The second integral of the restricted problem in regularized elements

A perturbation series integral for the restricted problem of three bodies is derived by use of a new set of canonical elements for the regularized two-body problem. These elements are similar to theKS elements of Stiefel and Scheifele, but they contain small parameters other than the semimajor axis. The variable analogous to the longitude of perihelion not only remains well defined as the orbit approaches a circle, but also it can be used as a second small parameter. Regularized elements permit canonical use of the eccentric anomaly as independent variable, but most of the major benefits of regularization in the two-body problem do not carry over to perturbation theory.