  We study the existence of non-collision periodic solutions with Newtonian
potentials for the following planar restricted 4-body problems: Assume that the
given positive masses $m_{1},m_{2},m_{3}$ in a Lagrange configuration move in
circular obits around their center of masses, the sufficiently small mass moves
around some body. Using variational minimizing methods, we prove the existence
of minimizers for the Lagrangian action on anti-T/2 symmetric loop spaces.
Moreover, we prove the minimizers are non-collision periodic solutions with
some fixed wingding numbers.
