  Consideration of the asteroid belt (Kuiper belt) as a jammed-granular media
establishes a bridge between condensed matter physics and astrophysics. It
opens up an experimental possibility to determine the deformation parameters
for noncommutative space-time. Dynamics of the Kuiper belt can be simplified as
dynamics of a dynamical effective mass for a jammed granular media under a
gravitational well. Alongside, if one considers the space-time to be
noncommutative, then an experimental model for the determination of the
deformation parameters for noncommutative space-time can be done.
  The construction of eigenfunctions and invariance for this model is in
general a tricky problem. We have utilized the Lewis-Riesenfeld invariant
method to determine the invariance for this time-dependent quantum system. In
this article, we have shown that a class of generalized time-dependent
Lewis-Riesenfeld invariant operators exist for the system with dynamical
effective mass in jammed granular media under a potential well in
noncommutative space. To keep the discussion fairly general, we have considered
both position-position and momentum-momentum noncommutativity. Since, up to a
time-dependent phase-factor, the eigenfunctions of the invariant operator will
satisfy the time-dependent Schr\"{o}dinger equation for the time-dependent
Hamiltonian of the system, the construction of the invariant operator fairly
solve the problem mathematically, the results of which can be utilized to
demonstrate an experiment.
