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I've tried looking on google but I've found nothing that directly answers my question. I've found that around Earth there is around 1000 grains in every cubic kilometre, but I'd assume that there is more in the asteroid belt, due to the presence of asteroids and lack of a planet to collect them up

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Spacecraft equipped with specialized instruments designed to detect and characterize interplanetary dust particles (IDPs) have traversed the solar system in search of them, detecting the more numerous small particles (<1 μm). One of them was Juno spacecraft. Juno was bound for Jupiter orbit insertion on a trajectory that was through asteroid belt. Although it was not instrumented with a dedicated dust detection instrument, it did however carried cameras that were dedicated to provide accurate attitude determination for the magnetic sensors. Juno encountered IDP traveling at ∼5 to ∼15 km/s relative velocity and are thought to range from ∼1 to ∼100 μm in size, representative of the dust population associated with the Zodiacal light.

Based on the 15,278 IDP impacts experienced by Juno during its 5-year cruise to Jupiter, astronomers analyzed and confirmed that the number density of IDPs observed close to the ecliptic plane varies from a few to 8 × 10−13 per cubic meter and it decrease to one-third of its value at higher ecliptic latitude (4.5°). The approximate total number of IDPs confirmed based on a model distribution was N ∼ 2 × 1022 particles.

You can find more information in the references.

Reference

  1. Jorgensen, J. L. et.al (2021). Distribution of interplanetary dust detected by the Juno spacecraft and its contribution to the Zodiacal Light. Journal of Geophysical Research: Planets, 126, DOI: 10.1029/2020JE006509
  2. On the amount of Dust in the Asteroid Belt by Whipple, F. L., Physical Studies of Minor Planets, Proceedings of IAU Colloq. 12, 1971 (link)
  3. Asteroidal Dust by Stanley F. Dermott, Daniel D. Durda, Keith Grogan, Thomas J. J. Kehoe (PDF)
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  • $\begingroup$ $8 × 10^{−13}$ per cubic meter is roughly 1 particle in a 10×10×10 km cube. That's rather sparse! $\endgroup$
    – PM 2Ring
    Nov 11, 2022 at 6:27
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Not that different. On the one hand, asteroids are grinding down (on the cosmic timescale) against each other. On the other hand, comets are barely shedding, since they’re far from the Sun, poorly illuminated, and cold. There’s some point where the two effects cancel, and it’s somewhere near the Main Belt.

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