Abstract
Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is θ=(p+q)λ jup −pλ−qϖ, exact corotations are double resonant motions defined by the conditionsdθ/dt=0 andd(ϖ−ϖ jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev 5-resonance. This paper presents the symmetric solutions θ=0 (mod π), ϖ=ϖ jup (mod π). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as θ and ϖ are close to the equilibrium values.
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Ferraz-Mello, S., Tsuchida, M. & Klafke, J.C. On symmetrical planetary corotations. Celestial Mech Dyn Astr 55, 25–45 (1993). https://doi.org/10.1007/BF00694393
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DOI: https://doi.org/10.1007/BF00694393