ANOMALY, in Astronomy, is the Distance of a Planet from the Aphelion or Apogee; or an irregularity in the Motion of a Planet, whereby it deviates from the Aphelion or Apogee. See PLANET, APHELION, and APOGEE.
Kepler distinguishes three kinds of Anomalies; Mean, Eccentric and True. Mean or Simple ANOMALY in the ancient Astronomy, is the Distance of a Planet’s mean place from the Apogee. See PLACE.
In the modern Astronomy, it is the Time wherein the Planet moves from its Aphelion A, to the mean Place or Point of its Orbit I. (Tab. ASTRONOMY, fig. 1.) Hence, as the Arch, or the Angle, or the Elliptic Area A Si, is proportional to the Time wherein the Planet describes the Arch AI; that Area may represent the mean Anomaly. Or thus: The Area SK A found by drawing through the Planet’s place, perpendicular to the Line of the Apsides PA, till it cuts the Circle DA, and drawing the Line SK, may represent the mean Anomaly; for this Area is everywhere proportional to the former Area SLA, as is demonstrated by Dr. Gregory, Lib. 3. Gen. Astron. Physic. Math.
Anomaly of the Eccentric, or of the Centre, in the new Astronomy, is an Arch of the Eccentric Circle AK, fig. 1. included between the Aphelion A, and a right Line KL drawn through the Centre of the Planet K, perpendicularly to the Line of the Apsides AP. See ECCENTRIC.
In the ancient Astronomy, it is an Arch of the Zodiac, terminated by the Line of the Apsides, and the Line of the mean Motion of the Centre. True or Equated ANOMALY, is the Angle at the Sun, ASI, which a Planet’s distance from the Aphelium, AJ, appears under; or it is the Angle or Area, taken proportional to the time in which the Planet moves from the mean Place I, to its Aphelion A.
And hence, in the Sun’s Motion, it will be the distance of his true place, from the Apogee. The true Anomaly being given, the mean one is easily found; but it is difficult to find the true Anomaly from the mean one given.
The Geometrical Method of Wallis and Newton, by the protracted Cycloid, are not fit for Calculation; nor yet the Methods of Series, as being too laborious. Hence Astronomers are forced to have recourse to Approximation. Ward, in his "Astronomia Geometrica" takes the Angle ASI, at the Focus where the Sun is not, for the mean Anomaly; which will nearly represent it, if the Orbit of the Planet be not very Eccentric; and thus easily solves the Problem. But this Method does not hold of the Orbit of Mars, as being more Eccentric than those of the other Planets. Sir Isaac Newton shows how to effect even this; and when his Correction is made, and the Problem solved, according to Ward's Hypothesis, Sir Isaac affirms that even in the Orbit of Mars, there will scarce ever be an Error of above a Second.
