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Does Newton's Theory with Retarded potentials give rise to the motion of perihelion of Planets

If we take into account the retarded potentials and the motion of the Sun(due to the planet), does Newton's Gravitational theory give rise to the motion of Perihelion of planets (qualitatively, not ...
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Experimental limits on non-Newtonian gravitational force at length scales larger than 1 meter?

This answer from 2012 shows some information on an exponential term characterized by relative strength and range parameters $\alpha$ and $\lambda$, One potential tested here is here $$V(r)=-G\frac{...
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