All Problems

Universal Gravitation

Problem 1.208

Using the conservation laws, demonstrate that the total mechanical energy of a planet of mass mm moving around the Sun along an ellipse depends only on its semi-major axis a. Find this energy as a function of aa.

Reveal Answer
1.208. E=T+U=−γmmS/2aE=T+U=-\gamma m m_{S} / 2 a, where mSm_{S} is the mass of the Sun.
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