Question: 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

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 α R and its speed is v0. To place the probe in an elliptic orbit which will bring it closer to the planet, its speed is reduced from v0 to (v0, where ( < 1, by firing its engine for a short interval of time. Determine the smallest permissible value of ( if the probe is not to crash on the surface of the planet?

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