  We analytically work out the orbital effects caused by a Rindlertype
extra-acceleration ARin which naturally arises in some recent models of
modified gravity at large distances. In particular, we focus on the
perturbations induced by it on the two-body range {\rho} and range-rate
{\rho}\cdot which are commonly used in satellite and planetary investigations
as primary observable quantities. The constraints obtained for ARin by
comparing our calculations with the currently available range and range-rate
residuals for some of the major bodies of the solar system, obtained without
explicitly modeling ARin, are 1 - 2 \times 10-13 m s-2 (Mercury and Venus), 1
\times 10-14 m s-2 (Saturn), 1 \times 10-15 m s-2 (Mars), while for a
terrestrial Rindler acceleration we have 5 \times 10-16 m s-2 (Moon). Another
approach which could be followed consists of taking into account ARin in
re-processing all the available data sets with accordingly modified dynamical
models, and estimating a dedicated solve-for parameter explicitly accounting
for it. Anyway, such a method is time-consuming. A preliminary analysis likely
performed in such a way by a different author yields A <= 8\times10-14 m s-2 at
Mars' distance and A < = 1\times10-14 m s-2 at Saturn's distance. The method
adopted here can be easily and straightforwardly extended to other long-range
modified models of gravity as well.
