LUNAR THEORY. A theory dealing with the disturbances, in the moon's orbit produced by the other heavenly bodies which attract the moon. (If these, the sun is the only one that affects the moon directly. The planets also act upon the moon, hut their mass is too small and their dis tances too great to produce any sensible effect. They do, however. disturb the earth in her orbit. and so in an indireet way affect the moon. The fact that the earth is not a perfect sphere pro duces also a few disturbances.
The lunar theory is the most ditlieult part of mathematical astronomy. and is still inemnplete, involving as it does the 'Problem of the Three Bodies' (q.v.). The three bodies are the moon. the earth. and the sun. The stm's mass is 330, 000 times that of the earth. and its distance 389 times that of the moon from the earth. Since the attraction of one body on another varies di rectly as the mass and inversely as the square of the distance, the suet's attraction on the moon 3300fIn equals = 2.1S times that of the earth.
Thus the sun's attraction is more than twice as great as that of the earth. and if both were fixed in space the sun would naturally pull tl moon away from the earth. since this is Dot the case and the sun attracts the earth almost as much as it does the moon. the result is that both fall toward it, combining this motion with that in the orbit.
At. new moon the moon is nearer the :sun than at any other place in the orbit. and the -qi': at traction is then the greatest. Therefore. at new moon the curvature of the moon's orbit toward the earth is diminished. while at pindrature (q.v.) it is increased. It is convenient to the disturbing force of the sun into three oompo nents, the radial, tangential, and nrthoqmpal. The effect of the radial component is to draw the moon toward or away from the earth. This force is a maximum at svzvgies and quadra hire, and vanishes whenever the disturbing force becomes perpendicular to the radius, which rippens at 54° 44' on each side of line of syzy gies. It is negative more than half-way round. The effect of this is to lessen the earth's at traction for the moon by nearly 1/360 and to increase its mean distance. This makes the mouth about an hour longer than it would be otherwise.
The diminution of the earth's attraction for the moon at apogee (q.v.) and the reverse of this at perigee (q.v.) causes an oscillation of the line of apsides (q.v,). The disturbing force at apo gee, however. predominates, and the line of apsides completes a revolution in about nine years.
The tangential component retards and accel erates the motion of the moon. This is the main cause of an inequality, called the variation. Its maximum amount is 39' 30", and this is attained half-way between the syzygies and quadrature. The orthogonal component tends to draw the moon toward the ecliptic. This causes the in equality known as the regression of the nodes (q.v.), which complete a revolution in about nine years. This force vanishes twice a year when the sun is at the nodes of the moon's orbit, since then they are both in the same plane.
Evection is another disturbance which puts the moon forward or backward in the orbit about 11/4°. It has a period of about Pk years, the time required by the sun to pass from the line of apsides to the same line again. The cause of this inequality is the increase and decrease of the eccentricity in the moon's orbit, caused by the in crease and decrease in the earth's attraction on the moon.
The annual equation is an inequality produced by an increase in the sun's disturbing force. when the earth is nearer to the sun than its mean dis tance. As a result of this the month is length ened or shortened, depending upon whether the increased disturbing force aids or retards the motion of the moon.
The secular acceleration of the moon's mean motion was discovered by Halley by comparing aneient and modern eclipses, and the moon is be lieved to have gained in this way one degree dur ingtheChristian Era. La place ( q.v.) explained this secular acceleration by the fact that the earth's orbit, under the action of other planets. is grow ing less eccentric. Asa result of this the aver age disturbing force of the sun is diminished, and the month is shortened little by little. The pe riod of this inequality is 25,000 years.
Of these irregularities, eveetion is the only one which was known to the ancients. It may affect the time of an eclipse by nearly six hours, and was discovered by Ilipparcln; (ax. 150) while observing an eclipse. The variation was discov ered by Tycho Brahe. This does not affect the time of an eclipse, and therefore escaped the Greek astronomers. The inequalities mentioned above are only the principal ones. In the com putation of nautical almanacs, about 70 are taken into consideration for determination of longitude, and half that number for latitude. See MOON. Consult Chauvenet. S'pherical and Practi cal Astronomy (Philadelphia, IS63).