  It has been recently suggested by Dvali and Vikman that the superluminal
neutrino phenomenology of the OPERA experiment may be due to an environmental
feature of the Earth, naturally yielding a long-range fifth force of
gravitational origin whose coupling with the neutrino is set by the scale M_*,
in units of reduced Planck mass. Its characteristic length lambda should not be
smaller than one Earth's radius R_e, while its upper bound is expected to be
slightly smaller than the Earth-Moon distance (60 R_e). We analytically work
out some orbital effects of a Yukawa-type fifth force for a test particle
moving in the modified field of a central body. Our results are quite general
since they are not restricted to any particular size of lambda; moreover, they
are valid for an arbitrary orbital configuration of the particle, i.e. for any
value of its eccentricity $e$. We find that the dimensionless strength coupling
parameter alpha is constrained to |alpha| <= 1 10^-10-4 10^-9 for 1 R_e <=
lambda <= 10 R_e by the laser data of the Earth's artificial satellite LAGEOS
II, corresponding to M_* >= 4 10^9 -1.6 10^10. The Moon perigee allows to
obtain |alpha| <= 3 10^-11 for the Earth-Moon pair in the range 15 R_e <=
lambda <= 60 R_e, which translates as M_* >= 3 10^10 - 4.5 10^10. Our results
are neither necessarily limited to the superluminal OPERA scenario nor to the
Dvali-Vikman model, in which it is M_* = 10^-6 at lambda = 1 R_e, in contrast
with our bounds: they generally extend to any theoretical scenario implying a
fifth-force of Yukawa-type.
