### How many micrometeorites are falling in my garden?

Micrometorites are falling constantly everywhere. Their origin is unclear, according to some studies, most of them could come from comet dust. They are the oldest materials of the solar system. They are beautiful.

They are everywhere. On your doorstep, on your home roof, on your car roof. Any step you take outdoor, you step on many of them.

But you cannot see them. They are too small.

A very good question is : How many are they?

This apparently easy question is actually quite hard to answer. It depends on what you call a micrometeorite and what is your source of information. Next we are going to make an attempt answering.

The first definition of micrometeorites was actually only referring to unmelted particles. But in the last 20 years it happens scientist are calling micrometeorites to both melted and unmelted particles. Let us consider as "micrometeorite" any particle less than 1 mm in diameter coming from the space "as it" (not from a bigger body that broke up during the atmosphere entrance) and after the earth formation.

Approximately about 40 000 tons of cosmic dust enters the earth atmosphere.

They are always entering the atmosphere at very high speed. The exact speed depends on the earth rotation and the path of the particle before collision with earth. But the minimum speed is the escape velocity of the earth which is about 11 km/s. This is due to the Energy conservation. The potential Energy of the particle when "infinitely" far away from the earth is entirely transformed to Kinetic Energy. A simple calculation matching both Energy will show the mass of the particle has no effect and the minimum end speed only depends on the earth mass. And it is of 11 km/s.

Unless they are very big bodies that will leave a meteorite, bodies bigger than 1 mm in diameter do not resist the atmosphere impact. They burn in the atmosphere and vaporise into nanometric particles.

Particle less than 0.5 mm resist better the atmosphere entrance. Roughly this is due to this particles reduce their speed earlier, in the higher layers of the atmosphere so the speed reduction is much less in the lower layers.

Particles less than 0.2 mm resist very good to the atmosphere entrance. But they are very difficult to identify.

Let us focus on cosmic particles between 0.2 mm and 0.5 mm.

How many of this are falling on the earth?

My source: Geochemical Tracers of Extraterrestrial Matter in Sediments by Bernhard Peucker-Ehrenbrink, Greg Ravizza, and Gisela Winckler.

Our interest is the peak shown between $\10^{-4}$m and $\10^{-3}$m.

The different lines show the results of different investigations.

1: Cosmic dust flux (Hughes 1978)
2: Long Duration Exposure Facility impact record (Love and Brownlee 1993)

The upper axis uses a logarithmic scale. $log_{10}(0.0002)=-3.7$ and $log_{10}(0.0005)=-3.3$ are shown here:

The radar micrometeor observation shows very different results and we will discard this. Let us focus on lines 1 and 2. The mass (lower axis) is a bit unclear but it assumes a density of $\2.5 g/cm^{3}$ . Supposing a spherical shape of the micrometeorites we can calculate accurately the mass:

For a 0.2 mm diameter particle it is of $2.5 \frac{4\pi r^{3}}{3}=1.05\:10^{-5} g$

For a 0.5 mm diameter particle it is of $2.5 \frac{4\pi r^{3}}{3}=1.64\:10^{-4} g$

Log mass interval is: $log_{10}(1.05\:10^{-5}) - log_{10}(1.64\:10^{-5}) = 3.786 - 4.978 = -1.193$

The result for line 1 is 7.08 x 1.193 = 8.45 Gg/y and for line 2: 4 x 1.193 = 4.75 Gg/y.

There is a huge difference depending on the source. We are going to use the arithmetical average: 6.60 Gg/y

The average mass of a particle is of $8.73\:10^{-5} g$
Here we are. $7.5\:10^{13}$ particles are falling on the earth each year.
Saint Google says he earth is $510\:10^{6} km^{2}$. That is $51\:10^{13} m^{2}$

$\frac{7.5}{51}=0.15$ particles are falling each year on a surface of one square meter.

If your garden is 100 square meters, 15 micrometeorites are falling there each year.

But remember this depends a lot on the source of information and the size range of the particle you are considering. There are much more of the size 0.2 mm than 0.5 mm. But very very roughly this is a kind of answer to the question "How many micrometeorites are falling in my garden?".