What is the relationship between the size of the planet and its distance from the sun?

P^2 (Earth years) = a^3 (astronomical units)

P = period
a = semi-major axis of elliptical orbit

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Kepler's third law of planetary motion is a mathematical relation between orbital periods and distances. It allows astronomers to measure masses of celestial objects. Johannes Kepler went to work for Tycho Brahe near the end of Tycho's life. When Tycho died, Kepler used Tycho's data to deduce three laws of planetary motion. Because Tycho's data were far more accurate than any previously collected data on planetary positions neither Ptolemy's nor Copernicus's models of the cosmos worked.

C. gemstones they are the only non metallic mineral from the list.