We constrained the age of the main belt binary asteroid system, (152830) Dinkinesh, through secular dynamics and assuming the secondary, Selam, is at equilibrium. We reproduced Selam’s current semi-major axis and rotation period and Dinkinesh’s current rotation period, starting from the initial conditions of the spin-up fission event. The method presented here includes the secular effects of YORP, BYORP, and tidal interactions, while also allowing for the strengths of these effects to be constrained. Based on this method, we performed a Monte Carlo simulation, which indicates that Selam’s age is likely to be ∼1–10 Ma. Derivations for improved equations that describe tidal-BYORP equilibria in binary asteroid systems are also presented in this work. In particular, we derived: (1) a tidal-BYORP equilibrium equation that scales appropriately with the secondary mass and accounts for differences in the primary and secondary densities; and (2) an equation for YORP-driven primary spin stability, with the secondary being at equilibrium.

中文翻译：

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(152830) Dinkinesh I Selam 的年龄受到长期潮汐 BYORP 理论的约束

我们通过长期动力学并假设次要带双小行星系统 Selam 处于平衡状态，限制了主带双小行星系统 (152830) Dinkinesh 的年龄。我们从自旋裂变事件的初始条件开始，再现了塞拉姆当前的半长轴和自转周期以及丁基内什当前的自转周期。这里介绍的方法包括 YORP、BYORP 和潮汐相互作用的长期影响，同时还允许限制这些影响的强度。基于该方法，我们进行了蒙特卡罗模拟，结果表明Selam的年龄可能为∼1–10 Ma。这项工作还提出了描述双小行星系统中潮汐-BYORP 平衡的改进方程的推导。特别是，我们推导出：（1）潮汐-BYORP平衡方程，该方程与次生质量适当成比例，并考虑了初级和次级密度的差异； (2) YORP 驱动的初级自旋稳定性方程，次级处于平衡状态。