A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky – as viewed from the Earth or another celestial body of the Solar System – thus completing a full cycle of astronomical seasons.
Another type is the sidereal year (or sidereal orbital period), which is the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars, resulting in a duration of 20 minutes longer than the tropical year, because of the precession of the equinoxes.
The entry for "year, tropical" in the Astronomical Almanac Online Glossary states:[1] the period of time for the ecliptic longitude of the Sun to increase 360 degrees.
Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar.
Whenever the longitude reaches a multiple of 360 degrees the mean Sun crosses the vernal equinox and a new tropical year begins".
[6] Hipparchus also discovered that the equinoctial points moved along the ecliptic (plane of the Earth's orbit, or what Hipparchus would have thought of as the plane of the Sun's orbit about the Earth) in a direction opposite that of the movement of the Sun, a phenomenon that came to be named "precession of the equinoxes".
[6] During the Middle Ages and Renaissance a number of progressively better tables were published that allowed computation of the positions of the Sun, Moon and planets relative to the fixed stars.
The Alfonsine Tables, published in 1252, were based on the theories of Ptolemy and were revised and updated after the original publication.
Erasmus Reinhold used Copernicus' theory to compute the Prutenic Tables in 1551, and gave a tropical year length of 365 solar days, 5 hours, 55 minutes, 58 seconds (365.24720 days), based on the length of a sidereal year and the presumed rate of precession.
[7] Newton's three laws of dynamics and theory of gravity were published in his Philosophiæ Naturalis Principia Mathematica in 1687.
Newton's theoretical and mathematical advances influenced tables by Edmond Halley published in 1693 and 1749[10] and provided the underpinnings of all solar system models until Albert Einstein's theory of General relativity in the 20th century.
The necessary theories and mathematical tools came together in the 18th century due to the work of Pierre-Simon de Laplace, Joseph Louis Lagrange, and other specialists in celestial mechanics.
Newcomb's tables were sufficiently accurate that they were used by the joint American-British Astronomical Almanac for the Sun, Mercury, Venus, and Mars through 1983.
Many new observing instruments became available, including The complexity of the model used for the Solar System must be limited to the available computation facilities.
[17] A key development in understanding the tropical year over long periods of time is the discovery that the rate of rotation of the earth, or equivalently, the length of the mean solar day, is not constant.
Mean solar time is corrected for the periodic variations in the apparent velocity of the Sun as the Earth revolves in its orbit.
However the rotation of the Earth itself is irregular and is slowing down, with respect to more stable time indicators: specifically, the motion of planets, and atomic clocks.
[22][23][24] As a consequence, the tropical year following the seasons on Earth as counted in solar days of UT is increasingly out of sync with expressions for equinoxes in ephemerides in TT.
The table below gives Morrison and Stephenson's estimates and standard errors (σ) for ΔT at dates significant in the process of developing the Gregorian calendar.
[25] The low-precision extrapolations are computed with an expression provided by Morrison and Stephenson:[25] where t is measured in Julian centuries from 1820.
The extrapolation is provided only to show ΔT is not negligible when evaluating the calendar for long periods;[27] Borkowski cautions that "many researchers have attempted to fit a parabola to the measured ΔT values in order to determine the magnitude of the deceleration of the Earth's rotation.
If the starting point is close to the perihelion (such as the December solstice), then the speed is higher than average, and the apparent Sun saves little time for not having to cover a full circle: the "tropical year" is comparatively long.
If the starting point is near aphelion, then the speed is lower and the time saved for not having to run the same small arc that the equinox has precessed is longer: that tropical year is comparatively short.
[11] These are smoothed values which take account of the Earth's orbit being elliptical, using well-known procedures (including solving Kepler's equation).
[31] Modern astronomers define the tropical year as time for the Sun's mean longitude to increase by 360°.
It is the number of solar days in a tropical year that is important for keeping the calendar in synch with the seasons (see below).