Given the 5 Lagrangian points of two large orbiting bodies:

enter image description here

(from wikipedia),

why isn't there a line of stability between L1 and L4 and L1 and L5 respectively (as depicted in red in the modified picture)?:

enter image description here

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    $\begingroup$ why should there be? $\endgroup$ – Akerai Sep 21 '19 at 21:29
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    $\begingroup$ Why isn’t there? Because the math says so. $\endgroup$ – G. Smith Sep 21 '19 at 21:30
  • $\begingroup$ There are 10 line segments between 5 points. If there were lines of stability (and there are not), why would they be those two? $\endgroup$ – G. Smith Sep 21 '19 at 21:34
  • $\begingroup$ I think the point is pretty clear now - before asking why something doesn't happen, one should have a reasonable argument as to why they would expect it happen. $\endgroup$ – Akerai Sep 21 '19 at 21:37
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/363178/2451 and links therein. $\endgroup$ – Qmechanic Sep 21 '19 at 22:07