The Yarkovsky effect for (99942) Apophis and observational predictions for the upcoming 2020-2021 close approach to Earth

It has been shown that for asteroid (99942) Apophis the leading source of uncertainty for predictions of its orbital motion is due to non-gravitational accelerations arising from anisotropic thermal re-emission of absorbed solar radiation, known as the Yarkovsky effect [1]. Yet, previous attempts to obtain this parameter from astrometry for Apophis have only yielded marginal detections [2]. Here, we present an independent estimation for the Yarkovsky effect on Apophis from optical and radar astrometry. Our approach is based on automatic differentiation techniques in terms of high-order Taylor series expansions both with respect to time and deviations with respect to a given orbital solution [3]. We implement our own planetary ephemeris integrator, which essentially reproduces the DE430 ephemeris integration [4]. Our dynamical model for Apophis takes into account post-Newtonian accelerations from the Sun, the eight planets, the Moon and Pluto, oblateness effects from Earth's J₂ zonal harmonic, perturbations from the 16 most-massive main-belt asteroids and a non-gravitational acceleration term accounting for the transverse Yarkovsky effect. Exploiting these techniques, we implement a Newton method for orbit determination, and perform two orbital fits to optical and radar astrometry: a 6 degrees-of-freedom (DOF) gravity-only orbital fit for the initial conditions, and a 7 DOF orbital fit, which includes the Yarkovsky coefficient A₂ as an additional fit parameter, obtaining A₂ = (-5.40 ± 3.29)×10^-14 au/d^-2. Our optical astrometry error model accounts for biases present in star catalogs [5], and accounts for other sources of systematic errors via an appropriate weighting scheme [6]. Using our orbital solutions, we provide predictions (nominal and 3-sigma uncertainty ellipses) for optical and radar observations for the upcoming close approach that Apophis will have with Earth during 2020-2021 (see Figs. 1 and 2). Finally, we project the orbital uncertainty onto the 2029 B-plane, and propose a parameterized orbit determination scheme, which allows us to compute the time-evolution of the line of variations for Apophis via a high-order Taylor series parametrization.

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