Orbital Contraction of Small Binary Asteroids Driven by the Binary Yarkovsky Effect on the Primary Asteroid

The Yarkovsky effect, a well-established mechanism in planetary science, results from anisotropic thermal re-emission on the surfaces of rotating small bodies (Vokrouhlicky et al 2015). As sunlight heats an asteroid’s surface, the re-radiation of this energy, especially from the afternoon hemisphere, creates a recoil force that alters the object’s orbit over time. This subtle but persistent force plays a key role in the long-term heliocentric orbital evolution of small bodies such as near-Earth asteroids. Until recently, however, its role in binary asteroid systems—where two bodies are gravitationally bound in mutual orbit—remained largely unexplored.

In a recent study, Zhou et al. (2024) discovered the so-called Binary Yarkovsky effect (BY), which governs the long-term evolution of mutual orbits within binary asteroid systems, separate from their heliocentric trajectories. This discovery significantly advances our understanding of small-body dynamics. In particular, Zhou et al. demonstrated that the Binary Yarkovsky effect on the secondary (BYS) can efficiently drive the secondary asteroid toward a synchronous state, where its spin period matches its orbital period. The direction of this evolution depends on whether the primary casts a shadow on the secondary's orbit. If shadowing occurs, BYS acts to synchronize the secondary; otherwise, it pushes the system away from synchronization. This mechanism provides a compelling explanation for the observational fact that most small binary asteroids possess synchronously rotating secondaries, even though the expected tidal dissipation in such low-mass systems (primary radius < 1 km) is too weak to induce synchronization.

In this work, we present a comprehensive analysis of BYP, including its physical modeling, numerical characterization, and observational implications (Zhou 2024). We numerically compute the radiation recoil forces acting on rapidly rotating primary asteroids, accounting for thermal inertia and geometric eclipses. An example of the eclipse is shown in Fig. 1. By fitting the numerical results, we derive an empirical formula for BYP and use it for estimate of the orbital drift rates of known binary asteroids.

Fig. 1. Left: Snapshots of the temperature field of the binary asteroids. Diagrams (a)-(d) illustrate the anti-clockwise orbit of the secondary asteroid around the primary. Both the primary and secondary have spin rates of 3 hours. The other properties of the binary system are detailed in Sect.~\ref{sec:frequency}. In phase (a) the primary is partially eclipsed by the secondary, while in phase (c) the primary fully eclipses the secondary. Right: Tangential accelerations due to thermal forces for the primary (blue) and secondary (red). The eclipse periods are represented by shaded areas. The net force averaged over one orbital period produces the Binary Yarkovsky effect.

Our simulations confirm that BYP acts to bring the primary’s spin toward the mutual orbital frequency, just as BYS does for the secondary. However, BYP does not require the secondary to be asynchronous—meaning it remains effective in many binaries previously thought to be dynamically static.

Fig. 2. The BYP-induced orbital drift rate for confirmed small binary asteroids, assuming thermal inertia of 100 tiu (left) and 500 tiu (right). The colours indicate the heliocentric semi-major axis, with bluer colours representing greater distances from the Sun. The size of each circle corresponds to the size of the primary asteroid. 

Our calculations reveal that BYP is actively shrinking the mutual orbits of most known small binary asteroids. The BYP-induced orbital drift rates for small binary asteroids (primary radius < 1 km) range from –0.001 to –1 cm yr^-1 (Fig. 2). We find that the predicted orbital drift rates of BYP for pre-impact asteroid Didymos and asteroid (175706) 1996 FG3 are consistent with the observed values (e.g. Scheirich et al. 2024 and references therein). However, the results show a discrepancy for systems 2001 SL9 and 1999 KW4, suggesting complex dynamics in these systems also involving the BYORP and tides (Cuk & Burns, 2005; Jacobson & Scheeres, 2011). We conclude that the BYP is changing the mutual orbits of most discovered binary asteroids and it should be considered along with BYORP and tidal effects when studying binary systems’ long-term dynamics.

 

References

Ćuk, M., & Burns, J. A. (2005). Effects of thermal radiation on the dynamics of binary NEAs. Icarus, 176(2), 418-431.

Jacobson, S. A., & Scheeres, D. J. (2011). Long-term stable equilibria for synchronous binary asteroids. The Astrophysical Journal Letters, 736(1), L19.

Scheirich, P., Pravec, P., Meyer, A. J., Agrusa, H. F., Richardson, D. C., Chesley, S. R., ... & Moskovitz, N. A. (2024). Dimorphos orbit determination from mutual events photometry. The Planetary Science Journal, 5(1), 17.

Vokrouhlický, D., Bottke, W. F., Chesley, S. R., Scheeres, D. J., & Statler, T. S. (2015). The Yarkovsky and YORP effects. In P. Michel, F. E. DeMeo, & W. F. Bottke (Eds.), Asteroids IV (pp. 509–531). University of Arizona Press.

Zhou, W. H., Vokrouhlický, D., Kanamaru, M., Agrusa, H., Pravec, P., Delbo, M., & Michel, P. (2024). The Yarkovsky effect on the long-term evolution of binary asteroids. The Astrophysical Journal Letters, 968(1), L3.

Zhou, W. H. (2024). The binary Yarkovsky effect on the primary asteroid with applications to singly synchronous binary asteroids. Astronomy & Astrophysics, 692, L2.