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Find the escape velocity $ v_0 $ that is needed to propel a rocket of mass $ m $ out of the gravitational field of a planet with mass $ M $ and radius $ R $. Use Newton's Law of Gravitation (see Exercise 6.4.33) and the fact that the initial kinetic energy of $ \frac{1}{2} mv^2_0 $ supplies the needed work.

$v_{0}=\sqrt{\frac{2 G M}{R}}$

Integration Techniques

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