I have some questions about the Lagrangian points. I´ve read the Wikipedia article on them, but unfortunately the math present in it makes my head hurt just looking at it, and it doesn´t adress two of the question questions at all.
1) The article mention that the L4 and L5 points, the Trojans, are stable if the mass ratio, M1/M2, is at least 24,96. What happens if the ratio falls below that? Do they not exist at all, or are they just unstable like the other points?
2) Intuitively, I would say that, the smaller the difference between M1 and M2, the more L1, the point between both bodies, would be to the midpoint between these bodies - to the point where, if M1 = M2, both the L1 point and the barycenter would be exactly at the midpoint between the two bodies. Is that correct?
3) In which direction do L2 and L3 "move" if the difference between M1 and M2 is smaller than in the Earth/Moon, Sun/Earth and Sun/Jupiter systems discussed in the Wikipedia article - say if we´re talking about a close binary consisting of two similar stars? Where would they be if M1 = M2?
Thanks in advance for taking the time to answer these questions.