Stratospheric is the adjective of
Stratosphere which means
the layer of the earth's atmosphere above the troposphere, extending to about 50 km above the earth's surface.
A stratospheric success, so what does it mean?
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The stratosphere is the layer above the troposphere but below the mesosphere and the thermosphere.
So while the stratosphere is only the 3rd highest atmospheric level for our planet, it is used in the word Stratospheric to describe something extremely high. So something that is a stratospheric success is an amazing success.
Tropospheric, Mesospheric and Thermospheric are also used as adjectives, but they are only used to describe atmospheric nouns and subjects. Stratospheric is the only atmosphere layer that is used as an adjective outside of atmospheric conditions.