Conversation so far:
who discovered the sun is the center of the solar system
The idea of the solar system was proposed by the Polish astronomer Nicolaus Copernicus who said that the Sun is the center of the Universe and planets move around it.
In what period was the discovery that the sun is the center of the solar system
The discovery of the solar system belongs to the Renaissance period, when philosophers decided to admit nothing but observation and logic in building the science enterprise, and to reject tradition.
Who supported the concept by the astronomer Nicolaus Copernicus of the solar system
German astronomer Johannes Kepler 1571-1630, supported the Copernican concept giving  planets elliptical orbits to describe their complicated motions, with the Sun in one of the foci of each ellipse.
what was the belief before Copernicus discovered the sun was the center of the solar system
The idea before Copernicus was from Ptolemy, an astronomer and mathematician who came up with the geocentric theory. He believed that the Earth was the center of the Universe.

Question: Who explained how the system moves
Self-contained rewrite: Who explained how the solar system moves