Abstract
We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin–orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter’s dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.
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Notes
the coordinates of the other point are \((5\pi /3,0)\). The permutation of the index 1 and 2 of the planets allows to exchange the two equilateral configurations, which are linearly stable for small enough planetary masses (namely, if \(\frac{m_0 m_1+m_1 m_2+m_0 m_2}{(m_0+m_1+m_2)^2} < \frac{1}{27} \approx 0.037\), see Gascheau 1843).
Note that since \(\xi _l\) depends only on \(\zeta _0\), the coefficients \(K_q\) depend only on the product \(p\delta \) instead of p and \(\delta \).
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Leleu, A., Robutel, P. & Correia, A.C.M. On the rotation of co-orbital bodies in eccentric orbits. Celest Mech Dyn Astr 125, 223–246 (2016). https://doi.org/10.1007/s10569-016-9681-4
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DOI: https://doi.org/10.1007/s10569-016-9681-4