The problem of the stressed-strained state which occurs in an elastic spherical body when it enters the planet atmosphere at a super-orbital (space) velocity is analytically solved. The analytical solution is obtained in the form of a series of Legendre polynomials for the case of a viscous gas flowing over an elastic sphere in a quasi-static formulation. It is shown that critical deformations arise due to aerodynamic forces inside the ball closer to his windward side and, as the time goes on, occupy more and more space inside the ball, leading to its failure. The solution makes it possible to describe the nature of the body failure and evaluate the height at which it starts for well-known meteoroids at a given entry velocity into the Earth's atmosphere
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