Scalar gravity with preferred frame: asymptotic post-Newtonian scheme and the weak equivalence principle

15 pages (in the format here), text of talk given at the 2nd Workshop "Gravity, Astrophysics and Strings at the Black Sea" (Kiten, Bulgaria, June 10-16, 2004). Published version is Open Access at http://www.tcpa.uni-sofia.bg/conf/GAS/files/gas04/arminjon.pdfInternational audienceA scalar theory of gravity with a preferred reference frame is presented. It is insisted on the dynamics, which involves a (non-trivial) extension of Newton's second law, and on the new version (v2) with isotropic space metric. We display the energy conservation equation obtained with v2. Then the principles of the asymptotic post-Newtonian approximation are discussed in some detail. The results of its application to the motion of a small extended body in a weakly-gravitating system are given and discussed: the weak equivalence principle was violated in v1, due to its anisotropic space metric (as the standard Schwarzschild metric), but is valid with v2