The quasi elliptical motion of the moon

Among the many perturbing effects exerted by the Sun on what would otherwise be the

Kepler’s ellipse of the Moon around the Earth, it is possible to set apart a particular class

of terms of periodic and secular nature related to the size of the eccentricity and to the

location of the perigee. These matters can be jointly treated by studying the behavior of a

single mathematical entity, the eccentricity vector, a complex number that in polar form has

the eccentricity as magnitude and the angle marking the position of perigee as argument.

The comparison between the theoretical behavior of this vector and the observations has

historically represented an important test of the inverse-square law of gravitation.