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It is known that a slight generalization of the Newtonian theory of gravity is compatible with all present-day observations. This 'super-Newtonian' theory is not a complete theory of gravity, since it applies only to static or quasistatic gravitational fields. We develop here a simple, complete theory of gravity that contains the super-Newtonian theory as a special case. The gravitational field is described in terms of two real functions, and the field equations are derived from a variational principle. The homogeneous cosmological solutions of the field equations all correspond to open universes. The gravitational 'constant' decreases with time in the version of the theory that is compatible with Dicke's measurement of the solar oblateness, but not in the version compatible with an almost spherical Sun. The gravitational field of a slowly rotating body is not of the Lense-Thirring form.
Peter Rastall (Thu,) studied this question.