The play stays generally faithful to Galileo's science and timeline thereof, but takes significant liberties with his personal life. Galileo did in fact use a telescope, observe the moons of Jupiter, advocate for the heliocentric model, observe sunspots, investigate buoyancy, and write on physics, and did visit the Vatican twice to defend his work, the second time being made to recant his views, and being confined to house arrest thereafter.
One significant liberty that is taken is the treatment of Galileo's daughter Virginia Gamba (Sister Maria Celeste), who, rather than becoming engaged, was considered unmarriageable by her father and confined to a convent from the age of thirteen (the bulk of the play), and, further, died of dysentery shortly after her father's recantation. However, Galileo was close with Virginia, and they corresponded extensively.