I read this Phys.SE thread which is similar Why are L4 and L5 lagrangian points stable?
but I did not want to necro that thread. It seems that most discussions of a three body problem are presented in two dimensions. I am thinking about the set of points where two cones intersect. One cone with the vertex at the sun and described by the angle sub tended by L4-sun-L5. The other cone defined by L4-earth-L5. The intersection of these two cones is a circle that includes L4 and L5. This circle is the set of locations where the gravity of the sun and earth cancel out. This circle is perpendicular to a line connecting the earth and sun. if we are considering L4 and L5 as stable points, why are we excluding all the other points on this circle?