I happened to catch two parts of two different episodes of Meteorite Men – a show about two guys that look for meteorites. In both of the snippets I saw, they were talking about a debris field for a meteor that breaks up. In these fields, the larger chunks of the meteorite are further down in the field. Why is this?

Let me approach this first from a terminal velocity view. This requires a model for air resistance. I will use the following:

Where:

- rho is the density of air
- A is the cross sectional area of the object
- C is a drag coefficient that depends on the shape of the object
- v is the speed of the object
- And this gives a force with a direction opposite of the velocity vector

Let me assume that all the pieces of a meteor have the same density and shape – for simplicity, I will assume a sphere. Here is a diagram for two different sized pieces falling (straight down) at the same speed.

Meteor A (the big one) has a greater gravitational force because it has more mass. It also has a greater air resistance because it’s cross sectional area is larger. I picked a speed so that meteor B would be at terminal velocity. This is when the air resistance has the same magnitude as the gravitational force. If I assume that meteor B has a radius of r_{B} and a density of rho_{m} then:

Where v_{T} is the terminal velocity. If I solve for this value, I get:

Here you can see the key point. The terminal velocity depends on the size. This is because the air resistance is proportional the area (r^{2}) and the weight is proportional to the ~~area~~ volume (r^{3}). These two things do not cancel.

## Modeling a debris field

I have created a python model for shooting bullets. I can simply modify this to calculate the trajectory of a dozen or so different sized (but same shape and density) meteor pieces.

The following is a plot of the trajectory of a few pieces of a meteor. I (for random reasons) started the model at 5,000 meters above the ground moving at 350 m/s aimed 30 degrees below the horizontal. Here is what I get:

So, the bigger the piece, the farther it will go. My biggest piece was 1 meter.