Badeni is a disgraced former monk who appears as a central figure in the second part of the story. His pursuit of knowledge above all else led him to break the strict regulations of the church, resulting in a severe punishment where his eyes were burned with candlewax. This traumatic event left him partially blind, and he now wears an eyepatch over his damaged right eye. Following this punishment, he was banished to a remote rural village.

Badeni possesses a brilliant and highly analytical mind, with an extraordinary amount of knowledge and exceptional calculative abilities. He is characterized by a bold, confident, and stubborn personality, willing to endure any pain or humiliation to continue his study of the heavens. Unlike ordinary clergymen who might self-flagellate to atone for sins, Badeni accepts physical punishment as a transaction that buys him time to conduct what the church considers profane research. His defining motivation is the search for the moment that makes life truly special, which he believes lies in uncovering the truths of the cosmos. He holds a conviction that heliocentrism does not contradict faith but rather reveals the beauty and complexity of God's creation, arguing that the church suppresses this knowledge out of fear of being wrong. When asked what is needed to change the world, he famously answers with a single word: knowledge.

In the narrative, Badeni forms an initially reluctant partnership with Oczy, a young man with excellent eyesight but a fear of looking at the sky. While Badeni provides the intellectual framework and understanding of astronomy, he relies on Oczy to perform the necessary observational work that his damaged eyesight prevents him from doing. Their relationship is pragmatic rather than altruistic, characterized by a clash of ideologies and personalities, yet it deepens into a powerful collaboration as they face adversity together. Badeni also enlists the help of Jolanta, a research assistant who aids their cause. His key conflict is with the Inquisition, particularly the inquisitor Nowak, who relentlessly pursues heretics who study heliocentrism.

Throughout his arc, Badeni undergoes notable development. Initially, his desire to be the sole possessor of his research leads him to consider destroying Oczy's book, reflecting a self-centered possessiveness over knowledge. However, his mindset evolves as he argues with Oczy and comes to understand the importance of passing knowledge to future generations. When he and Oczy are captured and tortured by the Inquisition, Badeni demonstrates empathy for his companion, remembering his own torture and ultimately revealing the location of his hidden documents to prevent Oczy from losing an eye. Facing execution, he devises a plan to ensure the survival of their heliocentric research, accepting that the chances of success are infinitesimally low but believing that even a single inspired reader could eventually lead to the theory being proven and accepted. He faces his death with a sense of inner peace, expressing hope that heaven awaits him. Among his notable abilities is his talent for simplifying complex astronomical concepts, demonstrated when he uses a circumambulatory model to explain retrograde planetary motion in a way that is accessible to both Oczy and the audience.