Functional differential equations. 4: Retarded gravitation
C. K. Raju
AlBukhary International University, Alor Setar, Malaysia
Are functional differential equations (FDEs) only about electrodynamics? No. They apply also to gravitation. We explain a recent reformulation of gravitation, called retarded gravitation theory (RGT), which is Lorentz covariant, and us es functional differential equations. RGT modifies the Newtonian “inverse square law” gravitational force: the RGT force depends upon (a) retarded distance, and (b) includes a velocity-dependent term. RGT, since Lorentz covariant, theoretically improves on Newtonian gravitation. At the same time, RGT has the practical advantage over general relativity theory (GRT) that a solution of the many-body problem is feasible in RGT. Hence, RGT can and ought to b e applied to the galaxy where Newtonian physics apparently fails but GRT cannot b e applied. The tiny velocity dependence of the RGT force is amplified across a hundred billion co-rotating stars in the galaxy, so that non-Newtonian velo cities of stars in spiral galaxies are to be expected on RGT, even without dark matter. Possible exp erimental tests of RGT include the flyby anomaly observed for NASA spacecraft which dep ends systematically on velocity-effects due to the rotation of the earth. We further clarify that Laplace’s objection to pre-relativistic naive theories of retarded gravitation (NRG) does not apply to RGT. We solve the 2-body FDEs of RGT for the sun-Jupiter case: the system is stable despite tiny differences from Newtonian gravitation. Thus, FDEs are a general feature of post-relativity physics.