Accuracy of view factor calculations for digital terrain models of comets and asteroids

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, Göttingen 37077, Germany
e-mail: rezac@mps.mpg.de
² Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, PR China
³ CAS Center for Excellence in Comparative Planetology, Chinese Academy of Sciences, Hefei 230026, PR China

Received: 21 May 2020
Accepted: 7 August 2020

Abstract

Context. Detailed shape and topographic models coupled with sophisticated thermal physics are critical elements to proper characterization of surfaces of small bodies in our solar system. Calculations of self-heating effects are especially important in the context of thermal evolution of non-convex surfaces, including craters, cracks, or openings between “rocks”.

Aims. Our aim is to provide quantitative comparisons of multiple numerical methods for computing view factors for concave geometries and provide a more rigorous criteria for the validity of their application.

Methods. We contrasted five methods of estimating the view factors. First, we studied specific geometries, including shared-edge facets for a reduced two-facet problem. Then, we applied these methods to the shape model of 67P/Churyumov-Gerasimenko. Nevertheless, the presented results are general and could be extended to shape models of other bodies as well.

Results. The close loop transformation of the double area integration method for evaluating view factors of nearby or shared-edge facets is the most accurate, although computationally expensive. Two methods of facet subdivision we evaluate in this work provide reasonably accurate results for modest facet subdivision numbers, however, may result in a degraded performance for specific facet geometries. Increasing the number of subdivisions improves their accuracy, but also increases their computational burden. In practical applications, a trade-off between accuracy and computational speed has to be found, therefore, we propose a combined method based on a simple metric that incorporates a conditional application of various methods and an adaptive number of subdivisions. In our study case of a pit on 67P/CG, this method can reach average accuracy of 2–3% while being about an order of magnitude faster than the (most accurate) line integral method.