The diurnal Yarkovsky effect of irregularly shaped asteroids

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The Yarkovsky effect plays an important role in the motions of small celestial bodies. Increasingly detailed observations bring the need for high-accuracy modelling of the effect. We used the multiphysics software COMSOL to model the diurnal Yarkovsky effect in three dimensions and compare the results with those derived from the widely adopted theoretical linear model. We find that the linear model shows high accuracy for spherical asteroids in most cases. We explored the range of parameters for which the relative error of the linear model is over 10%. For biaxial ellipsoidal asteroids (particularly oblate ones), the linear model systematically overestimates the transverse Yarkovsky force by ~10%. The diurnal effect on triaxial ellipsoids is periodic, and no linear model is available for this phenomenon. Our numerical calculations show that the average effects on triaxial ellipsoids are stronger than those on biaxial ellipsoids. We also investigated the diurnal effect on asteroids of real shapes and find it be overestimated by the linear model by 16% on average, with a maximum of up to 35%. To estimate the strength of the Yarkovsky effect directly from the shape, we introduced the quantity of ‘effective area’ for asteroids of any shape, and find a significant linear relationship between the Yarkovsky migration rate and the effective area. This brings great convenience to the estimation in practice.