  A new equivalence relation, named relation of 'similarity' is defined and
applied in the restricted three-body problem. Using this relation, a new class
of trajectories (named 'similar' trajectories) are obtained; they have the
theoretical role to give us new details in the restricted three-body problem.
The 'similar' coordinate systems allow us in addition to obtain a unitary and
an elegant demonstration of some analytical relations in the Roche geometry. As
an example, some analytical relations published in Astrophysical Journal by
Seidov in 2004 are demonstrated.
