Armed with nothing more than the sidereal periods of the planets, Copernicus was able to deduce the relative spacings of all of the planets (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.

Inner Planets

Outer Planets

It was for the outer planets that he needed to know the sidereal revolution periods.

So, given some rather fundamental numbers about the planets, Copernicus based on his helio-centric theory was able to deduce the size of the Solar System.