Tropical year

The tropical year, also called the solar year, is the time it takes for the Sun to return to the same apparent position in the sky as seen from Earth, which completes one full cycle of the astronomical seasons. This period is measured from one vernal equinox to the next, or from one summer solstice to the next, and forms the basis for tropical solar calendars. It is distinct from the sidereal year, which measures Earth’s orbit relative to the fixed stars and is about 20 minutes and 24.7 seconds longer due to the precession of the equinoxes. The word "tropical" derives from the Greek *tropikos*, meaning "turn," referencing the turning points of the Sun’s seasonal path at the Tropics of Cancer and Capricorn. Ancient Chinese, Hindu, Greek, and other civilizations made early approximations of its length. In the 2nd century BC, Hipparchus measured the year by timing equinoxes, finding it to be 365.24667 days, and also discovered the precession of the equinoxes. Later, the Alfonsine Tables (1252) gave a value of 365.24255 days, used for the Gregorian calendar of 1582. Ulugh Beg’s 1437 tables estimated 365.242535 days. Copernicus’s heliocentric model led to the less accurate Prutenic Tables (1551). Kepler’s Rudolphine Tables (1627) improved the mean tropical year to 365.24219 days, a value consistent with modern measurements. The mean tropical year in 2000 was 365.24219 ephemeris days (86,400 SI seconds each), or 365.24217 mean solar days. The Gregorian calendar approximates this through leap-day rules to keep the calendar year aligned with the solar year.