How did the Rudolphine Tables use Tycho Brahe's astronomical observations?

The Rudolphine Tables, published by Johannes Kepler in 1627, relied principally on the extensive and highly accurate astronomical observations amassed by Tycho Brahe during his lifetime.1

Kepler inherited this critical data after Tycho’s death in 1601. By utilizing these observations—which were accurate to within 2 minutes of arc—Kepler was able to reform the foundations of practical astronomy. The tables used Tycho's data in the following ways:2

• Star Catalog: Kepler expanded Tycho’s original list of 777 stars to include 1,005 positions, creating the most accurate pretelescopic star catalog of its time.1
• Planetary Motion: The precision of Tycho’s data was essential for Kepler to move beyond ancient circular models. It provided the empirical evidence necessary for Kepler to discover his laws of planetary motion, including the realization that Mars moves in an elliptical orbit.2
• Technical Improvements: The tables incorporated Tycho’s observations to include new corrective factors for atmospheric refraction and utilized logarithmic tables to improve calculation accuracy.1