Skip to main content# A new binary-YORP effect model combining full two rigid body dynamics and three-dimensional thermal evolution

Presentation #200.04 in the session Binary Asteroids and Radiation Forces.

Published onApr 25, 2022

A new binary-YORP effect model combining full two rigid body dynamics and three-dimensional thermal evolution

An extension of the YORP effect theory [e.g., 1] to a binary asteroid system is called binary-YORP (BYORP) effect, whereby the orbit of its secondary is modified on a long term due to a thermally induced torque [2]. BYORP adds additional torques and forces to the secondary, inducing its complex dynamical behavior. Within a long period, it expands/contracts the secondary’s orbit, particularly by controlling the semi-major axis, *a*, and the eccentricity, *e*. Together with mutual body tides (which dissipates energy and always expands *a*), BYORP is likely to be responsible for forming a wide variety of asteroid evolution processes leading to various geophysical configurations such as, contact binaries, asteroid pairs, and ternary [3].

Here, we introduce a new BYORP model which simultaneously simulates the highly coupled mutual gravitational interaction of the non-spherical bodies, known as the full two-body problem (F2BP) [4], and the three-dimensional (3D) thermophysical condition of the secondary. This model employs Finite Element Modeling approaches [5, 6]. The BYORP-induced orbital evolution can be thus described in unprecedented detail, compared to earlier models which neglect F2BP dynamics and detailed thermal evolution. With ongoing code development, future versions of the model will further capture complex behaviors driven by mutual gravity interactions and thermal conditions (e.g., eclipse and mutual heating due to scattered sunlight).

Using the model, we investigate the BYORP-induced evolution of the binary asteroid system (61839) Didymos, the target of NASA’s DART mission [7]. Based on historical observations, *a* is reported to be shrinking at -0.076 cm yr^{-1} [8].

Table 1 summarizes the physical and material properties. Dimorphos’ shape is currently assumed to be a tri-axial ellipsoid. Propagating the mutual dynamics for 1 day (~2 orbital periods) on Jan 1, 2021, we find that *a* is shrinking, compared to the case where BYORP is turned off (Fig. 1). This is consistent with the observation. Importantly, however, the illumination geometry changes over the system’s heliocentric orbit, and thus, it is possible that BYORP expands *a* for some epochs. In the presentation, we will present the semi-major axis evolution over the system’s one heliocentric orbit.

RN acknowledges support from NASA/FINESST (NNH20ZDA001N).

[1] Rubincam (2000) Icarus, 148 [2] Čuk and Burns (2005) Icarus, 176 [3] Jacobson et al. (2014) ApJ, 780 [4] Scheeres (2009) CMDA, 104 [5] Nakano et al. (2022) Submitted to PSJ [6] Nakano and Hirabayashi (2022) In preparation [7] Rivkin et al. (2021) PSJ, 2 [8] Richardson et al. (2022) Submitted to PSJ