Sentence:  The discussion that revolved around the admissibility of <WSD>eccentrics</WSD> and epicycles liedsic at the core of this theoretical discussion, and those who would not allow such concepts took the position that such <WSD>eccentrics</WSD> and epicycles would then introduce a center of heaviness, other than the Earth, around which celestial simple objects would then move. 
Meaning of the word marked with <WSD> tags:  A disk or wheel with its axis off centre, giving a reciprocating motion.