Good question.
One might even wonder whether the "astro" part of the word has something to do with stars, but it doesn't.
The original Greek roots are "trephein" and "strephein", which are very similar.
(The "e" and "y" English endings differ only because one of the roots was used as a noun and one as a verb.)
But a quick breakdown of the words into their original Greek parts, separating prefixes (and suffixes if there were any) shows:
- catastrophe = "cata" + "strophe" = "down" + "turn"
- atrophy = "a" + "trophe" = "not" + "nourishment"
The Online Etymology Dictionary is a great resource for tracing word origins:
1530s, "reversal of what is expected" (especially a fatal turning point in a drama, the winding up of the plot), from Latin catastropha, from Greek katastrophē "an overturning; a sudden end," from katastrephein "to overturn, turn down, trample on; to come to an end," from kata "down" (see cata-) + strephein "turn" (from PIE root *streb(h)- "to wind, turn"). The extension to "sudden disaster" is attested from 1748.
— catastrophe | Search Online Etymology Dictionary
"a wasting away through lack of nourishment," 1610s (atrophied is from 1590s), from French atrophie, from Late Latin atrophia, from Greek atrophia "a wasting away," abstract noun from atrophos "ill-fed, un-nourished," from a- "not, without" (see a- (3)) + trophē "nourishment," from trephein "to fatten" (see -trophy).
— atrophy | Search Online Etymology Dictionary