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I've been reading about the Leonid meteor showers and am struggling to understand one piece of information. On Wikipedia (Tempel-Tuttle), it states:

The orbit of 55P/Tempel–Tuttle intersects that of Earth near exactly, hence streams of material ejected from the comet during perihelion passes do not have to spread out over time to encounter Earth. This coincidence means that streams from the comet at perihelion are still dense when they encounter Earth, resulting in the 33 year cycle of Leonid meteor storms. For example, in November 2009, the earth passed through meteors left behind mainly from the 1466 and 1533 orbit.

Why are we going through the meteors left behind by the orbits from 1466 and 1533? What happened to the orbit of 1500 and every subsequent orbit?

My guess is that the perihelion moves slightly from orbit to orbit so the earth moves through a different one each time but I'd love to get an expert explanation!

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When material is shed from a comet, it mostly continues to follow the same orbit as the comet, but drifts out ahead or behind the comet in a complex way due to interactions with solar wind and the gravity of other objects.

If you imagine the elliptical orbit of 55P/Tempel-Tuttle, it will have patches of denser dust in clumps spaced out around the ellipse corresponding to different perihelion approaches. The 1466 clump will be in a different place than the 1500 clump, and they will both be travelling more or less around the comet's orbit.

Since the comet's orbit only crosses Earth's at one place, and we only cross that spot once a year, we will only encounter whatever clumps of dust happen to be at that point at the same time the Earth is.

Calculating exactly where these clumps of comet dust are is non-trivial. And that is a big reason why predicting how good a meteor shower will be is a rather tricky business.

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