Abstract
The vertical stability character of the families of short and long period solutions around the triangular equilibrium points of the restricted three-body problem is examined. For three values of the mass parameter less than equal to the critical value of Routh (μ R ) i.e. for μ = 0.000953875 (Sun-Jupiter), μ = 0.01215 (Earth-Moon) and μ = μ R = 0.038521, it is found that all such solutions are vertically stable. For μ > (μ R ) vertical stability is studied for a number of ‘limiting’ orbits extended to μ = 0.45. The last limiting orbit computed by Deprit for μ = 0.044 is continued to a family of periodic orbits into which the well known families of long and short period solutions merge. The stability characteristics of this family are also studied.
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