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Are the basins of attraction of two static gravitational sources two...
Consider the following setup:Two massive bodies of mass $M$ are fixed at the positions $\vec{A}=(d, 0)$ and $\vec{B}=(-d, 0)$.Now imagine a test particle $p$ with initial position $\vec{r}_0=(x_0,y_0)$...
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Answer by lineage for Are the basins of attraction of two static...
finallyIn the following $G=M=d=1$.The equipotentials look likeFor a particle starting from rest, the contours also represent the level curves of the first constant of motion, total energy $E$. Each...
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As stated, the problem is to start a particle at rest at every point in the plane and track its trajectory until it hits one of the stationary masses. The problem can be transformed to that of starting...
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Answer by Kasper for Are the basins of attraction of two static gravitational...
The good news is that your conjecture is true. The bad news is that my proof offers little insight. I'm not sure a small proof by some symmetry argument is possible, since it's not simply the symmetry...
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