Historical note

takes the form of a power series in . Despite the fact that, for the case of the Moon, takes the relatively small value , this series only converges very slowly to the value (Cook 1988), which corresponds to a precession period (for a full circuit) of the Moon's perigee of years. This estimate lies within 1 percent of the observed precession period [i.e., 8.848 years (Yoder 1995)]. The residual disagreement between theory and observations is largely due to the neglect of small terms involving , , , and in the previous expression (Delaunay 1867). The complete expression for (Delaunay 1867),

also takes the form of a power series in . Fortunately, for the case of the Moon, this series converges relatively quickly to the value (Cook 1988), which corresponds to a regression period (for a full circuit) of the Moon's ascending node of years. This estimate lies within half a percent of the observed regression period [i.e., 18.615 years (Yoder 1995)]. Again, the residual disagreement between theory and observations is largely due to the neglect of small terms involving , , , and in the previous expression (Delaunay 1867). The much faster convergence of series (11.342) compared to series (11.341) accounts for the fact that our prediction for the regression period of the lunar ascending node is considerably more accurate than that for the precession period of the perigee.