  It is not known if, in addition to the Newton's inverse square law component,
the gravitational force has some non-Newtonian, long-range components that have
escaped detection until now. For example, the non-Newtonian component of the
gravitational force naturally arises if gravity is interpreted as an entropic
force, or under far reaching hypothesis that quantum vacuum contains virtual
gravitational dipoles. We point out that some trans-Neptunian objects (for
instance a binary system or a dwarf planet with its satellite) might be a good
laboratory to establish the eventual existence of non-Newtonian components of
gravity. The key points are that, in the case of an ideal two-body system, the
perihelion precession can be caused only by a gravitational force that deviates
from the inverse square law and that the perihelion precession rate is larger
in systems with smaller mass. It is shown, that in some trans-Neptunian
(two-body) systems, the perihelion precession rate caused by internal
interactions might be larger than the (inevitable) precession induced by
external gravitational field.
