Lagrange Points ($L_1$ through $L_5$) in a restricted 3-body system are well documented. Traditionally body 1 (M1) is the central object with a mass much greater than the other two objects. M2 is the secondary object that will form the Lagrange Points, and M3 is a much much smaller object like an asteroid or spacecraft that will reside in the vicinity of an L point.
Normally L1, L2, and L3 are considered non-stable equilibrium points, while L4 and L5 are considered stable equilibrium points. In terms of potential, L1, L2, and L3 are "saddle points".
L1 and L2 are in the neighborhood of the smaller massive object (M2). L3, on the other hand, is 180 deg away in the orbit opposite the smaller massive object (M2). If we look at the Sun-Earth system, this means that L3 is an orbit around the sun at just slightly closer to the sun than the Earth, but still essentially at a distance of 1 AU.
However, as we all know, there are other planets around the sun. L1 and L2 will be much closer to the Earth than any other planet. However, for L3, Mars, Venus, and Mercury can be closer than Earth, which will always be 2 AU away. In particular Venus, which is has a mass comparable to Earth's, will be closer to the Sun-Earth L3 point than earth itself for a significant portion of time, coming as close as 0.3 AU.
Hence my question - in the "real world" of the solar system does the Sun-Earth L3 point still mathematically exist?
