  It is well-known that the planar and spatial circular restricted three-body
problem (CR3BP) is of contact type for all energy values below the first
critical value. Burgos-Garc\'ia and Gidea extended Hill's approach in the CR3BP
to the spatial equilateral CR4BP, which can be used to approximate the dynamics
of a small body near a Trojan asteroid of a Sun--planet system. Our main result
in this paper is that this Hill four-body system also has the contact property.
In other words, we can "contact" the Trojan. Such a result enables to use
holomorphic curve techniques and Floer theoretical tools in this dynamical
system in the energy range where the contact property holds.
