  The restricted four body problem studies the dynamics of a massless particle
under the gravitational force produced by three masses (primaries) in an
equilateral configuration. One primary, say m3, is considered too small
compared with the other ones. In a similar way as in the classical Hill
problem, we study the limit case when m3 tends to zero in the Hamiltonian of
the R4BP. In this paper we prove that such limit exists and the resulting limit
problem produces a new Hamiltonian that inherits some basic features of the
restricted three and four body problems. We analyze some dynamical aspects of
this new system that can be considered as a generalization of the Hill problem.
