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Orbits in the problem of two fixed centers on the sphere

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Figure

Figure 1: Location of the two Newtonian centers F 1 and F 2 in S 2 . The angular separation is 2θ f , with 0 < θ f < π 2
Figure 2: (a) Bifurcation diagram for two attractive centers in the plane. (b) Bifurcation diagram for two repulsive centers in the plane with the strengths (in modulus) exchanged with respect to the attractive potential
Figure 3: Global bifurcation diagram in S 2 with γ = 1 3 .
Figure 5: Graphics of the function |U (ζ)| corresponding to the values: Ω = √ 3, G = 2 √ 3 3 , σ = cos π6 , s u 0 = 0.
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