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In this paper, we present a new mathematical approach or solving procedurefor analysis of the Sundman inequality (for estimating the moment of inertia ofthe Solar system configuration) with the help of Lagrange-Jacobi relation,under additional assumption of decreasing of the total angular momentum closeto 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 themean-size of Solar system R via analysis of the Sundman inequality. So, toanswer the question "Does the ninth planet exist in Solar system?", one shouldmeet the two mandatory criteria for such the ninth planet, first is that itshould have the negligible magnitude of inclination of its orbit with respectto the invariable plane. The second condition is that the orbit of the ninthplanet should be located within the estimation for the mean-size of Solarsystem R.

Analysis of the size of Solar system close to the state with zero total angular momentum via Sundman inequality