Copernicus and Galileo opened the door to what is now modern science. What did they do that so profoundly changed the way we think today?
Copernicus altered the model of the solar system that stood for about 1500 years by placing the sun at the center, rather than the earth. When he made this change, his model became more useful at explaining observations, making predictions and opening up new areas of study.
When Galileo heard about a toy with two lenses that made things appear closer, he added to the understanding of the solar system. He modified the toy to create the telescope. With this telescope, he studied Jupiter. He noticed four objects that moved each night. He made notations of this motion and concluded that these objects must be moons orbiting Jupiter. This provided support for Copernicus because objects orbiting Jupiter, couldn't be orbiting Earth. This provided evidence that the Earth at the center of the solar system couldn't be supported any longer, therefore, Copernicus had created a model of the solar system that explained what Galileo observed.
So, the use of technology, the telescope, helped to demonstrate the heliocentric (sun centered) model was the best explanation for explaining the solar system.