Solving for vesc gives ' 2GM N1/2
Note that comparing vesc and vorb gives
Vesc = V2 Vorb
Therefore, the escape speed for the Earth is 11 km/s.
In considering travel to other planets, we use elliptical orbits. After all, an object whose orbit touches both the Earth and Mars cannot be a circular orbit about the Sun. (We should note that parabolic or hyperbolic orbits can be used for onetime flybys, such as Pioneer and Voyager.) When we studied binary stars, we found that the velocity of a particle in an elliptical orbit of semimajor axis a, when the object is a distance r, from a mass M at the focus, is v2 = GM
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