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