Copernicus deduced the scale of the Solar System. He did not figure out how big the Solar System was in kilometers, but he did figure out the relative size based on the size of the orbit of the Earth (i.e., on the Astronomical Unit).
Armed with nothing more than the sidereal periods of the planets, Copernicus deduced the relative spacings of all of the planets (the observable ones that is) of the Solar System. In fact, for the planets whose orbits were smaller than the Earth's, he did not even need this information.
Outer Planets
Planet Copernican Estimate (A.U.) Current Value (A.U.) Mercury 0.38 0.387 Venus 0.72 0.723 Earth 1.000 1.000 Mars 1.52 1.52 Jupiter 5.22 5.20 Saturn 9.17 9.54
The results are amazingly good.