Contact binary asteroid (153201) 2000 WO107: rotation, shape model, and density
We combine different methods to investigate the rotation, determine the shape and estimate the density of near-Earth asteroid (153201) 2000 WO$_{107}$. We carried out photometric observations of the asteroid during the 2020 apparition. Then we created a program able to simulate the lightcurves, and used it within a Markov chain Monte Carlo (MCMC) algorithm to reconstruct the asteroid shape model from the observational data. The Goldstone radar observations of the asteroid were used as an additional constraint on the asteroid model in the MCMC algorithm. The estimated shape and rotation rate of the contact binary were used to compute its density. The photometric observations of (153201) 2000 WO$_{107}$ obtained at a wide range of the phase angles from 5 to 68 degrees in the time interval November 28 -- December 8, 2020, show lightcurves typical for contact binary asteroids, which agrees with the results of the radar data. The lightcurves have a maximum amplitude of up to 1.24 mag. The best-fit modelled shape of the asteroid is composed of two ellipsoidal lobes with the axes $0.68\times 0.38 \times 0.36$ km and $0.44 \times 0.42 \times 0.16$ km. Its sidereal rotation period is determined to be $5.017\pm 0.002$ hr. The most probable solution for the angular velocity vector of the asteroid points at the ecliptic coordinates $λ=96^\circ \pm 8^\circ$ and $β=-78^\circ \pm 1^\circ$, whereas another less probable solution around $λ=286^\circ \pm 11 ^\circ$, $β=-76^\circ \pm 2 ^\circ$ cannot be disregarded. The estimated density of the asteroid $ρ=4.80^{+0.34}_{-0.63}$ g/cm$^3$ is consistent with its possible metallic composition. From the orbital simulation of this potentially hazardous asteroid, we find that its integral probability of colliding with the Earth in the next 10,000 years is $7\cdot 10^{-5}.$