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Context. The Arjuna asteroid belt is loosely defined as a diverse group ofsmall asteroids that follow dynamically cold, Earth-like orbits. Most of themare not actively engaged in resonant, co-orbital behavior with Earth. Some ofthem experience temporary but recurrent horseshoe episodes. Objects inhorseshoe paths tend to approach Earth at a low velocity, leading to capturesas Earth's temporary satellites or mini-moons. Four such objects have alreadybeen identified: 1991 VG, 2006 RH120, 2020 CD3, and 2022 NX1. Here, we focus on2023 FY3, a recent finding, the trajectory of which might have a co-orbitalstatus and perhaps lead to temporary captures. Aims. We want to determine thephysical properties of 2023 FY3 and explore its dynamical evolution. Methods.We carried out an observational study of 2023 FY3 using the OSIRIS cameraspectrograph at the 10.4 m Gran Telescopio Canarias, to derive its spectralclass, and time-series photometry obtained with QHY411M cameras and two unitsof the Two-meter Twin Telescope to investigate its rotational state. N-bodysimulations were also performed to examine its possible resonant behavior.Results. The visible reflectance spectrum of 2023 FY3 is consistent with thatof an S-type asteroid; its light curve gives a rotation period of 9.3$\pm$0.6min, with an amplitude of 0.48$\pm$0.13 mag. We confirm that 2023 FY3 roams theedge of Earth's co-orbital space. Conclusions. Arjuna 2023 FY3, an S-typeasteroid and fast rotator, currently exhibits horseshoe-like resonant behaviorand in the past experienced mini-moon engagements of the temporarily capturedflyby type that may repeat in the future. The spectral type result furtherconfirms that mini-moons are a diverse population in terms of surfacecomposition.

When the horseshoe fits: Characterizing 2023 FY3 with the 10.4 m Gran Telescopio Canarias and the Two-meter Twin Telescope