We study the dynamics in the neighborhood of the collinear Lagrangian points
in the spatial, circular, restricted three--body problem. We consider the case
in which one of the primaries is a radiating body and the other is oblate
(although the latter is a minor effect). Beside having an intrinsic
mathematical interest, this model is particularly suited for the description of
a mission of a spacecraft (e.g., a solar sail) to an asteroid.
The aim of our study is to investigate the occurrence of bifurcations to halo
orbits, which take place as the energy level is varied. The estimate of the
bifurcation thresholds is performed by analytical and numerical methods: we
find a remarkable agreement between the two approaches. As a side result, we
also evaluate the influence of the different parameters, most notably the solar
radiation pressure coefficient, on the dynamical behavior of the model.
To perform the analytical and numerical computations, we start by
implementing a center manifold reduction. Next, we estimate the bifurcation
values using qualitative techniques (e.g. Poincar\'e surfaces, frequency
analysis, FLIs). Concerning the analytical approach, following \cite{CPS} we
implement a resonant normal form, we transform to suitable action-angle
variables and we introduce a detuning parameter measuring the displacement from
the synchronous resonance. The bifurcation thresholds are then determined as
series expansions in the detuning. Three concrete examples are considered and
we find in all cases a very good agreement between the analytical and numerical
results
