Out of nine known stable Mars Trojans, seven appear to be members of anorbital grouping including the largest Trojan, Eureka. In order to test if thiscould be a genetic family, we simulated the long term evolution of a tightorbital cluster centered on Eureka. We explored two cases: cluster dispersalthrough planetary gravity alone over 1 Gyr, and a 1 Gyr evolution due to bothgravity and the Yarkovsky effect. We find that the dispersal of the cluster ineccentricity is primarily due to dynamical chaos, while the inclinations andlibration amplitudes are primarily changed by the Yarkovsky effect. Currentdistribution of the cluster members orbits are indicative of an initially tightorbital grouping that was affected by a negative acceleration (i.e. one againstthe orbital motion) consistent with the thermal Yarkovsky effect. We concludethat the cluster is a genetic family formed either in a collision or throughmultiple rotational fissions. The cluster's age is on the order of 1 Gyr, andits long-term orbital evolution is likely dominated by the seasonal, ratherthan diurnal, Yarkovsky effect. If confirmed, Gyr-scale dominance of theseasonal Yarkovsky effect may indicate suppression of the diurnal Yarkovskydrift by the related YORP effect. Further study of Mars Trojans is essentialfor understanding the long-term orbital and rotational dynamics of small bodiesin the absence of frequent collisions.
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