The Years

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We define the year as the time that elapses as Earth makes one full revolution on its orbit. But what do we mean by "one full revolution on its orbit"? "One full revolution" relative to what? The possible answers to those questions give us different lengths for the year.

By convention we measure the year in days, but there, too, we have more than one possibility. We can use either sidereal days or solar days.

We describe the sidereal day thusly: extend a straight line from some point on Earth's axis, through a fixed point on Earth's surface, and toward a suitably distant star or quasar. The time elapsed between an instant when that line points to the star or quasar and the next instant when the line points to the same star or quasar constitutes one sidereal day. The sidereal day (as of AD2000 Jan 01 PM 12:00 (noon)) spans 23.934469583 hours (23 hours, 56 minutes, 4.0905 seconds).

To describe the solar day we imagine constructing a flat plane through one fixed meridian on Earth's surface (Earth's axis also lies entirely in that plane). We designate the instant when one point of that plane appears to pass through the sun's center as local noon for observers on the chosen meridian. One solar day, then, comprises the time that elapses between two successive occurrences of local noon on the same meridian.

Because Earth follows an elliptical orbit, the solar day does not have the same length at different times of the year. When Earth comes to perihelion the sun appears to move across the background of the starry sky faster than it does when Earth comes to aphelion, so the solar day near perihelion takes longer to complete than does a solar day occurring near aphelion. However, astronomers define a mean solar day by way of the statement that the actual (or measured) solar day equals the mean solar day plus or minus an increment/decrement calculated from the Equation of Time.

The mean solar day spans exactly 24 hours of 3600 ephemeris seconds each. By definition, the ephemeris second spans 9,192,631,770 oscillations of the radiation emitted by the transition of electrons between two hyperfine levels of the ground state of Cesium-133. In what follows I use the word day to refer to a mean solar day.

The Sidereal Year

Imagine drawing a straight line from the center of the sun to a distant star or quasar in such a way that it crosses Earth's orbit. Using that frame tied to the rest of the Universe, we define the sidereal year as the time that elapses between one instant when Earth's center crosses that line and the next instant when Earth's center crosses the line. The sidereal year thus spans

365.256363051 days

365 days, 6 hours, 9 minutes, 9 seconds.

The Tropical Year

Named for the turning lines (from the Greek word tropos) that the sun's apparent path among the stars traces on the sky, the celestial projections of the Tropic of Cancer and the Tropic of Capricorn, the tropical year spans an interval defined by the points where the plane of Earth's equator crosses the plane of Earth's orbit. The sun's passage, as seen from Earth, through the two points on the sky where the plane of Earth's equator crosses the plane of Earth's orbit (the Ecliptic Plane) correspond to the equinoxes and we usually think of a tropical year as the amount of time that elapses between two successive vernal equinoxes. However, any point on Earth's orbit a fixed longitude east or west of the point of the vernal equinox can serve as a defining point for a tropical year. All of those possible tropical years differ ever so slightly from each other, so astronomers use the mean tropical year. Because the precession of Earth's axis makes the vernal equinox drift slowly westward, the mean tropical year spans less time than does the sidereal year, that time spanning

365.24218967 days

365 days, 5 hours, 48 minutes, 45 seconds

The Gregorian Year

The calendar year, consisting of 365 days into which we so insert leap days at the end of February that March 21 falls on or as near as we can make it to the vernal equinox. That formula necessitates that we insert a leap day into every year evenly divisible by four except for century years not evenly divisible by four hundred. The average length of a Gregorian year then works out to

365.2425 days

365 days, 5 hours, 49 minutes, 12 seconds

That exceeds the length of the mean tropical year by 27 seconds, which means the calendar year loses one day over the vernal equinox every 3225.463 years. If we skip a leap day every 3225 years, then we won't need to make the next order correction of one full day for another 22,470,000 years.

The Anomalistic Year

Defined as the time elapsed between two successive passages of Earth through one of its orbit's apsides (either perihelion or aphelion), the anomalistic year spans a time slightly longer than a sidereal year. Earth's gravitational interaction with the other planets and with the slightly non-spherical distribution of the sun's mass along with effects of General Relativity make Earth's orbit precess slowly in the prograde direction and that precession makes the apsides shift eastward relative to a frame anchored to any three non-collinear quasars. Thus the anomalistic year spans

365.259635864 days

365 days, 6 hours, 13 minutes, 52 seconds.

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