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How did Johannes Kepler use Tycho Brahe’s observations to develop the laws of planetary motion?

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Illustration showing the eight planets of the solar system in order from the Sun-Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune-depicted to scale by size, with labeled diameters in miles and kilometers. The Sun is partially visible on the left for comparison. — Solar system The planets (in comparative size) in order of distance from the Sun.

Johannes Kepler developed his laws of planetary motion by utilizing the exceptionally accurate observational data of Tycho Brahe, which he inherited following Tycho's death in 1601.12

Kepler initially sought to refine his own cosmological theories using Tycho’s data, specifically focusing on the motion of Mars. While attempting to model the orbit of Mars, Kepler found that traditional circular models—including those using Ptolemy’s equant law—could not reconcile with Tycho’s observations, which were accurate to within 2 minutes of arc.3

Because the discrepancy between his circular models and Tycho’s data remained at approximately 8 minutes of arc, Kepler was forced to abandon the assumption of circular orbits. By rigorously analyzing the data, he discovered that planets move in ellipses with the Sun at one focus and that they sweep out equal areas in equal times. These findings, published in Astronomia Nova (1609) and later Harmonice Mundi (1619), fundamentally transformed astronomy by replacing ancient geometric assumptions with empirical, mathematically derived laws.31