The main accomplishment of Oenopides as an astronomer was his determination of the angle between the plane of the celestial equator, and the zodiac (the yearly path of the sun in the sky). He found this angle to be 24°. In effect this amounted to measuring the inclination of the earth axis. Oenopides's result remained the standard value for two centuries, until Eratosthenes measured it with greater precision.
Oenopides also determined the value of the Great Year, that is, the shortest interval of time that is equal to both an integer number of years and an integer number of months. As the relative positions of the sun and moon repeat themselves after each Great Year, this offers a means to predict solar and lunar eclipses. In actual practice this is only approximately true, because the ratio of the length of the year and that of the month does not exactly match any simple mathematical fraction, and because in addition the lunar orbit varies continuously.
Oenopides put the Great Year at 59 years, corresponding to 730 months. This was a good approximation, but not a perfect one, since 59 (sidereal) years are equal to 21550.1 days, while 730 (synodical) months equal 21557.3 days. The difference therefore amounts to seven days. In addition there are the interfering variations in the lunar orbit. However, a 59 year period had the advantage that it corresponded quite closely to an integer number of orbital revolutions of several planets around the sun, which meant that their relative positions also repeated each Great Year cycle. Before Oenopides a Great Year of eight solar years was in use (= 99 months). Shortly after Oenopides, in 432 BC, Meton and Euctemon discovered the better value of 18 years, equal to 223 months (the so-called Saros period).
While Oenopides's innovations as an astronomer mainly concern practical issues, as a geometer he seems to have been rather a theorist and methodologist, who set himself the task to make geometry comply with higher standards of theoretical purity. Thus he introduced the distinction between 'theorems' and 'problems': though both are involved with the solution of an exercise, a theorem is meant to be a theoretical building block to be used as the fundament of further theory, while a problem is only an isolated exercise without further follow-up or importance.
Oenopides apparently also was the author of the rule that geometrical constructions should use no other means than compass and straightedge. In this context his name adheres to two specific elementary constructions of plane geometry: first, to draw from a given point a straight line perpendicular to a given straight line; and second, on a given straight line and at a given point on it, to construct a rectilineal angle equal to a given rectilineal angle.
Miscellaneous opinions attributed to Oenopides
Several more opinions in various areas are attributed to Oenopides: