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Observation of fast radio bursts (FRBs) are rising very quickly with theadvent of specialised instruments and surveys, and it has recently been shownthat some of them repeat quasi-periodically. In particular, evidence of a$P=16.35$ day period has been reported for FRB 180916.J0158+65. We seek anexplanation within the frame of our orbiting asteroid model, whereby FRBs areproduced in the plasma wake of asteroids immersed in the wind of a pulsar or amagnetar. We used the data reported by the CHIME/FRB collaboration in order toinfer the orbital characteristics of asteroid swarms, and performed parametricstudies to explore the possible characteristics of the pulsar, its wind, and ofthe asteroids, under the constraint that the latter remain dynamically andthermally stable. We found a plausible configuration in which a young pulsar isorbited by a main $\sim 10^{-3}M_\odot$ companion with a period $3P = 49$d,three times longer than the apparent periodicity $P$. Asteroids responsible forFRBs are located in three dynamical swarms near the L3, L4 and L5 Lagrangepoints, in a 2:3 orbital resonance akin to the Hildas class of asteroids in theSolar system. In addition, asteroids could be present in the Trojan swarms atthe L4 and L5 Lagrange points. Together these swarms form a carousel thatexplains the apparent $P$ periodicity and dispersion. We estimated that thepresence of at least a few thousand asteroids, of size $\sim20$km, is necessaryto produce the observed burst rate. We show how radius-to-frequency mapping inthe wind and small perturbations by turbulence can suffice to explaindownward-drifting sub-pulses, micro-structures, and narrow spectral occupancy.

Periodic activity from fast radio burst FRB180916 explained in the frameof the orbiting asteroid model