Why does the debris from comets and former comets hang around so long? So tonight's Quatrantids shower got me thinking.  Why does the debris from comets and former comets hang around so long?  Each year the earth sweeps through the region of space that the comet went through.  However, the comet doesn't come by each year, so the earth must be going through the same cloud numerous times.  And each time we get a meteor shower as a result.
I suspect an answer, but I'd rather hear from professionals.
 A: I'm not a professional, but I'll try to answer anyway.
Meteor showers occur when the Earth passes through the orbit of a comet (or, in at least one case, an asteroid).  Over time, the debris spreads over the entire orbit of the comet.
A shower can last for several days, which is an indication of how wide the debris stream is.  Assuming a duration of 1 day, and assuming the Earth's orbit is roughly at right angles to the debris stream, that gives a width of very roughly 2.5 million kilometers (and a length of several hundred million kilometers).  The Earth is only about 12,735 kilometers in diameter.
Say the comet's orbit is 1 billion kilometers long (that's probably shorter than average).  Then multiplying the length of the orbit by the area of a circle 2.5 million kilometers across gives the volume of the stream, and multiplying 2.5 million kilometers by the area of a circle 12,735 kilometers in diameter gives the volume of the stream through which the Earth passes (the hole it punches in the stream).  The ratio is about 15 million.
Other factors:


*

*Earth's gravity will pull in some debris that wouldn't otherwise have hit it, making its effective diameter a bit bigger (thanks to ghoppe's comment).

*The density of the stream is not uniform.  There are bound to be clumps of greater density.  There's probably also a systematic change of density with distance from the Sun.  The width of the stream probably varies as well. I have no idea of the details

*The Moon (and its gravity well) will also sweep up some debris -- but the Moon's effective area is a small fraction of Earth's.


But the blatant errors in my assumptions undoubtedly swamp any such effects, and I'm only looking for a rough estimate.
So yes, the Earth's passage through a meteor stream will effectively punch a hole in it, but it's a very small hole relative to the size of the entire stream.  It could have a significant effect over millions of years.
I'm making a lot of simplifying assumptions here, but the conclusion seems about right if I've gotten the result within one or two orders of magnitude.
Reference: http://www.amsmeteors.org/meteor-showers/meteor-faq/#5, plus some of my own extremely rough back-of-the-envelope calculations.
