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Yvonne,

Technically, our evidence lies in a phenomenon called parallax, although measurable stellar parallax is small and was not achieved until Friedrich Bessel did so in 1838.

Historically, Aristarchus of Samos first posited a heliocentric (sun-centered) solar system. Nicholas Copernicus would later poplularize the theory by providing a mathematical basis for the heliocentric system. The model he used to describe the motion in a heliocentric system had one failing. Copernicus' model was based on circular planetary orbits and his mathematical models became somewhat erratic when attempting to explain the apparent retrograde motion of the planets.

Later, Tycho Brahe would provide observations which tended to support the Copernican theory. While employed in this task Brahe would acquire, as an assistant, Johannes Kepler, whose mathematical work, known as Keplar's laws, and a redesign of the Copernican model (based on Brahe's observations) to include elliptical orbits, established the basis for modern physical astronomy.

It would not be until Galileo Galilei made his telescopic observations of the phases of Venus that incontrovertible proof of the Copernican theory was provided.

I hope this answers your question, and thanks for using Mad Scientist.

Joe

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