A Contribution to the Study of the Moon’s Physical Libration in Longitude

Abstract

The equation of the physical libration in longitude, as is only too well known, can be treated independently of the first two equations and, in particular, be placed in the form

$$\ddot \tau + A(g,g',\omega ,\omega ')\tau = B(g,g',\omega ,\omega ')$$

((1))

where g is the mean anomaly of the Moon, g’ the mean anomaly of the Sun, ω the distance of the Moon’s perigee from the ascending node of its orbit and, ω’ the distance of the Sun’s perigee from the ascending node of the orbit of the Moon. The functions A and B depend only on the time implicitly and can be expanded in a Fourier series in terms of multiples of four different frequencies. This equation is true if τ is small and this is the case for the Moon.