Introduction

Let $\lambda_S$ and $\lambda_M$ represent the ecliptic longitudes of the sun and the moon, respectively. The lunar-solar elongation is defined

$$D = \lambda_M - \lambda_S.$$ (132)

Since the moon is only visible because of light reflected from the sun, there is a fairly obvious relationship between lunar-solar elongation and lunar phase--see Fig. 26. For instance, a new moon corresponds to $D = 0^\circ$, a quarter moon to $D = 90^\circ$ or $270^\circ$, and a full moon to $D = 180^\circ$. New moons and full moons are collectively known as lunar-solar syzygies.

Figure 26: The phases of the moon.