Hi Aidan, great question! The sun does in fact heat up the air in our atmosphere directly because the light that the sun produces carries energy. That energy is what heats up the Earth in general and provides all of the energy that goes into the various cycles on Earth (i.e. carbon, nitrogen, and water cycles). Light is made up of photons, tiny packets of electromagnetic radiation. These photons can be absorbed by molecules in the atmosphere, causing the molecules to have higher energy; on a larger scale, that means that the air in the atmosphere is heating up. Some molecules called greenhouse gases, like carbon dioxide, are better at absorbing that energy and tend to not let photons back out of the atmosphere. This is the mechanism behind climate change. Beyond that, some areas of the globe might have a hotter atmosphere than other parts. This will create a pressure difference that leads to the movement of the molecules in air. To you and me, this is called wind!
To summarize, yes, the sun does directly heat up the air molecules in our atmosphere and this is essential to all life on earth as well as weather.
The sun does provide some heat directly to the atmosphere, but much of the heating of the atmosphere comes indirectly from the sun through other means. For light to directly provide heat to a substance, that substance must absorb the light. "Absorbing" light essentially means that the amount of energy in a photon of light causes the molecules, atoms, and electrons of the substance to change their motion.
A more detailed answer requires fairly advanced physics, but for now take that there are discrete levels of energy to the motion of these particles, and also discrete amounts of energy that can be transferred. Therefore, for a substance to absorb light, the light must have the right amount of energy to push a molecules/atom/electron into a new level or type of motion.
If light is absorbed, it obviously does not pass through the substance, and the substance is opaque. In contrast, a substance is transparent when the energy of the light is insufficient to excite the particle to that higher level, and instead the light passes through. Most gases in Earth's atmosphere are transparent to most wavelengths of incoming sunlight. Some of the other components of the atmosphere, primarily clouds (liquid water), water vapor (gaseous water), and certain compounds (e.g., ozone) do absorb these wavelengths, totalling ~23% of incoming energy contained in sunlight. However, the rest of the sunlight reaches the surface of Earth.
Going back a few sentences, recall that being opaque means that light is absorbed. Since the ground (and most other stuff on Earth's surface) is opaque, this means that the remaining 77% of sunlight is absorbed at Earth's surface. (Mostly. Some is reflected, but the majority is absorbed.) However, the process doesn't end there. Some of that absorbed energy heats and evaporates water, which then goes up into the atmosphere. Those warmer molecules can bump into other molecules and particles in the atmosphere, increasing the temperature. In addition, some of the energy which is absorbed is re-emitted from the ground as light with a different energy (and correspondingly a different wavelength). Some gases in the atmosphere do absorb light of these wavelengths, and thereby capture another portion of the energy which was in the incoming sunlight, albeit not directly from the sun.
This related question on ScienceLine may also be of interest.
Since the sun is not in direct contact with our atmosphere, the sun does not heat our atmospheric air directly. If it was heated directly, we would long have been carbonized.
Instead, the sun heats our atmosphere indirectly through radiation. Radiation does not require contact and can transfer heat through empty space. The sun gives off invisible, infrared rays, which are absorbed by molecules in our atmosphere, which then become heated.
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