Open Access

Fig. 5

image

Locations of the resonant equilibrium points in the ai+1ai vs. planes, i = 1, 2, for three equal-mass planets in a 3:2 – 2:1 mean motion resonance chain, close to which Kepler-305 resides. Orange vertical lines show the exact nominal commensurability, while dashed vertical lines show the observed a2a1 and a3a2 in the case of Kepler-305. As explained in the text, we select one equilibrium configuration (indicated by the red dot in both panels) by requiring that (a3a1)|eq ≡ (a3a1)|obs, which automatically fixes all orbital elements a2a1, a3a2, e1, e2 and e3 along the equilibrium curves.

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