THE FUNCTIONAL RELATION BETWEEN MEAN MOTION RESONANCES AND YARKOVSKY FORCE ON SMALL ECCENTRICITIES

This work examines asteroid’s motion with orbital eccentricity e in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag dtr, the strength of the resonance (SR), and the semimajor axis drift speed da/dt with asteroids' orbital eccentricities in the range (0.1, 0.2). We analysed average values of dtr using this functional relation comparing with obtained values of dtr from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1) (Figure 1), on the present results for eccentricities in the range (0.1, 0.2) (Figure 2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids' orbital eccentricities (0, 0.2) and discussed it.