The Main Problem

If no other bodies were present, the moon's orbit around the earth would be simple and easily predicted from Kepler's laws. But, as we well know, the sun and other planets are present and they exert their influences on the moon's motion.

The moon moves in an elliptic orbit inclined at about 5° to the plane of eclipic. There are two major effects on the orbit due to the sun's gravitational pull :

a) Rotation of the line of apses (line joining perigee to apogee) on the lunar orbital plane.

b) Rotation of the line of nodes (nodal regression).

The variation in the eccentricity of the orbit of the moon caused by the sun's gravitational pull is called evection. The wabble caused by this effect results in a displacement of the moon from its true position by as much as 76 minutes of arc in a period of 31.8 days.

The moon's orbit being elliptical also means that the moon's speed is greater at perigee than at apogee so that in each revolution the moon will alternately be ahead of or behind the position if its velocity were constant. This irregularity can be quantified by the mean anomaly (the angle between the perigee, the earth and a fictitious moon having the same period as the real moon but travelling with a constant velocity), the true anomaly (the angle between the perigee, the earth and the moon measured in the direction of the moon's motion) and the equation of the centre (the difference between the true and the mean anomaly). The deviation has a miximun value of 6° in both direction in a period equal to the moon's revolution.

Another factor complicating the prediction of the moon's position is that the angle which the moon's orbital plane makes with the ecliptic, i , is not fixed. The irregularity in inclination has an amplitude of 9 minutes of arc and a period of half nodical year. i varies between 5° 18' and 4° 58' .