The long-term orbital evolution of meteoroids and small asteroids in the size range up to several kilometers is affected by the "seasonal" Yarkovsky force, caused by radiation pressure recoil on spinning bodies heated by solar radiation to different temperatures at different latitudes on their surfaces. This effect leads to a draglike, secular semimajor-axis decay, which may inject the bodies into chaotic zones associated with mean motion and secular resonances and eventually deliver them to near-Earth space. To model the Yarkovsky force, two kinds of simplifying assumptions have been frequently made: (1) a linearization in the ratio between temperature variation and average temperature and in the orbital eccentricity and (2) a plane-parallel geometry, that is, body sizes larger than the penetration depth of the seasonal thermal wave (typically, several meters). In a previous paper, we developed a new nonlinearized theory, and here we also remove the assumption of plane-parallel geometry and extend our theory to the more general spherical case, valid for all body sizes, by means of a new numerical approach. We also revise the linear theory, obtaining a fully analytical literal solution, which is well suited to develop analytical and semianalytical secular perturbation theories and allows us to perform a detailed comparison with the results of the more accurate numerical model. We find that the accuracy of the linear theory is relatively good (20% or better) for near-circular orbits. Although the temperature variations grow with the orbital eccentricity, we show that the linear theory can still predict the averaged drift rates of the mean orbital elements up to eccentricities of 0.4–0.5.
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