Johannes Kepler sends his book Mysterium Cosmographicum to scholars and nobles, hoping to discuss his theories, but receives only a brief reply from Galileo Galilei. Galileo initially examines Kepler’s ideas to disprove them, yet their correspondence gradually develops into a collaboration. Kepler suggests that lenses might be used to observe distant objects, inspiring Galileo to construct a more advanced telescope.

Although they live in Germany and Italy and have never met, they exchange letters while observing the night sky. They study the Moon’s uneven surface, Jupiter’s satellites, the phases of Venus, and previously unseen stars. These discoveries strengthen their belief in heliocentrism, and they decide to publish despite the danger of being accused of heresy.

The publication provokes the Church and costs Galileo the support of the Medici family. His daughter Maria Celeste, living in a convent, resents him because the controversy has cast doubt on her own faith. When Galileo is summoned before the Inquisition, Kepler travels to Italy and urges him to escape, but Galileo chooses to stand trial.

Maria discovers the letters between the two scientists and threatens to denounce Kepler. He asks her to look through a telescope before deciding. After observing the sky and reading her father’s work, she begins to understand what drove their research.

At the trial, Galileo challenges the geocentric model with their observations. When Kepler and Maria try to share responsibility, Galileo claims all the discoveries as his own to protect them. Realizing that evidence will not change the verdict, he recants and is released.

Back at home, Galileo prepares to leave with Maria. Kepler arrives with a solution to the remaining errors in planetary motion: planets travel in elliptical rather than circular orbits. Reunited by discovery, Galileo, Kepler, and Maria lie together beneath the stars.