Investigation of the hydrodynamic analogy in the restricted problem of three bodies

The hydrodynamic analogy concept is examined from the standpoint of the possibility of physical realization of an analog device. The conditions that must be satisfied, conservation of mass and momentum and uniqueness of physical properties, are discussed in detail and applied to examples, including the Birkhoff formulation. The transformation of the restricted problem into a velocity field does not insure that an analog flow can be constructed, as demonstrated by two cases that correspond to physically impossible flows. Conservative force fields are certainly incapable of producing the desired results. The physical possibility of simulating the Birkhoff velocity field remains uncertain, but a practical consideration in the visualization seemingly eliminates all possibility of this analogy being useful.