His contribution was to discover a method of using the observed dates of two equinoxes and a solstice to calculate the size and direction of the displacement of the Sun’s orbit. With Hipparchus’s mathematical model one could calculate not only the Sun’s orbital location on any date, but also its position as seen from Earth. The history of celestial mechanics until Johannes Kepler (1571–1630) was mostly an elaboration of Hipparchus’s model.

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Hipparchus also tried to measure as precisely as possible the length of the tropical year—the period for the Sun to complete one passage through the ecliptic. He made observations of consecutive equinoxes and solstices, but the results were inconclusive: he could not distinguish between possible observational errors and variations in the tropical year. However, by comparing his own observations of solstices with observations made in the 5th and 3rd centuries bce, Hipparchus succeeded in obtaining an estimate of the tropical year that was only six minutes too long.

He was then in a position to calculate equinox and solstice dates for any year. Applying this information to recorded observations from about 150 years before his time, Hipparchus made the unexpected discovery that certain stars near the ecliptic had moved about 2° relative to the equinoxes. He contemplated various explanations—for example, that these stars were actually very slowly moving planets—before he settled on the essentially correct theory that all the stars made a gradual eastward revolution relative to the equinoxes. Since Nicolaus Copernicus (1473–1543) established his heliocentric model of the universe, the stars have provided a fixed frame of reference, relative to which the plane of the equator slowly shifts—a phenomenon referred to as the precession of the equinoxes, a wobbling of Earth’s axis of rotation caused by the gravitational influence of the Sun and Moon on Earth’s equatorial bulge that follows a 25,772-year cycle.

Hipparchus also analyzed the more complicated motion of the Moon in order to construct a theory of eclipses. In addition to varying in apparent speed, the Moon diverges north and south of the ecliptic, and the periodicities of these phenomena are different. Hipparchus adopted values for the Moon’s periodicities that were known to contemporary Babylonian astronomers, and he confirmed their accuracy by comparing recorded observations of lunar eclipses separated by intervals of several centuries. It remained, however, for Ptolemy (127–145 ce) to finish fashioning a fully predictive lunar model.

In On Sizes and Distances (now lost), Hipparchus reportedly measured the Moon’s orbit in relation to the size of Earth. He had two methods of doing this. One method used an observation of a solar eclipse that had been total near the Hellespont (now called the Dardanelles) but only partial at Alexandria. Hipparchus assumed that the difference could be attributed entirely to the Moon’s observable parallax against the stars, which amounts to supposing that the Sun, like the stars, is indefinitely far away. (Parallax is the apparent displacement of an object when viewed from different vantage points). Hipparchus thus calculated that the mean distance of the Moon from Earth is 77 times Earth’s radius. In the second method he hypothesized that the distance from the centre of Earth to the Sun is 490 times Earth’s radius—perhaps chosen because that is the shortest distance consistent with a parallax that is too small for detection by the unaided eye. Using the visually identical sizes of the solar and lunar discs, and observations of Earth’s shadow during lunar eclipses, Hipparchus found a relationship between the lunar and solar distances that enabled him to calculate that the Moon’s mean distance from Earth is approximately 63 times Earth’s radius. (The true value is about 60 times.)