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Pravec P.,Academy of Sciences of the Czech Republic | Scheirich P.,Academy of Sciences of the Czech Republic | Durech J.,Charles University | Pollock J.,Appalachian State University | And 17 more authors.

Our photometric observations of Asteroid (99942) Apophis from December 2012 to April 2013 revealed it to be in a state of non-principal axis rotation (tumbling). We constructed its spin and shape model and found that it is in a moderately excited Short Axis Mode (SAM) state with a ratio of the rotational kinetic energy to the basic spin state energy E/E0=1.024±0.013. (All quoted uncertainties correspond to 3σ.) The greatest and intermediate principal moments of inertia are nearly the same with I2/I3=0.965-0.015+0.009, but the smallest principal moment of inertia is substantially lower with I1/I3=0.61-0.08+0.11; the asteroid's dynamically equivalent ellipsoid is close to a prolate ellipsoid. The precession and rotation periods are Pφ=27.38±0.07h and Pψ=263±6h, respectively; the strongest observed lightcurve amplitude for the SAM case is in the 2nd harmonic of P1=Pφ-1-Pψ-1-1=30.56±0.01h. 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). An implication of the retrograde rotation is a somewhat increased probability of the Apophis' impact in 2068, but it is still very small with the risk level on the Palermo Scale remaining well below zero. Apophis is a member of the population of slowly tumbling asteroids. Applying the theory of asteroid nutational damping by Breiter et al. (Breiter, S., Rożek, A., Vokrouhlický, D. [2012]. Mon. Not. R. Astron. Soc. 427, 755-769), we found that slowly tumbling asteroids predominate in the spin rate-size range where their estimated damping times are greater than about 0.2. Gyr. The appearance that the PA/NPA rotators transition line seems to follow a line of constant damping time may be because there are two or more asteroid spin evolution mechanisms in play, or the factor of μQ (the elastic modulus times the quality factor) is not constant but it may decrease with decreasing asteroid size, which would oppose the trend due to decreasing collisional age or excitation time. © 2014 Elsevier Inc. Source

Hanus J.,French National Center for Space Studies | Hanus J.,University Of La Cote Dazur | urech J.,Charles University | Oszkiewicz D.A.,Adam Mickiewicz University | And 157 more authors.
Astronomy and Astrophysics

Context. Asteroid modeling efforts in the last decade resulted in a comprehensive dataset of almost 400 convex shape models and their rotation states. These efforts already provided deep insight into physical properties of main-belt asteroids or large collisional families. Going into finer detail (e.g., smaller collisional families, asteroids with sizes 20 km) requires knowledge of physical parameters of more objects. Aims. We aim to increase the number of asteroid shape models and rotation states. Such results provide important input for further studies, such as analysis of asteroid physical properties in different populations, including smaller collisional families, thermophysical modeling, and scaling shape models by disk-resolved images, or stellar occultation data. This provides bulk density estimates in combination with known masses, but also constrains theoretical collisional and evolutional models of the solar system. Methods. We use all available disk-integrated optical data (i.e., classical dense-in-time photometry obtained from public databases and through a large collaboration network as well as sparse-in-time individual measurements from a few sky surveys) as input for the convex inversion method, and derive 3D shape models of asteroids together with their rotation periods and orientations of rotation axes. The key ingredient is the support of more that 100 observers who submit their optical data to publicly available databases. Results. We present updated shape models for 36 asteroids, for which mass estimates are currently available in the literature, or for which masses will most likely be determined from their gravitational influence on smaller bodies whose orbital deflections will be observed by the ESA Gaia astrometric mission. Moreover, we also present new shape model determinations for 250 asteroids, including 13 Hungarias and three near-Earth asteroids. The shape model revisions and determinations were enabled by using additional optical data from recent apparitions for shape optimization. © 2016 ESO. Source

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