Callippus ( // ; Ancient Greek : Κάλλιππος; c. 370 BC – c. 300 BC) was a Greek astronomer and mathematician.
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
Callippus was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato. He also worked with Aristotle at the Lyceum, which means that he was active in Athens prior to Aristotle's death in 322. He observed the movements of the planets and attempted to use Eudoxus' scheme of connected spheres to account for their movements. However he found that 27 spheres was insufficient to account for the planetary movements, and so he added seven more for a total of 34. According to the description in Aristotle's Metaphysics (XII.8), he added two spheres for the Sun, two for the Moon, and one each for Mercury, Venus, and Mars.
Cyzicus was an ancient town of Mysia in Anatolia in the current Balıkesir Province of Turkey. It was located on the shoreward side of the present Kapıdağ Peninsula, a tombolo which is said to have originally been an island in the Sea of Marmara only to be connected to the mainland in historic times either by artificial means or an earthquake.
Eudoxus of Cnidus was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. Sphaerics by Theodosius of Bithynia may be based on a work by Eudoxus.
An academy is an institution of secondary education, higher learning, research, or honorary membership. Academia is the worldwide group composed of professors and researchers at institutes of higher learning.
Callippus made careful measurements of the lengths of the seasons, finding them (starting with the spring equinox) to be 94 days, 92 days, 89 days, and 90 days. This variation in the seasons implies a variation in the speed of the Sun, called the solar anomaly. He also followed up on the work done by Meton of Athens to measure the length of the year and construct an accurate lunisolar calendar. The Metonic cycle has 19 tropical years and 235 synodic months in 6940 days. The Callippic cycle synchronizes days per orbit and rotations per orbit within the Metonic cycle, noting the difference of one after 4 Metonic cycles, a duration of 76 years. Distinguishing rotations and days infers knowledge of the precession cycle.
An equinox is commonly regarded as the instant of time when the plane of Earth's equator passes through the center of the Sun. This occurs twice each year: around 20 March and 23 September. In other words, it is the moment at which the center of the visible Sun is directly above the Equator. In the northern hemisphere, the equinox in March is called the Vernal or Spring Equinox; the September equinox is called the Autumnal or Fall Equinox.
Meton of Athens was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the 5th century BC. He is best known for calculations involving the eponymous 19-year Metonic cycle which he introduced in 432 BC into the lunisolar Attic calendar.
A lunisolar calendar is a calendar in many cultures whose date indicates both the Moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.
Callippus started his observation cycle on the summer solstice, 330 BC, (28 June in the proleptic Julian calendar). The cycle's begin position, the stellar position and sidereal hour timing the eclipse, are used by later astronomers for calibrating their observations in relation to subsequent eclipses. The Callippic cycle of 76 years appears to be used in the Antikythera mechanism, an ancient astronomical mechanical clock and observational aide of the 2nd century BC (discovered in Mediterranean waters off Greece). The mechanism has a dial for the Callippic cycle and the 76 years are mentioned in the Greek text of the manual of this old device. The crater Calippus on the Moon is named after him.
The proleptic Julian calendar is produced by extending the Julian calendar backwards to dates preceding AD 8 when the quadrennial leap year stabilized. The leap years that were actually observed between the implementation of the Julian calendar in 45 BC and AD 8 were erratic: see the Julian calendar article for details.
The Antikythera mechanism is an ancient Greek analogue computer used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance. It could also be used to track the four-year cycle of athletic games which was similar to an Olympiad, the cycle of the ancient Olympic Games.
Calippus is a small lunar impact crater that is located on the eastern edge of the rugged Montes Caucasus mountain range in the northern part of the Moon. It was named after Greek astronomer Callippus of Cyzicus. It lies to the southwest of the crater remnant Alexander, to the northwest of the Mare Serenitatis.
Hipparchus of Nicaea was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.
Astronomy is the oldest of the natural sciences, dating back to antiquity, with its origins in the religious, mythological, cosmological, calendrical, and astrological beliefs and practices of prehistory: vestiges of these are still found in astrology, a discipline long interwoven with public and governmental astronomy. It was not completely separated in Europe during the Copernican Revolution starting in 1543. In some cultures, astronomical data was used for astrological prognostication.
For astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years that is nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens observed that a period of 19 years is almost exactly equal to 235 synodic months and, rounded to full days, counts 6,940 days. The difference between the two periods is only a few hours, depending on the definition of the year.
Eclipses may occur repeatedly, separated by certain intervals of time: these intervals are called eclipse cycles. The series of eclipses separated by a repeat of one of these intervals is called an eclipse series.
The saros is a period of approximately 223 synodic months, that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros.
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In particular, it can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 25,772 years. This is similar to the precession of a spinning-top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.
An exeligmos is a period of 54 years, 33 days that can be used to predict successive eclipses with similar properties and location. For a solar eclipse, after every exeligmos a solar eclipse of similar characteristics will occur in a location close to the eclipse before it. For a lunar eclipse the same part of the earth will view an eclipse that is very similar to the one that occurred one exeligmos before it. It is an eclipse cycle that is a triple saros, 3 saroses long, with the advantage that it has nearly an integer number of days so the next eclipse will be visible at locations and times near the eclipse that occurred one exeligmos earlier. In contrast, each saros, an eclipse occurs about 8 hours later in the day or about 120° to the west of the eclipse that occurred one saros earlier.
The cosmological model of concentric or homocentric spheres, developed by Eudoxus, Callippus, and Aristotle, employed celestial spheres all centered on the Earth. In this respect, it differed from the epicyclic and eccentric models with multiple centers, which were used by Ptolemy and other mathematical astronomers until the time of Copernicus.
The Attic calendar or Athenian calendar is the calendar that was in use in ancient Attica, the ancestral territory of the Athenian polis. It is sometimes called the Greek calendar because of Athens's cultural importance, but it is only one of many ancient Greek calendars.
In astronomy, an octaeteris is the period of eight solar years after which the moon phase occurs on the same day of the year plus one or two days.
Autolycus of Pitane was a Greek astronomer, mathematician, and geographer. The lunar crater Autolycus was named in his honour.
For astronomy and calendar studies, the Callippic cycle is a particular approximate common multiple of the year and the synodic month, that was proposed by Callippus during 330 BC. It is a period of 76 years, as an improvement of the 19-year Metonic cycle.
Sosigenes the Peripatetic was a philosopher living at the end of the 2nd century AD. He was the tutor of Alexander of Aphrodisias and wrote a work On Revolving Spheres, from which some important extracts have been preserved in Simplicius's commentary on Aristotle's De Caelo.
Cleostratus was an astronomer of ancient Greece. He was a native of Tenedos. He is believed by ancient historians to have introduced the zodiac and the solar calendar. According to J. Webb, Cleostratus took his ideas from the Babylonians.
Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.
Babylonian astronomy was the study or recording of celestial objects during early history Mesopotamia. These records can be found on Sumerian clay tablets, inscribed in cuneiform, dated approximately to 3500–3200 BC.
In lunar calendars, a lunar month is the time between two successive syzygies. The precise definition varies, especially for the beginning of the month.
Edmund Frederick Robertson is a Professor emeritus of pure mathematics at the University of St Andrews.
The MacTutor History of Mathematics archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathematicians, as well as information on famous curves and various topics in the history of mathematics.
The University of St Andrews is a British public university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland and the third oldest university in the English-speaking world. St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy.