Rotation state of asteroid (99942) Apophis and its change during the 2029 flyby

The excited non-principal axis rotation state of asteroid Apophis can be described by two periods - rotation and precession. These periods (263 h and 27.38 h, respectively), together with other spin parameters and a convex shape model, were derived by [1] from photometric observations in 2012/13. Radar observations from the same apparition are consistent with the spin state derived from light curves and suggest that the shape of Apophis might be bifurcated [2]. During another favorable apparition in 2020/21, Apophis was observed extensively, and an updated shape and spin model was derived [3].We carried out photometric observations of Apophis between November 2020 and May 2021 with the Danish 1.5m telescope at La Silla, ESO. This data set consists of 1280 calibrated photometric measurements in Cousins R filter distributed over 67 individual nights.We used all available photometric data from 2012/13 and 2020/21 to determine Apophis's spin state and convex shape with the light curve inversion method [4]. Due to the large gap of eight years between observations, the rotation parameters cannot be determined uniquely. However, all acceptable models have about the same orientation in 2029 due to the same separation of eight years between 2021 and 2029. This enables us to reliably predict Apophis attitude during the close approach in 2029 and estimate the change of its spin state caused by the Earth's gravitation torque during the encounter.Acknowledgments: This work was supported by the grant 23-04946S of the Czech Science Foundation.References: [1] Pravec P. et al. (2014) Icarus, 233, 48. [2] Brozovic M. et al. (2018) Icarus, 300, 115. [3] Lee H.-J. et al. (2022) A&A, 661, L3. [4] Kaasalainen M. (2001) A&A, 376, 302.