1911 Encyclopædia Britannica/Anomaly

ANOMALY (from ἀνωμαλία, unevenness, derived from ἀν-, privative, and ὁμαλός, even), a deviation from the common rule. In astronomy the word denotes the angular distance of a body from the pericentre of the orbit in which it is moving. Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body. The anomaly is then the angle BFP which the radius vector makes with the major axis. This is the actual or true anomaly. Mean anomaly is the anomaly which the body would have if it moved from the pericentre around F with a uniform angular motion such that its revolution would be completed in its actual time (see Orbit). Eccentric anomaly is defined thus:—Draw the circumscribing circle of the elliptic orbit around the centre C of the orbit. Drop the perpendicular RPQ through P, the position of the planet, upon the major axis. Join CR; the angle CRQ is then the eccentric anomaly.

In the ancient astronomy the anomaly was taken as the angular distance of the planet from the point of the farthest recession from the earth.

Kepler’s Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent—given the mean anomaly—to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.

The anomalistic revolution of a planet or other heavenly body is the revolution between two consecutive passages through the pericentre. Starting from the pericentre, it is completed on the return to the pericentre. If the pericentre is fixed, this is an actual revolution; but if it moves the anomalistic revolution is greater or less than a complete circumference.

An Anomalistic year is the time (365 days, 6 hours, 13 minutes, 48 seconds) in which the earth (and similarly for any other planet) passes from perihelion to perihelion, or from any given value of the anomaly to the same again. Owing to the precession of the equinoxes it is longer than a tropical or sidereal year by 25 minutes and 2.3 seconds. An Anomalistic month is the time in which the moon passes from perigee to perigee, &c.

For the mathematics of Kepler’s problem see E. W. Brown, Lunar Theory (Cambridge 1896), or the work of Watson or of Bauschinger on Theoretical Astronomy.