Revised analytic theory of the Yarkovsky force

. IntroductionThe Yarkovsky effect is a recoil force from the emitted thermal radiation that causes a slow change of asteroids’ orbits [1]. Its evolutionary significance includes spreading asteroid families and delivery of asteroids to the Kirkwood gaps thus re-supplying the population of near-Earth asteroids by the new members from the main belt, whereas its practical applications range from asteroid mass determination to prediction of asteroid hazard. Ordinarily the Yarkovsky effect is either estimated from an oversimplified linearized thermal model of a spherical asteroid or simulated fully numerically. The former path compromises the accuracy, whereas the latter conceals the physics. We choose the middle path between the spherical Scylla and the numerical Charybdis, and create a compromise theory that is simple for understanding and parametric analysis, sufficiently precise for practical use, and thoroughly verified at each step by comparison with numerical simulations.2. Thermal modelFor each surface element of the asteroid express the mean Yarkovsky force FY asHere, A is the asteroid’s Bond albedo, LΘ is the solar luminosity, S is the area of the surface element, r is the asteroid’s distance from the Sun, c is the speed of light, and p is what we call the dimensionless Yarkovsky pressure. This pressure is computed from the solution of the 1D heat equation under a surface element of a convex asteroid with zero obliquity. Under such assumptions, the solution of the non-dimensional heat equation depends on only two free parameters, namely the latitude ψ of the asteroid surface element and the thermal parameter θ, defined as in [2]. In addition to the commonly used analytic solution of the linearized heat equation valid for θ>>1, we also apply the approach of [3] to construct the opposite approximation θ1 and θ