The effect of the mass ratio on families of retrograde periodic orbits in the planar CR3BP and their bifurcations

Abstract We compute 2D families of retrograde symmetric periodic orbits (SPOs) in the planar circular restricted 3-body problem (CR3BP) and investigate how these change with increase in the mass ratio. In particular, we compute 1/-1, 1/-2 and 2/-1 resonant families, showing that these exhibit period multiplication bifurcations at specific mass ratios. Moreover, we show that the width of the gap that divides the circular family in outer and inner branches at the 1/-1 resonance location increases with mass ratio. Finally, we show that similar to previous results for small mass ratios (Jupiter–Sun and Neptune–Sun), there are three 1/-1 resonant modes which correspond to stable branches of distinct SPO families up to mass ratio $$\mu = 0.32$$ μ = 0.32 , from which point there is no 1/-1 resonant mode that bifurcates from the outer circular family.