The Lucy mission  will be the first mission to study the Jupiter Trojans (JT) population up close. Among the targets is (3548) Eurybates, the largest member of a collisonal family . JTs are thought to be outer solar system planetesimals. They orbit the Sun in a 1:1 resonance with Jupiter in two swarms around the L4 and L5 Lagrangian points of the Sun-Jupiter system where they lead/trail Jupiter by 60° respectively. In this work we study the collisional evolution of the JT and the Eurybates family to understand i) their material strength, and ii) the age of the Eurybates family and newly discovered satellite Queta . By modelling the collisional evolution of the L4 swarm using the Boulder collisional code [4,5] we find that to a degree the age and strength of the Eurybates family and Queta are correlated and depend on the size frequency distribution (SFD) of the JT at small sizes (< 1 km). To assess the survival probability of Queta we monitor impacts on the Eurybates-Queta system over time. Catastrophic impacts on either Queta or Eurybates directly limit the lifetime of the system, while sufficient impacts on either body can disturb Queta’s orbit enough for it to become unbound. We find a lower bound for the collisional strength needed for Queta to survive the age of the Solar System at intermediate case between the collisional strength found for “weak ice”  and basalt targets . From there, as the collisional strength increases so does the survival probability of Queta. The SFD of the Eurybates family shows a significantly steeper slope at 10-20 km than the L4 swarm. This is indicative of a collisional family and we will show that the family SFD most closely resembles outcomes of impacts on rubble piles  thus implying weak material strength. In combination with the survival probability of Queta this suggests an upper limit for the age of the Eurybates family of 3.5 Gy. Finally, we find that an unconventional collisional strength where the minimum in the critical impact energy lies at diameters of 20 m best satisfies all constraints: i) the survival of Queta, ii) the Eurybates SFD, and iii) the JT SFD. This type of strenght might also be in line with observations from the Edgeworth-Kuiper belt [9,10].
 Levison et al. (2017), LPSC, 2025.  Brož & Rozehnal (2011), MNRAS, 414, 565.  Noll et al. (2020), PSJ, 1, 44.  Morbidelli et al. (2009), Icarus, 202, 310.  Nesvorný et al. (2011), AJ, 141, 159.  Leinhardt & Stewart (2009), Icarus, 199, 542.  Benz & Asphaug (1999), Icarus, 142, 5.  Benavidez et al. (2012), Icarus, 219, 57.  Singer et al. (2019), Science, 363, 955.  Morbidelli et al. (2021), Icarus, 356, 114256.