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Results tagged with laplace-runge-lenz-vector
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The Laplace–Runge–Lenz vector describes the shape and orientation of the orbit of one astronomical body around another. In general, the LRL vector is conserved (it's a constant of the motion) in all problems in which two bodies interact by a central force that varies as the inverse square of the distance between them (Kepler problem). Its conservation is significant in the quantization of the Hydrogen atom.
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What exactly are the 12 conserved quantities in the Two-Body Problem?
The Two-Body problem consists of 6 2nd-order differential equations
\begin{equation}
\ddot{\mathbf{r}}_1 = \frac{1}{m_1}\ \mathbf{F_g} \\
\ddot{\mathbf{r}}_2 = -\ \frac{1}{m_2}\ \mathbf{F_g}
\end{equa …
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