1911 Encyclopædia Britannica/Ecliptic

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ECLIPTIC, in astronomy. The plane of the ecliptic is that plane in or near which the centre of gravity of the earth and moon revolves round the sun. The ecliptic itself is the great circle in which this plane meets the celestial sphere. It is also defined, but not with absolute rigour, as the apparent path described by the sun around the celestial sphere as the earth performs its annual revolution. Owing to the action of the moon on the earth, as it performs its monthly revolution in an orbit slightly inclined to the ecliptic, the centre of the earth itself deviates from the plane of the ecliptic in a period equal to that of the nodal revolution of the moon. The deviation is extremely slight, its maximum amount ranging between 0.5′ and 0.6″. Owing to the action of the planets, especially Venus and Jupiter, on the earth, the centre of gravity of the earth and moon deviates by a yet minuter amount, generally one or two tenths of a second, from the plane of the ecliptic proper. Owing to the action of the planets, the position of the ecliptic is subject to a slow secular variation amounting, during our time, to nearly 47″ per century. The rate of this motion is slowly diminishing.

The obliquity of the ecliptic is the angle which its plane makes with that of the equator. Its mean value is now about 23° 27′. The motion of the ecliptic produces a secular variation in the obliquity which is now diminishing by an amount nearly equal to the entire motion of the ecliptic itself. The laws of motion of the ecliptic and equator are stated in the article Precession of the Equinoxes.

Attempts have been made by Laplace and his successors to fix certain limits within which the obliquity of the ecliptic shall always be confined. The results thus derived are, however, based on imperfect formulae. When the problem is considered in a rigorous form, it is found that no absolute limits can be set. It can, however, be shown that the obliquity cannot vary more than two or three degrees within a million of years of our epoch.

The formula for the obliquity of the ecliptic, as derived from the laws of motion of it and of the equator, may be developed in a series proceeding according to the ascending powers of the time as follows: we put T, the time from 1900, reckoned in solar centuries as a unit. Then,

Obliquity=23° 27′ 31.68″ − 46.837″ T − 0.0085″ T² + 0.0017″ T³.

From this expression is derived the value of the obliquity at various epochs given in the following table. The left-hand portion of this table gives the values for intervals of 500 years from 2000 B.C. to A.D. 2500 as computed from modern data. For dates more than three or four centuries before or after 1850 the result is necessarily uncertain by one or more tenths of a minute, and is therefore only given to 0.1′.

B.C. 2000; obl. = 23° 55.5″    A.D. 1700; obl. = 23° 28′ 41.91″
1500 = 23 52.3 1750 = 23 28 18.51
1000 = 23 48.9 1800 = 23 27 55.10
 500 = 23 45.4 1850 = 23 27 31.68
  0 = 23 41.7 1900 = 23 27  8.26
A.D.  500 = 23 38.0 1950 = 23 26 44.84
1000 = 23 34.1 2000 = 23 26 21.41
1500 = 23 30.3 2050 = 23 25 57.99
2000 = 23 26.4 2100 = 23 25 34.56
2500 = 23 22.5          
(S. N.)