On the Assessment of Disturbances in the Rotational Dynamics of Small Asteroids During Their Approach to the Earth

Abstract

Through numerical experiments, the influence of the angular velocity of proper rotation, rotation axis orientation, and asteroid shape parameters on the magnitude of perturbations in its rotational dynamics during close approaches to the Earth has been studied. The dynamics of three asteroids was considered: (99 942) Apophis, (367 943) Duende and 2012 TC4. It was found that asteroids with relatively slow rotation (period P > 5 h) are characterized by significant disturbances: in the case of Apophis (P ≈ 30 h) when approaching the Earth in 2029, changes in the rotation period can reach tens of hours, and deviations in the orientation of the rotation axis of ten degrees. In the case of Duende (P ≈ 8 h) when approaching the Earth in 2013, the change in P did not exceed several hours, deviations in the orientation of the rotation axis could amount to tens of degrees. For asteroids with rapid rotation (P < 1 h) the disturbances are negligible: in the case of asteroid 2012 TC4 (P ≈ 12 min) during its approach to the Earth in 2017, the changes in P did not exceed 10^–5 min, the deviations of the rotation axis were less than 0.01°. It is shown that for asteroids with slow rotation, errors in determining the parameters of the asteroid’s figure can lead to noticeable inaccuracies in estimating the magnitudes of disturbances. In contrast, the uncertainty in knowing the figure of an asteroid with rapid rotation does not affect the assessment of disturbances in its rotational dynamics. In the case of Apophis, disturbances in the rotational motion during the upcoming approach to the Earth in 2029 can lead to a decrease in the value of the A₂ parameter, which characterizes the Yarkovsky effect, to –2.4 × 10^–14 AU/day² or to an increase to –3.2 × 10^–14 AU/day². Perturbations in the rotational dynamics of Duende during its approach to the Earth in 2013 and of asteroid 2012 TC4 during its approach to the Earth in 2017 did not have a noticeable effect on their A₂ values.