The only force acting on the object is gravity, so it has a mechanical energy given by: \[\begin{aligned} E&=U+K\\ E&=-G\frac{Mm}{r}+\frac{1}{2}mv^2\end{aligned}\] In order for the object to just esca...The only force acting on the object is gravity, so it has a mechanical energy given by: \[\begin{aligned} E&=U+K\\ E&=-G\frac{Mm}{r}+\frac{1}{2}mv^2\end{aligned}\] In order for the object to just escape the gravitational pull of \(M\), it’s mechanical energy must be equal to zero: \[\begin{aligned} E&=0\\ \therefore K_{esc}&=-U\end{aligned}\] Since the object is in a circular orbit, we can use Newton’s Second Law to find an expression for \(v^2\): \[\begin{aligned} F_{net}&=\frac{mv^2}{r}\\ \fr…
