A study of the effects of the forces in the ballistic capture by the major primary

The objective of the present paper is to study the ballistic gravitational capture performed by the first primary in a system formed by three bodies: a large central mass, the primary, a second small body that is in orbit of the primary, the secondary, and a massless particle that is moving around the two primaries. The forces involved in this system are explained and analytical equations for their effects are derived, based on the integral of their effects with respect to time from the entrance of the massless body in the sphere of influence of the primary until the periapsis of its trajectory. Then, closed form approximate equations are obtained to estimate the magnitude of its effects and to show the best directions of approach for the maneuver.