Chapter 10.6, Problem 51AYU

Challenge Problem Escape Velocity From physics, the equation for the free-flight trajectory of a satellite launched a distance $r_0$ from the center of the earth is given by the polar equation

$\frac{1}{r}=\frac{1}{r_0}\left(1-\frac{G{M}_e}{r_0{v}_0^2}\right)\cos \theta +\frac{G{M}_e}{r_0^2{v}_0^2}$ where $M_e$ is the mass of the earth, $G$ is the gravitational constant, and $v_0$ is the initial velocity of the satellite. If the initial velocity is equal to the escape velocity (the velocity needed to overcome Earth's gravitational pull) then the resulting trajectory follows a parabolic path. What is the escape velocity?