Chapter 3.4, Problem 197E

Using Kepler’s laws, it can be shown that $v_0=\sqrt{\frac{2GM}{r_0}}$ is the minimum speed needed when $\theta =0$ so that an object will escape from the pull of a central force resulting from mass M. Use this result to find the minimum speed when $\theta =0$ for a space capsule to escape from the gravitational pull of Earth if the probe is at an altitude of $300\text{km}$ above Earth’s surface.