  We study orbits near collision in a non-autonomous restricted planar
four-body problem. This restricted problem consists of a massless particle
moving under the gravitational influence due to three bodies following the
figure-eight choreography. We use regularized coordinates in order to deal
numerically with motions near collision, and reversing symmetries to study both
theoretically and numerically certain type of symmetric periodic orbits of the
restricted system. The symmetric periodic orbits (initial conditions) were
computed with the help of some boundary-value problems.
