The spin state of asteroid Apophis and a prediction of its change during the 2029 close encounter with Earth

On April 13, 2029, the asteroid Apophis will pass near Earth at a geocentric distance of about 38, 000 km. This will provide a unique opportunity to study the effects of Earth's gravitational torque on the asteroid's spin state and figure. Numerical models have suggested that the post-encounter spin state will critically depend on the orientation of Apophis during the flyby. We aim to determine the spin state of Apophis from its photometric observations collected during two apparitions in 2012--2013 and 2020--2021. This will enable us to accurately predict the pre-encounter rotation state and, by accounting for Earth's gravitational torque, predict a range of possible post-encounter states. We used the light curve inversion method for tumbling asteroids to reconstruct the spin state of Apophis and its convex shape model. The result is adopted as the initial condition of a numerical model describing Apophis's future rotation state. The data from the two apparitions are insufficient to determine Apophis's rotation and precession periods uniquely. The formally best-fit solution is P_ϕ = 27. 374 ± 0. 001, h for the precession period and P_ψ = 262. 2 ± 0. 1, h for the rotation period, but at least two other combinations of the periods provide a similarly good fit to the available data. All the currently acceptable models result in approximately the same pre-encounter orientation of Apophis in early 2029 (within 20^̧irc in terms of Euler angles). This is because the accurate photometric data were collected during two apparitions separated by 8 years, which is the same interval as from 2021 to 2029. Although the close encounter with Earth in April 2029 hugely increases the post-encounter uncertainty of Apophis's spin state, the short-axis spin mode will be preserved with a high likelihood. Additional observations taken in 2027 and 2028 will break the ambiguity in Apophis's pre-encounter spin solution and allow us to get a more accurate post-encounter spin state prediction.