3 Astronomical years

The sidereal yearThe sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. The sidereal year is the orbital period of Earth. A sidereal year equals 365. 2564 mean solar days. The sidereal year is 20 minutes a 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:

365.256363051 days (365d 6h 9m 9s) (at the epoch J2000.0 = 2000 January 1 12:00:00 TT).

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:

365.24218967 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 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 is also longer than the tropical year (the basis of Gregorian calendar) and so the date of the perihelion gradually advances every year. It takes 21,000 tropical years for the ellipse to revolve once relative to the fixed stars, or for either apside to advance once through all dates of the Julian or Gregorian year. The average duration of the anomalistic year is:

365.259635864 days (365d 6h 13m 52s) (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 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:

346.620075883 days (346d 14h 52m 54s) (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 (411d 18h 49m 34s) (at the epoch J2000.0).

A heliacal year is the interval between the heliacal risings of a star. It equals the sidereal year only if the star is on the ecliptic. It differs from the sidereal year for stars north or south of the ecliptic because of the significant angle (23.5°) between Earth's celestial equator and the ecliptic.

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.

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:

365.2568983 days (365d 6h 9m 56s).

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 = 2000 + (JD - 2451544.53)/365.242189

4 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 shape of the Earth's orbit.

Tidal drag between the Earth and the Moon and Sun increases the length of the day and of the month. This in turn depends on factors such as continental rebound and sea level rise.

5 Summary of various kinds of year

• 353, 354 or 355 days — the lengths of regular 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; ~31.53 million seconds
• 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; the light year is based on it; it is 31,557,600 seconds
• 365.2564 days — a sidereal year
• 366 days — a leap year in many solar calendars; 31.62 million seconds
• 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.

The 400-year cycle of the Gregorian calendar has 146097 days and hence exactly 20871 weeks.

See also Numerical facts about the Gregorian calendar.

6 See also

• 1 E7 s

Units of time

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