A space probe is describing a circular orbit about a planet of radius $R$. The altitude of the probe above the surface of the planet is $\alpha R$ and its speed is $v_0$. To place the probe in an elliptic orbit which will bring it closer to the planet, its speed is reduced from $v_0$ to $\beta v_0$, where $\beta<1$, by firing its engine for a short interval of time. Determine the smallest permissible value of $\beta$ if the probe is not to crash on the surface of the planet.