Asteroid missions are now an important component of space exploration, and binary asteroids compose approximately 16% of the near Earth asteroids (NEA) population. This fact, combined with the planned mission to binary asteroid 65803 Didymos, makes them a subject of interest for the study of spacecraft dynamics. Binary asteroid systems are composed of two bodies orbiting their barycenter. The presence of two sources of gravitational potential and the rotation of the system makes the study of the dynamics of a spacecraft in their vicinity more challenging than in the vicinity of a single asteroid. The present study is presenting an advanced dynamical model of the motion of a spacecraft in the vicinity of a binary asteroid that includes a fourth-order gravitational potential model and the solar radiation pressure (SRP). Based on this model, trajectories under the form of periodic orbits compatible with the SRP are designed and presented. The stability of the different orbits is then compared. This study is novel by the inclusion of the SRP early in the design of the trajectories.