Calendars usually aim to predict the seasons, but because it is hard to determine the length of the seasonal year, they instead use an astronomical year as a surrogate for the seasonal year. For example, the ancient Egyptians used the heliacal rising of Sirius to predict the flooding of the Nile.
A Julian year is exactly 365.25 days, the average length of the year in the Julian calendar. It is still used in ephemerides because of the very simple conversion between Julian dates and Julian years: 100 Julian years is just another way of saying 36525 days.
An astronomical year is the time between two recurrences of an astronomical event.
The sidereal year is the time for the Earth to complete one revolution of its orbit, as measured in a fixed frame of reference (such as the fixed stars, Latin sidus). Its duration is on average:
A tropical year is the time for the Earth to complete one revolution with respect to the framework provided by the intersection of the ecliptic (the plane of the orbit of the Earth) and the plane of the equator (the plane perpendicular to the rotation axis of the Earth). Because of the precession of the equinoxes, this framework moves slowly backwards along the ecliptic with respect to the fixed stars (with a period of about 26,000 years); as a consequence, the Earth completes this year before it completes a full orbit as measured in a fixed reference frame. Therefore a tropical year is shorter than the sidereal year. The exact length of a tropical year depends on the chosen starting point: for example the vernal equinoctial year is the time between successive vernal equinoxes. The mean tropical year (averaged over all tropical ecliptic points) is:
- 365.24218967 days (365d 5h 48m 45s) (at the epoch J2000.0).
The anomalistic year is the time for the Earth to complete one revolution with respect to its apsides. The orbit of the Earth is elliptical; the extreme points, called apsides, are the perihelion, where the Earth is closest to the Sun (January 2 in 2000), and the aphelion, where the Earth is furthest from the Sun (July 2 in 2000). Because of gravitational disturbances by the other planets, the shape and orientation of the orbit are not fixed, and the apsides slowly move with respect to a fixed frame of reference (with a period of about 21,000 years). Therefore the anomalistic year is slightly longer than the sidereal year: on average it is:
- 365.259635864 days (at the epoch J2000.0).
The eclipse year or ecliptic year is the time for the Sun (as seen from the Earth) to complete one revolution with respect to a node of the Moon's orbit (the points where the Moon's orbit intersects the ecliptic). This period is associated with eclipses: these occur only when both the Sun and the Moon are near these nodes; so eclipses occur within about a month every half eclipse year. Hence there are two eclipse seasons every eclipse year. The average duration of the eclipse year is:
- 346.620075883 days (at the epoch J2000.0).
The full moon cycle or fumocy is the time for the Sun (as seen from the Earth) to complete one revolution with respect to the perigee of the Moon's orbit. This period is associated with the apparent size of the Full Moon, and also with the varying duration of the synodic month. The duration of one full moon cycle is:
- 411.78443029 days (at the epoch J2000.0).
- 365.2568983 days.
The Besselian year is a tropical year that starts when the mean Sun reaches the ecliptic longitude of 280°. This is currently on or close to 1 January. It is named after the 19th century astronomer and mathematician Friedrich Bessel. An approximate formula to compute the current time in Besselian years from the Julian day is:
- B = 2000 + (JD - 2451544.53)/365.242189
See also: Besselian epoch.
Variation in the length of the year and the day
The exact length of a year changes over time. The main sources of this change are as follows:
- The precession of the equinoxes changes the position of astronomical events with respect to the apsides of the Earth's orbit. An event moving toward perihelion recurs with a decreasing period from year to year; an event moving toward aphelion recurs with an increasing period from year to year.
- The gravitational influence of the Moon and planets changes the shape of the Earth's orbit.