<p>This study proposes an alternative analytical criterion for defining regions of influence around a planet by introducing a new approach. For the circular restricted three-body problem, the approach yields a family of three-dimensional configurations around the planet, named planetary regions of influence; they help to predict the acceptable transition to the two-body problem by utilizing a tolerance-adjustable parameter and other additional constraints, which are obtained analytically. In this study, by employing the non-dimensional governing equations of the circular restricted three-body problem, the first time derivative of the particle’s specific angular momentum relative to the planet is obtained as a spatial vector field; thus, its magnitude yields a spatial scalar field around the planet, named the non-Keplerian scalar filed; by confining it to a prescribed tolerance, the equations of the geometrical boundaries of the corresponding region of influence around the planet are obtained, which are the level surfaces of the non-Keplerian scalar field for small tolerance values; whereas, its gradient vector field introduces the directions that can be employed to intensively approach/depart the planar motion around the planet. Moreover, a new particle parameter P is introduced; while by confining the changes of other particle parameters to the prescribed tolerance, additional constraints are obtained to employ the two-body approximation for the particle’s trajectory inside the region of influence. This study presents a new analytical framework that provides general insights to help the interplanetary mission design and the particle’s trajectory propagation in the planetary close encounter analysis.</p>