Abstract
In this work, we have revealed a new model emerged from the restricted three-body problem within a framework of a non-isotropic variation of mass. This variation is taken when the escaping or incoming mass occurs from $$n$$ points of an infinitesimal body. The collinear, triangular and out-of-plane equilibrium points are determined in the cases of $$n = 1$$ and $$n \ne 1$$ , as well as graphical investigations are shown when $$n = 1$$ . We demonstrate that this model can be applied to explore small objects such as cosmic dust or grains. It also has interesting applications for future space colonization and the parking of vehicles and spacecraft. Moreover, it can be used to study the dynamics of Earth–Moon rocket system.