  In this paper, we present a new mathematical approach or solving procedure
for analysis of the Sundman inequality (for estimating the moment of inertia of
the Solar system configuration) with the help of Lagrange-Jacobi relation,
under additional assumption of decreasing of the total angular momentum close
to the zero absolute magnitude in the final state of Solar system in a future.
By assuming such the final state for Solar system, we have estimated the
mean-size of Solar system R via analysis of the Sundman inequality. So, to
answer the question "Does the ninth planet exist in Solar system?", one should
meet the two mandatory criteria for such the ninth planet, first is that it
should have the negligible magnitude of inclination of its orbit with respect
to the invariable plane. The second condition is that the orbit of the ninth
planet should be located within the estimation for the mean-size of Solar
system R.
