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In this work, we model the collisional evolution of the Jupiter Trojans anddetermined under which conditions the Eurybates-Queta system survives. We showthat the collisional strength of the Jupiter Trojans and the age of theEurybates family and by extension Queta are correlated.  The collisional grinding of the Jupiter Trojan population over 4.5 Gy resultsin a size-frequency distribution (SFD) that remains largely unaltered at largesizes (>10 km) but is depleted at small sizes (10 m to 1 km). This results in aturnover in the SFD, the location of which depends on the collisional strengthof the material. It is to be expected that the Trojan SFD bends between 1 and10 km.  Based on the SFD of the Eurybates family, we find that the family was likelythe result of a catastrophic impact onto a 100 km rubble pile target. Thiscorresponds to objects with a rather low collisional strength (10 times weakerthan that of basaltic material studied in Benz & Asphaug1999).  Assuming this weak strength, and an initial cumulative slope of the sizefrequency distribution of 2.1 between diameters of 2 m and 100 km when theTrojans were captured, the existence of Queta, the satellite of Eurybates,implies an upper limit for the family age of 3.7 Gy. Alternatively, wedemonstrate that an unconventional collisional strength with a minimum at 20 mis a plausible candidate to ensure the survival of Queta over the age of theSolar System.  Finally, we show how different collisional histories change the expectednumber of craters on the targets of the Lucy mission and that Lucy will be ableto differentiate between them.

Implications for the collisional strength of Jupiter Trojans from the Eurybates family