where per day and are the mean angular velocity and major radius, respectively, of the terrestrial orbit about the Sun. Here, . On the other hand, the Moon's equation of motion takes the form

where per day and are the mean angular velocity and major radius, respectively, of the lunar orbit about the Earth. Note that we have retained the perturbing influence (

Let

be the position vectors of the Moon and Sun, respectively, relative to the Earth. It follows, from Equations (1119)-(1122), that in a non-inertial reference frame, (say), in which the Earth is at rest at the origin, but the coordinate axes point in

respectively.

Let us set up a conventional Cartesian coordinate system in
which is such that the (apparent) orbit of the
Sun about the Earth lies in the - plane. This implies that the
- plane corresponds to the so-called *ecliptic plane*. Accordingly, in , the Sun
appears to orbit the Earth at the mean angular velocity
(assuming that the -axis points
toward the so-called north ecliptic pole), whereas the
projection of the Moon onto the ecliptic plane orbits the Earth at the mean angular velocity
.

In the following, for the sake of simplicity, we shall neglect the small eccentricity,
, of the Sun's apparent orbit about the
Earth (which is actually the eccentricity of the Earth's orbit about the Sun), and approximate the solar orbit as a *circle*, centered on the Earth. Thus, if , , are the Cartesian coordinates of the Sun in then
an appropriate solution of the solar equation of motion, (1124), is