Final answer:
Copernicus hesitated to publish his heliocentric model due to fear of persecution and the contradiction it posed to the Church-supported Ptolemaic system, but he eventually published 'On the Revolutions of the Heavenly Spheres' in 1543.
Step-by-step explanation:
Nicolaus Copernicus was reluctant to publish his ideas regarding the heliocentric model of the solar system primarily due to fear of religious persecution and the clash with established astronomical beliefs. The prevalent Ptolemaic system was deeply supported by the Church, which held Earth at the center of the universe, making any contrary assertion potentially heretical. After Copernicus's longtime hesitation, his friend Rheticus published a precursor to his work which prompted Copernicus to finally release "On the Revolutions of the Heavenly Spheres" in 1543, which he dedicated to the pope in hopes of mitigating backlash. This pivotal moment marked the beginning of a gradual but profound shift in astronomical understanding, leading to the Scientific Revolution.