The essential development of a new mathematical ansatz for estimating the size of the solar system with help of Sundman inequality via Lagrange–Jacobi relation has been implemented in this research. Mean size R of the solar system has been estimated using Sundman inequality at the expanding scenario of the solar system (with existing planets’ configuration) for the obtained partial class of solutions for this type of differential inequality by assuming constant total angular momentum for the entire dynamical configuration. The obvious physically reasonable assumption is that the solar system will increase its size during evolution in the future (due to losses of the total angular momentum via tidal interactions), albeit we can assume the compressing scenario.