  We apply the many-particle Schr\"{o}dinger-Newton equation, which describes
the co-evolution of an many-particle quantum wave function and a classical
space-time geometry, to macroscopic mechanical objects. By averaging over
motions of the objects' internal degrees of freedom, we obtain an effective
Schr\"odinger-Newton equation for their centers of mass, which are degrees of
freedom that can be monitored and manipulated at the quantum mechanical levels
by state-of-the-art optoemchanics experiments. For a single macroscopic object
moving quantum mechanically within a harmonic potential well, we found that its
quantum uncertainty evolves in a different frequency from its classical
eigenfrequency --- with a difference that depends on the internal structure of
the object, and can be observable using current technology. For several
objects, the Schr\"odinger-Newton equation predicts semiclassical motions just
like Newtonian physics, yet they do not allow quantum uncertainty to be
transferred from one object to another through gravity.
