Age of (152830) Dinkinesh I Selam constrained by secular tidal-BYORP theory

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 similar to 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.