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The shape and rotation of the tumbling asteroid (99942) Apophis

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Conference abstracts ACM 2014, Helsinki, Finland

The shape and rotation of the tumbling asteroid (99942) Apophis

P. Scheirich1, P. Pravec1, J. Durech2, J. Pollock3, P. Kusnirak1, K. Hornoch1, A. Galad1, E. Jehin4, J.

Manfroid4, C. Opitom4, M. Gillon4, F. Colas5, J. Oey6, J. Vrastil1,2, D. Reichart7, K. Ivarsen7, J. Haislip7,

and A. LaCluyze7

1

Astronomical Institute, Academy of Sciences of the Czech Republic, Fricova 1, CZ-25165 Ondrejov, Czech Republic

2

Institute of Astronomy, Faculty of Mathematics and Physics, Charles University, Prague, V Holesovickach 2, CZ-18000 Prague 8, Czech Republic

3

Physics and Astronomy Department, Appalachian State University, Boone, NC 28608, U.S.A.

4

Institut d’Astrophysique de l’Universite de Liege, Alle du 6 Aout 17, B-4000 Liege, Belgium

5

IMCCE-CNRS-Observatoire de Paris, 77 avenue Denfert Rochereau, 75014, Paris, France

6

Leura Observatory, Leura, N.S.W., Australia

7

Physics and Astronomy Department, University of North Carolina, Chapel Hill, NC 27514, U.S.A.

Photometric observations of the asteroid (99942) Apophis taken from December 2012 to April 2013 revealed that it is in a non-principal axis rotation state. We constructed a numerical model of the asteroid’s shape and rotation. The asteroid is in a short-axis mode (SAM) of excited rotation. The precession and rotation periods are Pφ= 27.38±0.07 h and Pψ= 263±6 h, respectively. The rotation is retrograde with the angular

momentum vector’s ecliptic longitude and latitude of 250° and -75° (the uncertainty area is approximately an ellipse with the major and minor semiaxes of 27° and 14°, respectively).

The shape of the asteroid is dynamically close to a prolate ellipsoid, with the lengths of largest and inter-mediate axes of 1.64 ± 0.09 and 1.14+0−0.08.04, respectively (the shortest axis is normalized to unity); the largest and intermediate moments of inertia differ by 3–4 % only.

The asteroid is close to the lowest-energy rotation state, the rotational kinetic energy is greater than the minimum kinetic energy (for rotation around the principal axis with the largest moment of inertia) by only 2–3 %. Despite this low-energy level of excitation, the figure with the two principal moments of inertia nearly equal results in the wobbling angle reaching substantial values of 50–60°.

Figure: The convex shape model of the nominal solution shown in three viewing geometries; x and z are the principal axes with the smallest and largest moments of inertia, respectively.

Acknowledgements: The work at Ondrejov and the Charles University Prague was supported by the Grant Agency of the Czech Republic, Grants P209/12/0229 and 209/10/0537, and by the Ministry of Education of the Czech Republic, Grant LG12001. A.G. was supported by the Slovak Grant Agency for Science VEGA, Grant 1/0670/13. Support for PROMPT has been provided by the National Science Foundation under awards CAREER-0449001, AAG- 0707634, and MRI-0836187. TRAPPIST is a project funded by the Belgian Fund for Scientific Research (Fonds de la Recherche Scientifique, F.R.S FNRS) under grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Fundation (SNF). E.J. and M.G. are FNRS Research Associates, J.M. is Research Director FNRS. C.O. thanks the Belgian FNRS for funding her PhD thesis. Based on data collected with the Danish 1.54-m telescope at the ESO La Silla Observatory within the NEOSource project.

References: Pravec, P. Scheirich, P., Durech, J. et al. 2014, Icarus, 233, 48.

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