A new type of connection between the families of periodic orbits of the restricted problem.

A mechanism of connection through the z-coordinate between families of periodic orbits is proposed for the three-dimensional circular restricted three-body problem. The periodic orbits having the property of reachability have the special property of being vertical critical orbits, while the periodic orbits that connect the reachable orbits are three-dimensional. A numerical example of such a connection through the z-coordinate is presented in which it is shown that the three-dimensional family which starts from the vertical critical orbit c1v of the family c of the Copenhagen problem passes through the vertical critical orbit m2v of the plane family m; i.e., the orbit m2v is reachable from c1v. Initial conditions are given for some orbits of the three-dimensional family.