The objective of this work is to predict the optimal speed of an aerospace vehicle by aerothermochemical analysis of the hypersonic flow during atmospheric re-entry, out of equilibrium vibrational and chemical behind a detached strong shock. This study focuses on the influence of the ionization process that plays a significant role in the absorption of heat, because the characteristics of hypersonic flows are that molecules behind a strong shock wave become vibrationally excited, partially or

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... mpletely dissociated and ionized depending on their bond energy, and the velocity of flow. On the other hand, we present the mathematical model that governs the flow of reactive gas mixture out of vibrational and chemical equilibrium that is composed of 79% nitrogen N2 and 21% oxygen O2. Conservation and relaxation equations (chemistry-vibration) are presented with particular importance to the expression of source terms. The numerical resolution method used is based on physical modeling, governed by the Euler equations, supplemented by the equations of chemical kinetics using the finite difference method. The results obtained are in good agreement with the specialized literature.