ANOMALY (from Gr. lwvw)

This article appears in Volume V02, Page 80 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: ANC-APO

ANOMALY (from Gr. lwvw) .iaXta, unevenness, derived from dv- privative, and i aXos, even), a deviation from the common

rule

RULE

. In astronomy the word denotes the angular distance of a

body

BODY

from the pericentre of the orbit in which it is moving. Let AB be the major

axis

AXIS (Lat. for " axle ")

of the orbit, B the pericentre, F the

focus

FOCUS (Latin for " hearth " or " fireplace ")

or centre of motion, P the position of the

body

BODY

. The anomaly is then the

angle

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

BFP which the radius vector makes with the major

axis

AXIS (Lat. for " axle ")

. This is the actual or true anomaly. Mean
R 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

PLANET (Gr. ssXavirrns, a wanderer)

, upon the major axis. Join CR; the

angle

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

CRQ is then the eccentric anomaly,
In the ancient astronomy the anomaly was taken as the angular distance of the

planet

PLANET (Gr. ssXavirrns, a wanderer)

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 equivalentgiven the mean anomalyto 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 thepericentre. 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

HOURS, CANONICAL

, 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

WORK

of Watson or of Bauschinger on Theoretical Astronomy.

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