Rotational changes of the asteroid 99942 Apophis during the 2029 close encounter with Earth

¹ Observatoire de Paris, Systèmes de Référence Temps Espace (SYRTE), CNRS/UMR 8630, UPMC, 75014 Paris, France
e-mail: jean.souchay@obspm.fr; damya.souami@obspm.fr
² NAXYS, Namur Center for Complex Systems, Department of Mathematics, University of Namur, 5000 Namur, Belgium
e-mail: damya.souami@math.unamur.be
³ Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France
⁴ Dipartimento di Matematica, Universita di Roma Tor Vergata, 00173 Roma, Italy
e-mail: lhotka@mat.uniroma2.it
⁵ Sección Departamental de Astronomía y Geodesia, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
e-mail: vdpuente@gmail.com; marta_folgueira@mat.ucm.es

Received: 25 July 2013
Accepted: 9 December 2013

Abstract

Context. The close approach of the asteroid (99942) Apophis to Earth on April 13, 2029, at a distance of about 38 330 km, is naturally considered a dramatic and fascinating event by the astronomical community, as well as by the public.

Aims. Although the orbital changes of the asteroid (due to the gravitational perturbations of our planet during the encounter) have been abundantly investigated, the simultaneous changes in the rotational characteristics of the asteroid have been poorly studied.

Methods. In this paper, after numerically computing the perturbing rotational potential of Apophis due to Earth, we used a classical way of calculating variations in the precession ψ and the obliquity ε, which enables us to determine the changes in position of the instantaneous pole of rotation in space during the encounter. By assigning a reasonable value of the unknown dynamical ellipticity of Apophis, deduced from a statistical study of a full sample of small asteroids, it follows that the changes in the precession Δψ and in the obliquity Δε of the asteroid during the 2029 encounter could be of a few degrees, which makes them an interesting challenge of detection by modern ground-based observations.

Results. This study confirms the possible observability of the asteroid rotational change during a close approach. It should be updated and refined in the future, when orbital, physical, and rotational parameters of Apophis become more precise.