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:
- 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 rB and a density of rhom then:
Where vT 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 (r2) and the weight is proportional to the
area volume (r3). 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.