Changes of spin axis and rate of the asteroid (99942) Apophis during the 2029 close encounter with Earth: A constrained model

¹ SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, UPMC Univ. Paris 06, LNE, 61 avenue de l’Observatoire, 75014 Paris, France
e-mail: jean.souchay@obspm.fr
² Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
³ LATMOS/IPSL, UVSQ Université Paris-Saclay, UPMC Univ. Paris 06, CNRS, Guyancourt, France
⁴ Sección Departamental de Astronomía y Geodesia, Facultad de Ciencas Matemáticas, Universidad Complutense Madrid, 28040, Spain

Received: 27 February 2018
Accepted: 13 May 2018

Abstract

Context. The dramatic event of the 2029 close encounter between the Earth and the asteroid Apophis on April 13 2029 at a minimum distance of 38 400 km constitutes an opportunity to make investigations about the modeling of the rotational changes of the asteroid during the event.

Aims. In this paper we deepen a previous study of the rotational changes of Apophis caused by gravitational effects during the close encounter, using important constraints on initial conditions brought by new recent observational data. We also evaluate the effects of the triaxial form of the asteroid on the motion of its axis of rotation in space, as well as the modifications of the spin rate due to tidal deformation.

Methods. First we used more drastic constraints for the physical and geometrical parameters of Apophis, deduced from recent observational campaigns. Second we evaluated the disturbing potential due to the Earth depending not only on the asteroid flattening, but also on the component due to its triaxiality, to deduce the equations of motion and investigate the displacement of the spin axis. Third we estimated what should be the zonal deformation of the asteroid due to the tide exerted by the Earth during the close encounter and we measured the consequences on variations of the spin rate.

Results. We show that the variations of obliquity and precession in longitude of Apophis during the 2029 close encounter can reach very large values, at the level of of respectiveley 1–10° and 10–40° depending on geometrical parameters. On the contrary, effects on the spin rate should be relatively small, leading to variations of the sidereal angle of rotation not exceeding 30 s.

Conclusions. The tribute of this paper is to give a constrained model of the important rotational variations of Apophis during its 2029 close encounter with the Earth.