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Regression of lunar ascending node

According to Equations (11.207) and (11.314), the mean ecliptic longitude of the lunar ascending node evolves in time as

$\displaystyle \gamma = \gamma_0 - \gamma'\,n'\,t,$ (11.339)


$\displaystyle \gamma' = g\,m = \frac{3}{4}\,m - \frac{9}{32}\,m^{\,2} + {\cal O}(m^{\,3}).$ (11.340)

Equation (11.339) implies that the ascending node regresses (i.e., its longitude decreases in time) at the mean rate of $ 360\,\gamma'$ degrees per year. As before, it is clear that this regression is entirely due to the perturbing influence of the Sun. Moreover, we find that the ascending node retreats by $ 19.63^\circ$ degrees per year. Hence, we predict that the ascending node completes a full circuit about the Earth every $ 1/\gamma'=18.3$ years. In fact, the lunar ascending node completes a full circuit every $ 18.6$ years, so our prediction is fairly accurate.

Richard Fitzpatrick 2016-03-31