Newton's Gravity and the Theories with an Arbitrary RØ2 Coupling

It is shown that Einstein's gravitational theory with an arbitrary RO coupling agrees with Newton's law of universal gravitation. It is also shown that under suitable conditions the same is true for higher order derivative gravity plus a scalar field arbitrarily coupled to the curvature scalar. Few theories can compare in the accuracy of tlieir predictions with Newton's theory of universal gravitation. The discovery of Neptune, and the rediscovery of Ceres, are among the spectacular sucesses that test,ify to the accuracy of the theory. Unfortunately Newton's theory is not perfect: the predicted motions of the perihelia for the inner planets deviate somewhat from the observed values. Although Newton's theory is not perfect, it is an excellent approximation in the limiting case of motion at low velocity in a weak gravitational field. As a consequence, any relativistic theory of gravitation ought to agree with Newton's theory in this limiting case. On the other hand, the reasons for adding to Einstein's action for gravitation a nonminimal functional of a scalar field are manifold[']. It is widely believed, moreover, that this nonminimal functional may be written in the following f~rm[~]