Wrong hypotheses in the generalized RTBP

Abstract

Generalized restricted three body problems consist of adding some extra hypotheses to the Restricted three body problem (RTBP) in order to have a new problem, not very different of the original RTBP. However, not any additional hypothesis is allowed; it must satisfy the laws of Physics. Among the several generalizations found in literature, we prove that at least there are two hypotheses that cannot be used, namely: 1) Perturbation in Coriolis and/or centrifugal forces, and 2) primaries are spheroids moving on elliptical orbits.

Combined effect of Poynting-Robertson (P-R) drag, oblateness and radiation on the triangular points in the elliptic restricted three-body problem

“…In a recent paper, Elipe 40 has stated that the assumption of the primaries being oblate spheroids is only applicable to the circular restricted three-body problem (CR3BP). In the context of the present paper, it is worth to note that the elliptic restricted three-body problem (ER3BP) in which the eccentric anomaly is considered as an independent variable (instead of the true anomaly), can be dynamically treated as the circular restricted three-body problem (CR3BP).…”