Abstrakt
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/Eo = 1.024 +/- 0.013. (All quoted uncertainties correspond to 3a.) The greatest and intermediate principal moments of inertia are nearly the same with 1(2)/1(3) = 0.9651(-0.015 ')(+0.009) but the smallest principal moment of inertia is substantially lower with 1(1)/1(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 phi = 27.38 +/- 0.07 h and P psi = 263 +/- 6 h, respectively; the strongest observed lightcurve amplitude for the SAM case is in the 2nd harmonic of P1 = (P phi(-1) - P phi(-1))(-1) = 30.56 +/- 0.01 h. The rotation is retrograde with the angular momentum vector's ecliptic longitude and latitude of 250 degrees and -75 degrees (the uncertainty area is approximately an ellipse with the major and minor semiaxes of 27 degrees and 14 degrees, respectively).