  A scalar theory with a preferred reference frame is summarized. To test that
theory in celestial mechanics, an "asymptotic" post-Newtonian (PN) scheme has
been developed. This associates a conceptual family of self-gravitating systems
with the given system, in order to have a true small parameter available. The
resulting equations for a weakly-self-gravitating system of extended bodies
include internal-structure effects. The internal-structure influence subsists
at the point-particle limit--a violation of the weak equivalence principle. If
one could develop an "asymptotic" approximation scheme in general relativity
also, this could plausibly be found there also, in a gauge where the PN space
metric would not be "conformally Euclidean".
