In which of the four time periods did the sun-centered model gain widespread acceptance, meaning that nearly everyone who looked at the evidence concluded that it was correct?
a. ancient greece (through ptolemy, ~150 a. d.)
b. early copernican revolution (about 1543 – 1600)
c. later copernican revolution (about 1609-1630)
d. newton and beyond (after about 1687)

c. Later Copernican Revolution (about 1609-1630)

Explanation:

During the Middle Ages, it was believed that the Earth remained motionless, occupying the center of a universe subject to uniform circular motion where Earth was the only world. All this because the only accepted idea was that of Ptolemy.

Until the Polish astronomer Nicolaus Copernicus proposed that the Earth annually orbits the Sun and rotates once a day on its own axis.  He also dared to affirm that the other planets also orbited the Sun as a fixed point. This meant the Earth was no longer unique, nor did it occupy the center of the known universe.

It was on this main idea that the Copernican revolution was based, by changing the Earth for the Sun as the center of the Universe, bringing with it a paradigm shift from the ptolemaic model of the heavens (the stationary Earth in the center of the universe) to the heliocentric model with the Sun in the center of the solar system.

These ideas were published by Copernicus in De revolutionibus orbium coelestium.

this is a good question! i'll do some research and come back when i have the answer!