  We study influence of noncommutativity of coordinates and noncommutativity of
momenta on the motion of a particle (macroscopic body) in uniform and
non-uniform gravitational fields in noncommutative phase space of canonical
type with preserved rotational symmetry. It is shown that because of
noncommutativity the motion of a particle in gravitational filed is determined
by its mass. The trajectory of motion of a particle in uniform gravitational
field corresponds to the trajectory of harmonic oscillator with frequency
determined by the value of parameter of momentum noncommutativity and mass of
the particle. The equations of motion of a macroscopic body in gravitational
filed depend on its mass and composition. From this follows violation of the
weak equivalence principle caused by noncommutativity. We conclude that the
weak equivalence principle is recovered in rotationally invariant
noncommutative phase space if we consider the tensors of noncommutativity to be
dependent on mass. So, finally we construct noncommutative algebra which is
rotationally invariant, equivalent to noncommutative algebra of canonical type,
and does not lead to violation of the weak equivalence principle.
