Generalizing the Bicircular Restricted Four-Body Problem

The bicircular restricted four-body problem (BCR4BP) consists of assuming an infinitesimal mass body under the gravitational influence of other three bodies. A study is conducted to apply a straightforward four-body problem to study asteroid deflections under Jupiter’s influence. Researchers propose a different formulation for the BCR4BP to cope with the limitations faced by the usual BCR4BP applied to other systems than the Earth–moon–sun. They assume that they can neglect the gravitational interaction between the smaller primary and the third body. Although this enable us to approximate the orbit of the third body as circular around the larger primary, which is physically more reasonable, it comes at the expense of neglecting indirect effects of the smaller primary. This leads researchers to find a way to cope with these indirect effects and deriving a more general BCR4BP that reduces to the usual BCR4BP when applied to a binary system of primaries.