All Problems Universal Gravitation
Problem 1.208
Using the conservation laws, demonstrate that the total mechanical energy of a planet of mass \(m\) moving around the Sun along an ellipse depends only on its semi-major axis a. Find this energy as a function of \(a\).
1.208. \(E=T+U=-\gamma m m_{S} / 2 a\), where \(m_{S}\) is the mass of the Sun.