On the perturbations of the five outer planets by the four inner ones

Abstract

The expressions given by Clemence were checked by the comparison of numerical values of their second differentials with the numerical values of the perturbing forces. Agreement was good in most cases, save that the use of the second differentials unduly magnified some terms rightly neglected by Clemence. In the appendix the work of Clemence is compared with that of Carpenter and the differences are found to be all smaller than the contributions from the secular variation of the eccentricity, which are so small that they were neglected by Clemence. The differences can be removed by considering the secular variation of the eccentricity and by making a small adjustment in the integration constants.