Scalar-tensor propagation of light in the inner solar system including relevant c-4 contributions for ranging and time transfer

In a recent paper (Minazzoli and Chauvineau 2009 Phys. Rev. D 79 084027), motivated by forthcoming space experiments involving propagation of light in the solar system, we have proposed an extension of the IAU metric equations at the c(-4) level in general relativity. However, scalar-tensor theories may induce corrections numerically comparable to the c(-4) general relativistic terms. Accordingly, one first proposes in this paper an extension of Minazzoli and Chauvineau (2009) to the scalar-tensor case. The case of a hierarchized system (such as the solar system) is emphasized. In this case, the relevant metric solution is proposed. Then, the corresponding isotropic geodesic solution relevant for distance measurements and time transfers in the inner solar system is given in explicit form.