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 (mu) over bar between mu(4) and mu(5) 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 mu(2) and mu(4), with slight difference in evolution details.