Here are some examples:
Not capitalized:
* The Earth's atmosphere is composed mostly of nitrogen and oxygen.
* The atmosphere was thick with smoke after the fire.
Capitalized:
* The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission is studying the Martian atmosphere.
* We learned about the atmosphere in our science class. (If "atmosphere" refers to a specific course title)
In most cases, "atmosphere" is a common noun referring to the layer of gas surrounding a planet or celestial body. It's only capitalized when it's part of a proper noun, like a specific mission or title.