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

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 P_φ = 27.38 ± 0.07 h and P_ψ = 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 intermediate axes of 1.64 ± 0.09 and 1.14^{+0.04}_{-0.08}, respectively (the shortest axis is normalized to unity); the largest and intermediate moments of inertia differ by 3-4