Abstract
In this study, an exact solution of the problem on the dynamic compression of a cold gas sphere of finite size is constructed. The parameters at the shock-wave front and at the gas sphere boundary are mutually independent. The conditions of separation of variables and the initial differential equations in partial derivatives are formulated at a specified shock-wave trajectory for two ODE systems, one of which contains quantities that depend on time alone, and the second one contains quantities that depend on the dimensionless variable alone. The exponent in the dimensionless variable is determined from the condition of an absence of strong discontinuities in the gas flow between the shock wave and gas sphere boundary.
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