Hill’s curves

The classical Hill s curves of the restricted three-body problem are given in Figure 3 for equal primaries. The curves of constant ratio g/v are given in Figures 4 and 5 in terms of the position of mi with respect to m2 and m3 for the following mass ratios 2mi= m2 = m3 (Figure 4) and mi = m2 = m3 (Figure 5). 

The curve of constant ratio g/v represent the natural prolongation of Hill s curves with continuity between the corresponding Figures as Figures 3-5. The two minimums correspond to g/v = 1 at the equilateral Lagrangian points and the three collinear saddle points are the usual Euler equilibrium points. 

Figure 3. The classical Hill s curves for equal primaries. AB = 1 J = (rA +r )/2 +...

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