# Year

A year is the time between two recurrences of an event related to the orbit of the Earth around the Sun. By extension, this can be applied to any planet: for example, a "Martian year" is a year on Mars.

## Calendar year

A calendar year is the time between two dates with the same name in a calendar.

Solar calendars usually aim to predict the seasons, but because the length of individual seasonal years varies significantly, they instead use an astronomical year as a surrogate. For example, the ancient Egyptians used the heliacal rising of Sirius to predict the flooding of the Nile.

The Gregorian calendar aims to keep the vernal equinox on or close to March 21; hence it follows the vernal equinox year. The average length of its year is 365.2425 days.

Among solar calendars in wide use today, the Persian calendar is one of the most precise. Rather than being based on numerical rules, the Persian year begins on the day (for the time zone of Tehran) on which the vernal equinox actually falls, as determined by precise astronomical computations.

No astronomical year has an integer number of days or lunar months, so any calendar that follows an astronomical year must have a system of intercalation such as leap years.

In the Julian calendar, the average length of a year was 365.25 days. This is still used as a convenient time unit in astronomy, see below.

## Seasonal year

A seasonal year is the time between successive recurrences of a seasonal event such as the flooding of a river, the migration of a species of bird, the flowering of a species of plant, the first frost, or the first scheduled game of a certain sport. All of these events can have wide variations of more than a month from year to year.

An academic year refers to the annual period during which a student attends school or college.

The school year can be divided up in various ways, two of which are most common in North American educational systems. (1) Many schools divide the academic year into three roughly equal-length quarters, more or less coinciding with autumn, winter, and spring. A somewhat shortened summer session, not usually considered part of the regular academic year, is attended by students on a voluntary or elective basis. (2) Other schools break the year into two main semesters, a first (typically August through December) and a second (January through May). Each of these main semesters is split in half and each of the halves is referred to as a quarter. There is also an elective summer session.

In the southern hemisphere the academic year is the same as the calendar year and so the academic year is just referred to as the year.

## Astronomical years

### Julian year

The Julian year, as used in astronomy and other sciences, is a time unit defined as exactly 365.25 days. This is the normal meaning of the unit "year" (symbol "a" from the Latin annus, annata) used in various scientific contexts. The Julian century of 36525 days and the Julian millennium of 365250 days are used in astronomical calculations. Fundamentally, expressing a time interval in Julian years is a way to precisely specify how many days (not how many "real" years), for long time intervals where stating the number of days would be unwieldy and unintuitive. For the distance unit light year, by convention the Julian year is used in the computation.

### Sidereal year

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 in SI days of 86,400 SI seconds each is on average:

365.256 363 051 days (365 d 6 h 9 min 9 s) (at the epoch J2000.0 = 2000 January 1 12:00:00 TT).

### Tropical year

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 westward along the ecliptic with respect to the fixed stars (with a period of about 26,000 tropical 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 equinox year is the time between successive vernal equinoxes. The mean tropical year (averaged over all ecliptic points) is:

365.242 189 67 days (365 d 5 h 48 min 45 s) (at the epoch J2000.0).

### Anomalistic year

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 farthest 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. Therefore the anomalistic year is slightly longer than the sidereal year. It takes about 112,000 years for the ellipse to revolve once relative to the fixed stars. The anomalistic year is also longer than the tropical year (which calendars attempt to track) and so the date of the perihelion gradually advances every year. It takes about 21,000 years for the ellipse to revolve once relative to the vernal equinox, thus for the date of perihelion to return to the same place (given a calendar that tracks the seasons perfectly).

The average duration of the anomalistic year is:

365.259 635 864 days (365 d 6 h 13 min 52 s) (at the epoch J2000.0).

### Draconic year

The draconitic year, eclipse year or ecliptic year is the time for the Sun (as seen from the Earth) to complete one revolution with respect to the same lunar node (a point 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 of every half eclipse year. Hence there are two eclipse seasons every eclipse year. The average duration of the eclipse year is:

346.620 075 883 days (346 d 14 h 52 min 54 s) (at the epoch J2000.0).

This term is sometimes also used to designate the time it takes for a complete revolution of the Moon's ascending node around the ecliptic: 18.612 815 932 years (6798.331 019 days; at the epoch J2000.0).

### Fumocy

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:

411.784 430 29 days (411 d 18 h 49 min 34 s) (at the epoch J2000.0).

### Heliacal year

A heliacal year is the interval between the heliacal risings of a star. It equals the sidereal year except for a very minor difference due to the proper motion of the star and the precession of the equinoxes. (To visualise the latter: the constellation Crux which rose and set as seen from the Mediterranean in ancient Greek times, is never above the horizon in current times.)

### Sothic year

The Sothic year is the interval between heliacal risings of the star Sirius. Its duration is very close to the mean Julian year of 365.25 days.

### Gaussian year

The Gaussian year is the sidereal year for a planet of negligible mass (relative to the Sun) and unperturbed by other planets that is governed by the Gaussian gravitational constant. Such a planet would be slightly closer to the Sun than Earth's mean distance. Its length is:

365.256 898 3 days (365 d 6 h 9 min 56 s).

### Besselian year

The Besselian year is a tropical year that starts when the fictitious mean Sun reaches an ecliptic longitude of 280°. This is currently on or close to 1 January. It is named after the 19th century German astronomer and mathematician Friedrich Bessel. An approximate formula to compute the current time in Besselian years from the Julian day is:

B = 2,000 + (JD - 2,451,544.53) /365.242189

### Great year

The Great year, Platonic year, or Equinoctial cycle corresponds to a complete revolution of the equinoxes around the ecliptic. Its length is about 25,700 years, and cannot be determined precisely as the precession speed is variable.

## Variation in the length of the year and the day

The exact length of an astronomical year changes over time. The main sources of this change are:

1. The precession of the equinoxes changes the position of astronomical events with respect to the apsides of 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.
2. The gravitational influence of the Moon and planets changes the motion of the Earth from a steady orbit around the Sun.

Tidal drag between the Earth and the Moon and Sun increases the length of the day and of the month; since the apparent mean solar day is the unit with which we measure the length of the year in civil life, the length of the year appears to change. Tidal drag in turn depends on factors such as post-glacial rebound and sea level rise.

It is also to be expected that changes in the effective mass of the sun, caused by solar wind and radiation of energy generated by nuclear fusion, could affect the Earth's orbital period over a long time.

## Summary of various kinds of year

• 353, 354 or 355 days — the lengths of common years in some lunisolar calendars
• 354.37 days — 12 lunar months; the average length of a year in lunar calendars
• 365 days — a common year in many solar calendars
• 365.24219 days — a mean tropical year near the year 2000
• 365.2424 days — a vernal equinox year.
• 365.2425 days — the average length of a year in the Gregorian calendar
• 365.25 days — the average length of a year in the Julian calendar
• 365.2564 days — a sidereal year
• 366 days — a leap year in many solar calendars
• 383, 384 or 385 days — the lengths of leap years in some lunisolar calendars
• 383.9 days — 13 lunar months; a leap year in some lunisolar calendars

An average Gregorian year is 365.2425 days = 52.1775 weeks, 8,765.82 hours = 525,949.2 minutes = 31,556,952 seconds (mean solar, not SI).

A common year is 365 days = 8,760 hours = 525,600 minutes = 31,536,000 seconds.

A leap year is 366 days = 8,784 hours = 527,040 minutes = 31,622,400 seconds.

An easy to remember approximation for the number of seconds in a year is $\begin{matrix}\pi\end{matrix}$×107 seconds.

The 400-year cycle of the Gregorian calendar has 146,097 days and hence exactly 20,871 weeks.