The person who compiled the large set of accurate observations of planetary positions that formed the basis for proving that planets move in elliptical orbits around the sun was

Correct

Explanation:

Tycho Brahe (1546-1601) was a Danish astronomer who in his later years became official astronomer for Holy Roman Emperor Rudolph II.  He built an observatory there in Bohemia from which he made extremely detailed and accurate records of planetary positions.  Brahe's own theory of planetary motion was that both the earth and the sun were centers -- that the sun revolved around the earth but the other planets revolved around the sun.  Johannes Kepler served as Brahe's assistant. After Kepler's death, Kepler used Brahe's data on the planets' positions to show that all the planets (including earth) moved around the sun in elliptical orbits.

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