# 5 Lagrangian points: why isn't there a line of stability between $L_1$ and $L_4$ and $L_1$ and $L_5$ respectively? [duplicate]

Given the 5 Lagrangian points of two large orbiting bodies:

(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)?:

• why should there be? – Akerai Sep 21 '19 at 21:29
• Why isn’t there? Because the math says so. – G. Smith Sep 21 '19 at 21:30
• There are 10 line segments between 5 points. If there were lines of stability (and there are not), why would they be those two? – G. Smith Sep 21 '19 at 21:34
• 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. – Akerai Sep 21 '19 at 21:37
• Possible duplicates: physics.stackexchange.com/q/363178/2451 and links therein. – Qmechanic Sep 21 '19 at 22:07