(11.97) | ||||||

and | (11.98) |

respectively. (Actually, our ``geocentric'' ecliptic longitude of the Sun is measured with respect to the Earth-Moon barycenter.) Here, for the sake of simplicity, and also for the sake of consistency with our previous analysis, we have assumed that both objects are located at ecliptic longitude zero at time .

The following definitions are useful. The *lunar mean anomaly*,

is defined as the angular distance (in geocentric ecliptic longitude) between the mean moon and the lunar perigee. Here, is the

(11.100) |

is defined as the angular distance (in geocentric ecliptic longitude) between the mean moon and the lunar ascending node. Here, is the

(11.101) |

is defined as the difference between the geocentric ecliptic longitudes of the mean moon and the mean sun. Finally, the

is defined as the angular distance (in geocentric ecliptic longitude) between the mean Sun and the solar perigee. Here, for the sake of simplicity, and also for the sake of consistency with our previous analysis, we have assumed that the solar perigee lies at ecliptic longitude zero. Note that we are neglecting the precession of the solar perigee (which is really the precession of the Earth-Moon barycenter's perihelion), because such precession takes place on a far longer timescale than any characteristic timescale of the lunar motion. (See Sections 5.4 and 10.3.)

Finally, it is convenient to define

Thus, is the difference between the radial distance of the Moon from the Earth and that of the mean moon from the Earth, is the difference between the geocentric ecliptic longitudes of the Moon and the mean moon, and is the difference between the geocentric ecliptic latitudes of the Moon and the mean moon.