I'm surprised this would need to be verified experimentally. Why couldn't a density gradient like this be derived from fundamental laws?
And then another time my statistical mechanics prof informed me that "physics is just drawing cartoons of reality with math." That came as a huge existential relief by the way.
Popular science holds that physics is the study of "fundamental laws", but really it's just a special practice of articulating these very stable, ubiquitous patterns.
When you look at things holistically, you will notice that they are often irreducably dynamic, complex and full of potential surprises, along with fully actualized surprises.
So I'd imagine that all these relationships of atmospheric gases with things like the earth's magnetic field, weather patterns, chemical reactions in the atmosphere, interactions with extraterrestrial particles, the dynamics of other magnetic fields, etc. would all make this very difficult to model accurately.
First principles apply very well to our nice toy models, but the sheer vastness of existence usually out-scales our toy models very quickly.
What you've missed out is that a physicist would need to derive a collision cross section for a typical tree-sphere. That may be as complex or as simple as you like. The simple limit would take into account the trunk diameter and tree density within the forest. But perhaps the skier is particularly agile and can avoid most trees, so the cross section is smaller.
You could add other particles and cross sections, eg the bear in ski free.
>First principles apply very well to our nice toy models, but the sheer vastness of existence usually out-scales our toy models very quickly.
That said, this is how a lot of simulations in astronomy work. You take a bunch of physical laws and apply them at scale on millions of particles.
And to add a bit to how physicists simulate stuff. They build a model. Make it as simple as possible, while still approximating the natural phenomena under investigation. So the mean free path model would have a lot of parameters as the parent commenter noted (collisional cross-section, tree density, trunk diameter, etc.).
And it's also important to keep in mind that there are theory builders in physics (theorists), "applied physicists" (phenomenologists, who try to use the fancy theories, match it with real data) and derive future predictions (like climatologists, cosmologists doing large scale universe evolution simulation from the big bang, and so on), the experiment designers, who basically try to weed out the useless models/theories through very targeted experiments.
All of these are about the same natural world, but different aspects, different levels of details, different concerns. (Eg. experimental physicists place enormous care on quantifying the systemic and particular uncertainties of the experiment, whereas theoretical physicists instead focus on the fundamental workings of the theory - they test it through computation. All of those are math, math, math, just different.)
This way of thinking is a bit flawed.
Convenience is an important aspect, but it's not the entire reason. A physicist who wants to study how skiers might cause avalanches by modeling/simulation doesn't care about the details of the people they model because that's just not important. For what they want to study, it doesn't matter if they model the human as a sphere or as a real-life model with limbs and so on. It won't affect the grand picture.
On the other hands, a physicist who wants to study how an avalanche would crush a person? Then yes, modeling the limbs and the person's physical properties become much more important.
In modeling, you choose the model that best fits and represents what you aim to study. You start off with a complex system of equations and then you slowly go through and remove the parts that would be irrelevant. You don't need to account for turbulence if you know that you will never reach the high Reynolds numbers that require it. You don't need to model cellular biology if you're just trying to modeling how a piece of tissue stretches.
The exact claim is that such modeling, eg, fails to find avalanche dangers that truly exist in the world of skiers moving their body on physical skies, due to their shifting and localized weight, which is missing in the spherical skier model. Your post does nothing to address this.
The simplifications you call out are all cases of decreased accuracy in exchange for easier computations: that is, for less accurate results that are “good enough”. But the intersection of many such simplified models may fail to accurately model reality.
But yeah it was a joke! And basically I remember his joke having a tangential quip about choosing the shape based on the coordinate system you wanted to stay in.
And the point I got from it was that in modeling we often use crass approximations that are oversimplified in order to get a rough picture of what's going on with respect to certain dynamics, and that one shouldn't assume that the model resembles the full complexities of real life.
By the way, he was a cosmologist, if that helps you understand a little better why he was so flippant with the shapes.
You really can get a reasonable estimate of the drag on a cow in crossflow by approximating the cow as a cylinder.
One of the most formative and sublimely influential 'aha' remarks I've ever encountered was a line in a Willam Goldman book about screenwriting which simply read, in the manner of a final summation to a chapter: "POETRY IS COMPRESSION." Caps in the original. I had the same sense of instant resolution, like wearing glasses for the first time, that you seem to have had with your prof's insight.