next up previous
Next: Regression of lunar ascending Up: Lunar motion Previous: Summary of results

Precession of lunar perigee

According to Equations (11.206) and (11.284), the mean ecliptic longitude of the lunar perigee evolves in time as

$\displaystyle \alpha = \alpha_0 + \alpha'\,n'\,t,$ (11.337)

where

$\displaystyle \alpha' =c\,m= \frac{3}{4}\,m+ \frac{225}{32}\,m^{\,2} + {\cal O}(m^{\,3}).$ (11.338)

Equation (11.337) implies that the perigee precesses (i.e., its longitude increases in time) at the mean rate of $ 360\,\alpha'$ degrees per year. (Of course, a year corresponds to $ {\mit\Delta} t=2\pi/n'$ .) Furthermore, it is clear that this precession is entirely due to the perturbing influence of the Sun, because it depends only on the parameter $ m$ , which is a measure of this influence. Given that $ m=0.07480$ , we find that the perigee advances by $ 34.36^\circ$ degrees per year. Hence, we predict that the perigee completes a full circuit about the Earth every $ 1/\alpha' = 10.5$ years. In fact, the lunar perigee completes a full circuit every $ 8.85$ years. Our prediction is somewhat inaccurate because our previous analysis neglected $ {\cal O}(m^{\,2})$ , and smaller, contributions to the parameter $ c$ [see Equation (11.284)], and these turn out to be significant. (See Section 11.17.)


next up previous
Next: Regression of lunar ascending Up: Lunar motion Previous: Summary of results
Richard Fitzpatrick 2016-03-31