  We, first, analytically work out the long-term, i.e. averaged over one
orbital revolution, perturbations on the orbit of a test particle moving in a
local Fermi frame induced therein by the cosmological tidal effects of the
inhomogeneous Lemaitre-Tolman-Bondi (LTB) model. The LTB solution has recently
attracted attention, among other things, as a possible explanation of the
observed cosmic acceleration without resorting to dark energy. Then, we
phenomenologically constrain both the parameters K_1 = -\ddot R/R and K_2 =
-\ddot R^'/R^' of the LTB metric in the Fermi frame by using different kinds of
solar system data. The corrections $\Delta\dot\varpi$ to the standard
Newtonian/Einsteinian precessions of the perihelia of the inner planets
recently estimated with the EPM ephemerides, compared to our predictions for
them, yield K_1 = (4+8) 10^-26 s^-2, K_2 = (3+7) 10^-23 s^-2. The residuals of
the Cassini-based Earth-Saturn range, compared with the numerically integrated
LTB range signature, allow to obtain K_1/2 = 10^-27 s^-2. The LTB-induced
distortions of the orbit of a typical object of the Oort cloud with respect to
the commonly accepted Newtonian picture, based on the observations of the comet
showers from that remote region of the solar system, point towards K_1/2 <=
10^-30-10^-32 s^-2. Such figures have to be compared with those inferred from
cosmological data which are of the order of K1 \approx K2 = -4 10^-36 s^-2.
