A New Critical Value Concerning the Genealogy of Long Period Families at L4 in the Restricted Three-body Problem ∗

We found another critical mass ratio value between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.