The close alignment of the Sun's spin axis with the solar system's planetary angular-momentum vector after 5 billion yr implies that the post-Newtonian gravitational interaction is Lorentz invariant to high precision. A metric gravity first post-Newtonian order (PPN) coefficient α₂ is constrained to be of order 10⁻⁷ or less, and second post-Newtonian order (1/c⁴) aspects of the gravitational interaction are modestly constrained by the present-day solar system configuration. Observations related to possible precession of the spin axes of fast pulsars also are relevant to this precision test of the Lorentz invariance of gravity.
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Ken Nordtvedt (1987) studied this question.