Iuppiter comes from the vocative of the Indo-European *dyeus-patēr, cognate with Zeus in Greek. However, as *a > a in Latin and 'pater' survives elsewhere in Latin, one would expect Iuppater. How has the /a/ changed to an /i/?
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1"A well-known Latin sound change turned all short vowels in word-medial open syllables to i" (TKR) latin.stackexchange.com/a/1908/39 – Alex B. Jan 10 at 18:44
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You're absolutely right that PIE *a gives Old Latin /a/. But somewhere between Old Latin and Classical Latin, vowel reduction happened.
Basically, Old Latin stress was always on the first syllable. So short vowels in other (non-stressed) syllables tended to get reduced, sort of like how English keeps the i in "combine" but reduces it in "combination".
In most instances, the reduced vowels became /i/. This is why /i/ appears in lots of prefixed verbs: the a in faciō is reduced to the i in afficiō, for example. (It's not always an i: consonant clusters and r, for example, tend to turn it into an e instead, which is why the participle of afficiō is affectus.)
That's what happened in this case. In Old Latin, the word was something like Jup-pater, from Proto-Italic Djou-patēr; vowel reduction then turned the a into an i, giving Juppiter.
(Sometimes it's written Jūpiter, sometimes Juppiter; this alternation comes from the "littera rule", named for lītera~littera.)
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1As a small quibble, Iuppiter is thought to come from a vocative rather than a nominative, so *diou-pater. – TKR Jan 10 at 19:10
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