What organization lost credibility once the heliocentric theory was proven?

The Roman Catholic Church

Explanation:

Before Copernicus's Heliocentric Theory, The Catholic Church believed in Greek philosopher Aristotle's Geocentric Theory, where the Earth was the center of the universe. He believed - and I kid you not, that everything moving in the sky was propelled by the world-soul, or soul of the planet, and that their orbits were explained by huge, perfect, chrystalline spheres that contained the celestial bodies and surrounded Earth like a Russian nesting doll. The Catholic Church adopted this theory and sprinkled Jesus on top.

Copernicus (and after him, Galileo) contributed to the disproving of these literally ancient notions.