Calculating the periods of Galilean satellites from the <i>Sidereus nuncius</i> data

In October 1611, a papal diplomat and multi-talented scholar, Monsignor Giovanni Battista Agucchi, succeeded in calculating the periods of the Galilean satellites from the mere data disclosed by Galileo Galilei in Sidereus nuncius , published in March 1610. This was 6 months before Galileo published his first periods, which were not significantly better. This feat has so far been virtually ignored by historians of science, at least with regard to the method that may have been used. The author has been able to identify the method and tried to replicate the procedure used by Agucchi. Using two different strategies, he reached results of comparable accuracy. Several useful insights can also be drawn from this work into the procedures used by early observers in observing and deriving satellite periods.