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First the second order variation of radial position with respect to the
proper time of the gravitating mass is computed thus
which from (2.15) becomes
working this out yields
But
and insertion of this into (C.6) finally gives
which is the required relationship, expressed in the axes of D1 and the
parameter u. Substitution for u, (from (4.7)) and its spatial gradient, reduces
(C.8) to
being the equation of motion as a function of the proper time expressed fully in the axes of D1. Note that because the time dilatation effect is embodied in the proper time tp, the reactive acceleration term due to this in (3.18), is not present in (C.9).
G1 Version 2.2.4
Ó
P.G.Bass, November 2009
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