The tumbling spin state of (99942) Apophis

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 / E 0 = 1.024 ± 0.013 . (All quoted uncertainties correspond to 3 σ .) The greatest and intermediate principal moments of inertia are nearly the same with I 2 / I 3 = 0.965 - 0.015 + 0.009 , but the smallest principal moment of inertia is substantially lower with I 1 / I 3 = 0.61 - 0.08 + 0.11 ; the asteroid’s dynamically equivalent ellipsoid is close to a prolate ellipsoid. The precession and rotation periods are P ϕ = 27.38 ± 0.07 h and P ψ = 263 ± 6 h , respectively; the strongest observed lightcurve amplitude for the SAM case is in the 2nd harmonic of P 1 = P ϕ - 1 - P ψ - 1 - 1 = 30.56 ± 0.01 h . 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 μ Q (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.