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Fig. 6

image

Julia family in the space of proper elements (ap, ep, sinIp), as extracted by the hierarchical clustering method (HCM) with the cutoff velocity vcut = 80 m s−1. The ellipses correspond to a constant velocity difference with respect to (89) Julia, equal to the escape velocity vesc ≐115 m s−1 from the respective parent body. Their shape is determined by Gaussian equations, the true anomaly f, and the argument of perihelion ω at the time of breakup. In particular, we show the values f = 180°, 170°, 160°, and 150° (top panel); ω + f = 90°, 80°, 70°, and 60° (bottom panel). These ellipses indicate that the relation between Julia and its family is reasonable.

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