Synchronous spin–orbit resonances in earth co-orbital asteroids: A study using parametric and real-ephemeris models

Earth co-orbitals include quasi-satellites (QS), small bodies in the 1:1 mean-motion resonance that remain gravitationally unbound while tracing long-term loops in a geocentric frame. Their orbital dynamics are well studied, whereas their rotational states remain less explored. In particular, the possibility of synchronous spin–orbit locking (1:1) under solar torque has not yet been tested for real Earth co-orbital objects. Here we investigate the 1:1 resonance for triaxial bodies under realistic orbital constraints. We apply our method to JPL Horizons ephemerides of four near-Earth co-orbitals: 2002 AA${}_{29}$, (164207) Cardea (2004 GU${}_9$), (469219) Kamo‘oalewa (2016 HO${}_3$), and (706765) (2010 TK${}_7$) over a 30-year window. Our results show that $\Delta$ (the triaxiality parameter in the solar-torque spin model) controls the strength of the spin–orbit coupling, whereas increasing $e$ promotes diffusion. Only 2002 AA${}_{29}$ ($e\approx 0.013$) retains a compact synchronous island and non-zero capture fractions. For 2004 GU${}_9$, 2016 HO${}_3$, and 2010 TK${}_7$ ($e\gtrsim 0.10$), coherence is lost and capture becomes indistinguishable from zero. We also perform robustness tests with ephemeris cadence, stroboscopic sampling, and damping, confirming the physical nature of these results. Overall, we show that synchronous locking is detectable only at very low eccentricity and becomes unlikely for $e\gtrsim 0.10$, with potential implications for mission targets such as Kamo‘oalewa.