What is a "Year" (on Earth or Mars)?

Copyright © 2001 by Michael Allison
Goddard Institute for Space Studies
pcmda@giss.nasa.gov

A "year" refers to a planet’s period of orbital revolution. But the precise reckoning of this period depends upon the specifically adopted reference for the average interval between the beginning and end of an orbit. The anomalistic year refers to the repetition of the planet’s "mean anomaly" and corresponds to the mean interval between successive passages of its perihelion or closest approach to the Sun. The sidereal year refers to the planet’s mean orbital period as referenced with respect to the stars. The tropical year, often but imprecisely described as the mean interval between successive passages of the vernal equinox, is defined by astronomers as the slightly different interval during which the Sun’s mean longitude, referred to the mean equinox of date, increases by 360°. (The tropical year is shortened with respect to the sidereal year by the longitudinal precession of the planet’s pole vector, and can be estimated as the average of the four mean intervals for the repetition of each of the equinox and solstice seasons.) All these measures of the orbital year also change slowly with time.

Although the mean Gregorian calendar year of 365.2425 days is closely matched to the Earth’s current "vernal equinox year" of 365.2424 d, astronomers still use the Julian Century of 36525 Earth solar days or 100 Julian Years as a fundamental unit for emphemeris work. This definition has the advantage of a short and exact decimal representation for conversion to or from the Julian Date, and serves the specification of standard astronomical epochs. The current J2000 epoch is defined as JD 2451545.0 (2000 Jan 1.5), for example, exactly 36525 days after J1900 = JD 2415020.0 (1900 Jan 0.5).

Numerical values for the various measures of a "year" on both Earth and Mars are given in the accompanying table. Julian Year values provide common units for comparison, but are also converted to the equivalent solar days specific to each planet (as a "sol" on Mars). The evaluated "accuracy" of a Martian calendar will depend upon the type of year chosen for its intended intercalation and must necessarily confront a much larger difference among the mean seasonal intervals than for the Earth. Given the indicated five-thousandth sol difference between the Mars Vernal Equinox and Winter Solstice years, for example, a perfect intercalary match to one would produce a one-sol displacement for the date of the other over two hundred orbits.

Measured Year

Earth

Mars

Anomalistic (perihelion-to-perihelion)

1.0000264 Jy = 365.2596 d

1.8808917 Jy = 668.6146 sol

Sidereal (fixed star-to-fixed star)

1.0000174 Jy = 365.2564 d

1.8808481 Jy = 668.5991 sol

Vernal Eqnx (repetition of Ls=0°)

0.9999791 Jy = 365.2424 d

1.8808269 Jy = 668.5907 sol

Summ Solst (repetition of Ls= 90°)

0.9999771 Jy = 365.2416 d

1.8808168 Jy = 668.5880 sol

Autum Eqnx (repetition of Ls=180°)

0.9999781 Jy = 365.2420 d

1.8808336 Jy = 668.5940 sol

Winter Solst (repetition of Ls=270°)

0.9999800 Jy = 365.2427 d

1.8808387 Jy = 668.5958 sol

Tropical (repetition of mean solar lon)

0.9999786 Jy = 365.2422 d

1.8808284 Jy = 668.5921 sol

Units: 1 Jy = 1 Julian Year = 365.25 d ; 1 d = 1 Earth solar day = 86400 SI sec; 1 Sol= 1 Mars solar day =1.02749125 d

References

Allison, M. and M. McEwen, 2000. A post-Pathfinder evaluation of areocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies. Planet. Space Sci. 48, 215-235.

Explanatory Supplement to the Astronomical Almanac (P.K. Seidelmann, Ed.) 1992. University Science Books, Mill Valley.

Meeus, J. 1991. Astronomical Algorithms. Willmann-Bell, Richmond.

Steel, D., 2000. Marking Time: The Epic Quest to Invent the Perfect Calendar. John Wiley & Sons, New York.