Predicting Orbital Resonance of 2867 Šteins Using the Yarkovsky Effect

While gravitational forces have the largest impact on asteroid orbit determination, thermal forces such as the Yarkovsky and YORP effects also perturb asteroid orbits. We analyzed the impact of these thermal effects on the orbit of asteroid 2867 Šteins, an E-type asteroid measuring five kilometers in diameter. The orbit of Šteins lies within the range of a Kirkwood Gap, a region devoid of asteroids because of Jupiter’s gravitational pull. Given that thermal effects can perturb asteroids of similar properties, we sought to determine whether the Yarkovsky effect would push Šteins into a Kirkwood Gap within 50,000 years. Based on Šteins’ location and size, we hypothesized that the Yarkovsky effect will push Šteins into a Kirkwood gap. We computationally generated a thermal map of Šteins to approximate the Yarkovsky force and YORP torque. Analysis of the thermal map yielded an average Yarkovsky force parallel to velocity of -0.714 N and acceleration of -5.22 x 10^-15 m/s². The torque parallel to the angular velocity due to the YORP effect was 4.680 N m, with an angular acceleration of 1.217 x 10^-20 rad/s². We inputted the calculated Yarkovsky force into NASA’s GMAT to model the resulting change to Šteins’ orbit and found that the Yarkovsky force decays the semi-major axis of Šteins by 16.4 km in 242.2 years, and up to 5,365 km in 50,000 years within 95% confidence. This perturbation is unlikely to transfer Šteins into a Kirkwood Gap.