Radical:

• The Earth is moving.
• The Earth is not in the center of the universe.
• The Earth is just another planet - nothing special.
• Space is big - the distance from the Sun to the nearest stars is, at a minimum, hundreds of times the size of Saturn's orbit.

Conservative:

• Uniform Circular Motion - Copernicus still clung to this old notion.
• Epicycles - Since the planets are NOT moving along perfectly circular orbits with perfectly constant speed, Copernicus had to slip in a few epicycles to make his predictions of planetary positions match the observations.

However, while the Copernican Model was incorrect, the Copernican Hypothesis was.. Here in lies the much broader impact generated by Copernicus:

The Copernican Revolution
In Europe, the works of Aristotle and Ptolemy impressed officials of the Church in their breadth, depth, and apparent truth. An effort was made to incorporate the cosmology of Aristotle and the astronomy of Ptolemy with the dogma of the Church, culminating in the publication of Summa Theologica by Thomas Aquinas. The Catholic Church puts De Revolutionibus on its Index of Prohibited Books.

By the 15th century exploration of new trade routes via sea-going ships begins in earnest. New navigation technologies are needed (based on astronomical knowledge). The Catholic Church's power begins to erode. People begin asking for a new way of worship. The Protestant Reformation!

In 1962, Thomas Kuhn wrote The Structure of Scientific Revolution, and fathered, defined and popularized the concept of paradigm shift. Kuhn argues that scientific advancement is not evolutionary, but rather is a "series of peaceful interludes punctuated by intellectually violent revolutions", and in those revolutions "one conceptual world view is replaced by another".

Think of a Paradigm Shift as a change from one way of thinking to another. It's a revolution, a transformation, a sort of metamorphosis. It just does not happen, but rather it is driven by agents of change. These agents of change helped create a paradigm-shift moving scientific theory from the Ptolemaic system to the Copernican system.