Lifetime of a spacecraft around a synchronous system of asteroids using a dipole model

Space missions allow us to expand our knowledge about the origin of the solar system. It is believed that asteroids and comets preserve the physical characteristics from the time that the solar system was created. For this reason, there was an increase of missions to asteroids in the past few years. To send spacecraft to asteroids or comets is challenging, since these objects have their own characteristics in several aspects, such as size, shape, physical properties, etc., which are often only discovered after the approach and even after the landing of the spacecraft. These missions must be developed with sufficient flexibility to adjust to these parameters, which are better determined only when the spacecraft reaches the system. Therefore, conducting a dynamic investigation of a spacecraft around a multiple asteroid system offers an extremely rich environment. Extracting accurate information through analytical approaches is quite challenging and requires a significant number of restrictive assumptions. For this reason, a numerical approach to the dynamics of a spacecraft in the vicinity of a binary asteroid system is offered in this paper. In the present work, the equations of the Restricted Synchronous Four- Body Problem (RSFBP) are used to model a binary asteroid system. The main objective of this work is to construct grids of initial conditions, which relates semi- major axis and eccentricity, in order to quantify the lifetime of a spacecraft when released close to the less massive body of the binary system (modeled as a rotating mass dipole). We performed an analysis of the lifetime of the spacecraft considering several mass ratios of a binary system of asteroids and investigating the behavior of a spacecraft in the vicinity of this system. We analyze direct and retrograde orbits. This study investigated orbits that survive for at least 500 orbital periods of the system (which is approximately one year), then not colliding or escaping from the system during this time. In this work, we take into account the gravitational forces of the binary asteroid system and the solar radiation pressure (SRP). We found several regions where the direct and retrograde orbits of a spacecraft survive throughout the integration time (one year) when the solar radiation pressure is taken into account. Numerical evidence shows that retrograde orbits have a larger region initial conditions that generate orbits that survive for one year, compared to direct orbits.