The exhilaration of skiing isn't the only reason you're breathing hard --- you need more lungfuls of air to get the same number of oxygen molecules.
If you've ever woken up early in the morning, piled into the car, and spent the day skiing in the mountains, you probably found yourself huffing and puffing the whole time. Some of that was almost certainly due to the exhilaration of flying down the snowy slopes, but you'd have been struggling to catch your breath even when walking up the steps to buy a hot cocoa in the lodge. The usual explanation? "The air is thinner up there." That's true, as far as it goes, but here's a bit more detail.
Gravity
Everything on Earth is pulled by the same force --- gravitational attraction due to the mass of the Earth.
Everything on Earth is being pulled downward by the force of the Earth's gravity. And everything gets pulled downward with exactly the same acceleration, regardless of the size of the object. That is, a bowling ball, a tennis ball, and a ping pong ball all are subject to the same acceleration. Smaller objects are also subject to the same acceleration: a blueberry, your fingernail clippings, an eyelash -- all get pulled downwards by gravity, and all fall to the surface of the Earth. Now think even smaller. Every molecule of air is also pulled downward towards the Earth's surface. The difference is, most air molecules don't fall down to the surface. Another force opposes their fall.
Hydrostatic Equilibrium
The only reason that air molecules don't fall down to the Earth's surface is that another force pushes back against the force of gravity. That force is air pressure. You can imagine a column of air as being kind of like a spring. If you lay a spring on its side, it will be a certain length. If the spring is not too stiff and not too soft and you lay it on end, it will be shorter, because gravity is pulling it down. It won't flatten down into a pancake, because the spring pushes back against gravity. That's what keeps the air around the Earth from flattening into a tiny pancake layer on the ground: pressure pushes back against gravity.
Pressure vs. Altitude
Humans are accustomed to feeling about 15 pounds per square inch of pressure from the surrounding air.
The amount of pressure needed to push back against gravity at any given location depends upon how hard gravity is pushing down on the air. That depends upon how much air is above the spot. At sea level, the entire height of the atmosphere of the Earth is being pulled down, so the pressure is about 15 pounds per square inch. At 5,000 feet above sea level, there is less air above the spot and atmospheric pressure is about 12 pounds per square inch. So, when people say the air is "thinner" at higher altitudes, this is what they mean: the pressure is lower, the molecules of air are more spread out, and a lungful of air contains fewer molecules at high altitude.
Oxygen
The number of oxygen molecules in each lungful decreases as the altitude gets higher --- adding a few more can be a lifesaver.
Oxygen is of particular interest, because it sustains human life. Oxygen makes up about 21 percent of the atmosphere. That percentage stays the same for all altitudes within a few miles of the Earth's surface -- it isn't until dozens of miles higher that the chemistry of the atmosphere changes significantly. So at high altitudes, oxygen is still 21 percent of the total air volume, it's just that the total number of molecules in that volume has decreased. Although there are additional considerations because the human body's mechanisms for metabolizing oxygen are complex, the general rule is that the available oxygen goes down as the pressure does. So at 5,000 feet of altitude, the pressure is 80 percent of that at sea level, and the available oxygen is 80 percent of that at sea level, too.
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