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The effect of introducing a fifth large-scale space-time dimension to theequations of orbital dynamics was analysed in an earlier paper by the authors.The results showed good agreement with the observed flat rotation curves ofgalaxies and the Pioneer Anomaly. This analysis did not require themodification of Newtonian dynamics, but rather only their restatement in a fivedimensional framework. The same analysis derived a acceleration parameter ar,which plays an important role in the restated equations of orbital dynamics,and suggested a value for ar. In this companion paper, the principle ofconservation of energy is restated within the same five-dimensional framework.The resulting analysis provides an alternative route to estimating the value ofar, without reference to the equations of orbital dynamics, and based solely onkey cosmological constants and parameters, including the gravitationalconstant, G. The same analysis suggests that: (i) the inverse square law ofgravity may itself be due to the conservation of energy at the boundary betweena four-dimensional universe and a fifth large-scale space-time dimension; and(ii) there is a limiting case for the Tulley-Fisher relationship linking thespeed of light to the mass of the Universe.

The effect of a fifth large-scale space-time dimension on the conservation of energy in a four dimensional Universe