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For me, these two graphs are inherently different. The first graph portrays a "forbidden region" which is completely filled in, the other shows a collection of curves. Whats the difference here? Whats the difference in the interpretation?

How would one identify the forbidden regions of the second graph?

Are Lagrange points on the forbidden region?

Also, if you are initially at the Forbidden region, then what happens? The mathematics says you can't be there since velocity would have to be imaginary. So if I place a body on top of that region, then what happens to the dynamics of that body?

DLV
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  • http://farside.ph.utexas.edu/teaching/celestial/Celestial/node85.html – DLV Nov 27 '15 at 22:00
  • Maybe I misunderstood that page. But the Jacobi integral is $C=-(2U+v^2)$ in which case the zero velocity surfaces divide your plane, giving points where you cant be since points where $-2U<C$ have no solutions for $v^2$. – DLV Nov 27 '15 at 22:03

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