Physical models for the normal YORP and diurnal Yarkovsky effects

TL;DR

This paper develops analytical models for the normal YORP and diurnal Yarkovsky effects on convex asteroids, providing simplified solutions in different thermal regimes and comparing them with exact solutions.

Contribution

It introduces approximate analytical models for YORP and Yarkovsky effects, covering various thermal inertia limits, enhancing understanding of asteroid surface interactions.

Findings

Simplified models closely match exact solutions in their respective regimes.

Models cover zero, low, and high thermal inertia cases.

Analytical expressions facilitate faster computations for asteroid dynamics.

Abstract

We propose an analytic model for the normal YORP and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider 3 such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution.