Spin-orbit Dynamics of Binary Asteroids

To date, hundreds of asteroids have their rotational and orbital parameters well-determined (see [1]). The interest in this topic increased recently with the DART mission on the Didymos-Dimorphos system [2], and the Lucy mission on the Dinkinesh-Selam pair [3]. Focusing on the dynamics of the small secondary companions, a diversity of rotational and orbital configurations is known, e.g., capture into synchronous spin-orbit resonance and asynchronous secondaries (including fast rotators) [4-6]. Rotational dynamics of the small companions in double systems have been studied numerically and analytically in several works (see [7-10] and references therein). The most interesting cases are those where the satellite is out-of-round, since several structures rise inside the synchronous domain of the phase space, leading to more complex rotational scenarios. Among those sites, secondary resonances give rise to centers and saddles within the synchronism, which can occupy considerable volume in the rotational phase space. In this work, we apply the analytical and numerical models given in Wisdom (2004) [11] and Callegari (2024) [12] to map the secondary resonances of several satellites of asteroids and TNOs (including dwarf planets with satellites, like Quaoar and Weywot).  More general modelling and numerical simulations where the orbital dynamics is simulated in the domain of the full 2-body problem are also shown [13, 14].  We show a catalog of the resonances and estimate the amplitude of physical libration of a great deal of asteroid companions in all the centers associated with secondary islands. This mapping should be used in the determination of the current rotational state of several small moons of minor bodies.

 

References

 

[1] Katherine Minker. Origin and structure of binary asteroids. PhD thesis. Université Côte d’Azur (2025). 

[2] Agrusa, H. F. et al. (and more 14 authors). The excited spin state of Dimorphos resulting from the DART impact. Icarus 370 (2021) 114624.

[3] Levison, H. F. et al. (and more 118 authors). A contact binary satellite of the asteroid (152830) Dinkinesh. Nature 629 (2024) 1015.

[4] Pravec, P. et al. (and more 49 authors). Asteroid pairs: A complex picture. Icarus 333 (2019) 429–463.

[5] Pravec, P. et al. (and more 48 authors). Binary asteroid population. 3. Secondary rotations and elongations. Icarus 267 (2016) 267–295.

[6] Minker, K., Carry, B., Vachier, F. (more 36 authors). Orbits of very distant asteroid satellites. Astronomy and Astrophysics 698 (2025) A136.

[7] Cúk, M., Nesvorný, D. Orbital evolution of small binary asteroids. Icarus 207 (2010) 732–743

[8] Gkolias, I., Celletti, A., Efthymiopoulos, C., Pucacco, G. The theory of secondary resonances in the spin–orbit problem. MNRAS 459 (2016) 1327.

[9] Lei, H. Dynamical structures associated with high-order and secondary resonances in the spin–orbit problem. Astron J (2023) 167(3). id.121, 11 pp..

[10] Jafari-Nadoushan, M Surfing in the phase space of spin–orbit coupling in binary asteroid systems. MNRAS 520 (2023) 3514–3528.

[11] Wisdom, J. Spin-orbit secondary resonance dynamics of Enceladus. Astron J (2004) 128:484–91.

[12] Callegari Jr., N. A Hamiltonian for 1/1 rotational secondary resonances, and application to small satellites of Saturn and Jupiter. Commun Nonlinear Sci Numer Simulat 138 (2024) 108224.

[13] Scheeres, D. J. Stability of the planar full 2-body problem. Celest Mech Dyn Astr (2009) 104:103–128.
[14] Carita, G. A., Hussmann, H., Prado, A. F. B. A., Callegari Jr., N., Morais, M. H., Safwan, S., de Carvalho, R. E. Planar dynamics of non-spherical close tidally locked binaries and the restricted three body problem. Nonlinear Dynamics  (2025) 113:16343–16366.

 

Acknowledgments

The São Paulo Research Foundation (FAPESP) (process 2025/02325-1).