References

The families g and g ′ of periodic orbits of the restricted three-body problem —planar direct orbits around the smaller primary — evolve in a notably different way for different values of the mass parameter µ. In the limit cases of Strömgrem (µ = 1/2) and Hill (µ → 0) the family g continuously exists for decreasing values of the Jacobi constant, while g ′ bifurcates from it at some Jacobi constant value [1]. A notably different behavior is observed for 0 < µ < 1/2, where g ′ is no longer a bifurcated branch of g. On the contrary, g and g ′ are two different families without a connection in the (x, y) plane [2, 3], what suggests a redefinition of both families in a more consistent way. As the restricted three-body problem is a commonly used model in the design of space missions to planetary satellites, we compute the families g and g ′ for different values of µ corresponding to several cases of interest in the Solar system, and show that the link between both families is attained throug