Spins and Shapes of 11 Near-Earth Asteroids and 8 Main-Belt Asteroid Pairs with Evolving Spin Axes

Introduction

Understanding the physical and dynamical properties of asteroids is essential for planetary defense strategies and for the successful planning of spacecraft missions to small Solar System bodies. This study reports on our recent work (Fatka et al. 2025) modeling the spins and shapes of Near-Earth Asteroids (NEAs) and our ongoing study of  the spin evolution of main-belt asteroid pairs.

In Fatka et al. (2025), we analyzed dense photometric data for 18 NEAs obtained within the framework of the NEOROCKS project (Near-Earth Object Rapid Observation, Characterization, and Key Simulations; Dotto et al. 2021). From these, we successfully derived or constrained spin and shape models for 11 asteroids. A particularly noteworthy of the modeled NEAs  is (98943) 2001 CC21 (Torifune) that will be visited by JAXA's Hayabusa2#  extended mission in 2026 (Hirabayashi et al. 2021).

In parallel, we are conducting photometric observations and subsequent spin and shape modeling for 8 main-belt asteroid pairs. These are gravitationally unbound systems believed to have formed through recent break-up events (Pravec et al. 2019). Our goal is to investigate the evolution of their spin vectors and test hypotheses about their formation mechanisms.

Table 1. Successfully modeled NEAs (Fatka et al. 2025).

(5189) 1990 UQ	(6569) Ondaatje	(7025) 1993 QA	(8566) 1996 EN
(66251) 1999 GJ2	(86450) 2000 CK33	(98943) Torifune	(137199) 1999 KX4
(276786) 2004 KD1	(495615) 2015 PQ291	(512245) 2016 AU8

 

Methodology

To determine an asteroid’s shape and spin axis, we first need to know how fast it spins—its sidereal rotation period. This can be tricky when observations are spread out over many years or the asteroid spins quickly, leading to several possible solutions (called period aliases).

We used a widely accepted method called lightcurve inversion, implemented in software developed by Josef Ďurech and based on Kaasalainen & Torppa (2001) and Kaasalainen et al. (2001). 

To improve accuracy, we combined our detailed photometric data with additional observations from the ATLAS survey. While these sparse data don’t help with modeling shape, they do help resolve ambiguities in the spin period. In most unclear cases, this combination led us to a unique and reliable solution.

In some instances, even when multiple periods seemed possible, the resulting models still pointed to similar spin axes and shapes—though this wasn’t always true. We also found that asteroids with large brightness variations and observations from multiple apparitions were more likely to produce reliable models.

Finally, we note that such modeling tends to favor certain types of asteroids, introducing potential biases in the broader statistics of asteroid properties. Users of these models should keep these biases in mind when interpreting the results.

Case Study: (98943) Torifune

Asteroid (98943) Torifune, the planned 2026 fly-by target of the Hayabusa2# mission, is one of our best-modeled objects. Our data, spanning from 2002 to 2023, produced a sidereal rotation period of 5.021522 ± 0.000003 hours, in agreement with the independent result of 5.021516 ± 0.000106 hours by Popescu et al. (2025). Our nominal solution for its  spin axis is (λ, β) = (259°, +84°) with an 8° uncertainty radius, also in agreement with the Popescu et al. (2025) estimate of (λ, β) = (301, +89_-6⁺¹). Our derived convex shape model is presented in Fig. 1.

We are currently updating this model by joining or data with the data from Popescu et al. (2025), the latest ATLAS catalog, and additional unpublished observations. This refined model will be important for planning the s/c fly-by and maximizing the scientific return of the event. We plan further observations of (98943) in its upcoming apparition in October-December 2025 to further improve  its model.

Figure. 1. Convex shape model of the asteroid (98943) Trorifune. Left: view along the x-axis (the longest axis) from the asteroid’s equatorial plane. Middle: view along the  -axis from the asteroid’s equatorial plane. Right: view along the z-axis (rotational axis). Fatka et al. (2025). 

Asteroid Pairs and Spin Axis Evolution

In a parallel effort, we are studying 8 asteroid pairs—recently separated, gravitationally unbound systems. We obtained dense lightcurves for both components of each pair, allowing us to derive or refine their spin axis orientations and shape models.

Using N-body backward orbital integrations, we estimated the separation ages of each pair (e.g., Pravec et al. 2019). By evolving the current spin axis directions backward in time to the point of separation, we can assess whether the spin vectors were aligned at that moment.

One hypothesis for pair formation is that a gently separating proto-binary system—a temporarily bound pair formed by a rotational fission (e.g., Scheeres 2007, Pravec et al. 2010, 2019)—would result in aligned spin axes. Our models are designed to test this prediction. This study may provide new insights into their formation and the broader processes that shape asteroid dynamics in the Solar System.

Table 2. Selected asteroid pairs.

(2110) Moore-Sitterly - (44612) 1999 RP27	(4905) Hiromi - (7813) Anderserikson
(6070) Rheinland - (54827) Kurpfalz	(9068) 1993 OD - (455327) 2002 OP28
(18777) Hobson - (57738) 2001 UZ160	(54041) 2000 GQ113 - (220143) 2002 TO134
(56232) 1999 JM31 - (115978) 2003 WQ56	(60744) 2000 GB93 - (218099) 2002 MH3
(69142) 2003 FL115 - (127502) 2002 TP59	(80218) 1999VO 123 - (213471) 2002 ES90

Acknowledgements

This work has been supported by the Grant Agency of the Czech Republic, Grant 23-04946S, and by the "Praemium Academiae" award from the Academy of Sciences of the Czech Republic, grant AP2401.

References 

Dotto et al., 7th IAA Planetary Defense Conference, 221 (2021)

Fatka et al., A&A, 695, id.A139 (2025)

Hirabayashi et al.,  Adv. Space Res., 68 (2021)

Kaasalainen & Torppa Icarus, 153, 24 (2001)

Kaasalainen et al., Icarus, 153, 37 (2001)

Pravec et al. Nature 466, 1085 (2010)

Pravec et al. Icarus, 333, 429 (2019)

Popescu et al. PSJ 6, 2, id.42 (2025)

Scheers Icarus 189, 370 (2007)

Tonry et al., PASP, 130, 064505 (2018)