When an object of small mass \(m\) orbits a body of much larger mass \(M\), we can use conservation of energy considerations to find the smaller body's velocity \(v\) at radial distance \(r\). where t...When an object of small mass \(m\) orbits a body of much larger mass \(M\), we can use conservation of energy considerations to find the smaller body's velocity \(v\) at radial distance \(r\). where the quantity \(a\) is the radius for a circular orbit, the semi-major axis for an elliptical orbit, the negative of the semi-major axis for a hyperbolic orbit, or infinity for a parabolic orbit. -\frac{G M m}{2 a} & =\frac{1}{2} m v^{2}-\frac{G M m}{r} .