Why do strong Leonid meteor showers occur about every 33 or 34 years?

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The strong Leonid meteor showers occur approximately every 33 or 34 years because this timeframe corresponds to the orbital period of their parent comet, Tempel-Tuttle.

Unlike older meteor streams where debris has dispersed uniformly along the comet's orbit, the meteoroids associated with the Leonids are still largely clustered in a compact swarm that moves along the same path as the comet. When Earth intersects this dense concentration of debris during the comet's periodic return to the inner solar system, the visual strength of the shower increases dramatically. Over time, gravitational perturbations and the slightly different orbits of individual meteoroids will eventually disperse this swarm, leading to a more consistent but less intense annual display.1