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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