YORP torque as the function of shape harmonics

Abstract

The second order analytical approximation of the mean YORP torque components is given as an explicit function of the shape spherical harmonics coefficients for a sufficiently regular minor body. The results are based upon a new expression for the insolation function, significantly simpler than in previous works. Linearized plane parallel model of the temperature distribution derived from the insolation function allows to take into account a nonzero conductivity. Final expressions for the three average components of the YORP torque related with rotation period, obliquity, and precession are given in a form of Legendre series of the cosine of obliquity. The series have good numerical properties and can be easily truncated according to the degree of Legendre polynomials or associated functions, with first two terms playing the principal role. The present version fixes the errors discovered in the text that appeared in Monthly Notices RAS (388, pp. 297-944).Comment: 19 pages, 3 figures, published Mon. Not. R.A.S with minor errors that are corrected in the present versio

Obliquities of “top-shaped” asteroids may not imply reshaping by YORP spin-up

“…Thus, even axisymmetric spheroids, which have zero spin torque, will have their axes reoriented by YORP, and will have their obliquities changed if they have finite thermal inertia Γ. These results have been derived analytically by Breiter et al (2007), Breiter and Michalska (2008), and Kaasalainen and Nortunen (2013), but seem to have been underappreciated, perhaps owing to the highly mathematical presentations in those papers.…”

The YORP effect on 25 143 Itokawa

“…the remarks of Scheeres et al (2007) concerning the secondary illumination). Recalling that isothermal bodies reveal no YORP torque regardless of their shapes (Breiter & Michalska 2008), we should observe a key role of the temperature surface gradient. All classical assumptions, like zero conductivity, a plane-parallel model, or ignoring indirect lighting, tend to increase the gradient.…”

“…All known recipes for computing the YORP torques can be roughly divided in two main groups: most of them use a discrete mesh, summing the contributions from each triangular face (Vokrouhlický &Čapek 2002;Čapek & Vokrouhlický 2004;Scheeres 2007;Statler 2009), whereas others use a continuous shape model described in terms of spherical harmonics (Breiter & Michalska 2008;Mysen 2008;Nesvorný & Vokrouhlický 2008). The latter group cannot be applied to Itokawa, because its irregular shape, not being starlike, cannot be expressed in terms of spherical harmonics.…”

“…Čapek & Vokrouhlický (2004), Scheeres (2007), , Mysen (2008), Nesvorný & Vokrouhlický (2008), and Breiter & Michalska (2008) use various approximations to account for the nonzero conductivity. Their thermal models use a "plane parallel" approximation reducing the problem to a 1D heat diffusion model.…”

Compact YORP formulation and stability analysis

“…For convex bodies insolation is trivial, and they are the only ones for which exact analytical torques are possible. Various semianalytical approaches have developed small nonconvex perturbations while neglecting numerical raytracing within some perturbation size (e.g., Breiter & Michalska 2008;Nesvorný & Vokrouhlický 2007, 2008ahereafter NV07 and NV08). Unfortunately, the shadowing error cannot be estimated in terms of the perturbation parameter, so no validity regime can be established for such approximations even when the perturbation is very small.…”