A proper choice of variables for the study of a satelliteʹs close approaches in a ring assembly of N massive bodies

Close approaches occur very often in celestial mechanics, giving rise to troubles in the integration process of the equations of motion. To encounter the so-appearing difficulties in the restricted ring problem of N+1 bodies, we propose new dependent and independent variables which allow the less-massive body to come very close to the central primary as well as to any peripheral primary.