Image by kind permission of the Master and Fellows of Trinity College Cambridge.
Galileo gradually improved the power of his telescope, grinding lenses himself, and began observing the heavens. In the first two months of 1610, he was writing The Starry Messenger, and by 12 March, the book was already printed at Venice, dedicated to Cosimo de' Medici. Galileo continued his observations with his telescope, some of which he conveyed in ciphers to Johannes Kepler, who had already responded enthusiastically with the Conversation with Galileo's Sidereal Messenger. Galileo's discovery of the 'handles' of Saturn was encoded in 'Smaismrmilmepoetaleumibunenugttaviras', which could be unscrambled as 'Altissimum planetam tergeminum observavi': I have observed the highest of the planets three-formed. Kepler deciphered this within one letter as 'Salve umbistineum geminatum Martia proles': 'Be greeted, double knob, children of Mars.' For the discovery of the phases of Venus, the code 'Haec immatura a me jam frustra leguntur oy' (this was already tried by me in vain too early) hid the message, 'Cynthiae figurae aemulatur mater amorum' (The mother of lovers [Venus] imitates the shapes of Cynthia [the moon]). Despite this exchange, Galileo never accepted Kepler's elliptical orbits.
From 1616, Galileo tried to apply his knowledge of the satellites of Jupiter to the determination of longitude at sea. In order to ensure observation at sea, the Tuscan arsenal made for Galileo a headgear which had a telescope attached. Around this time, he also designed a brass 'Jovilabe', a computing device for prediction positions of the satellites. He hoped to gain support from the Spanish crown for this project, but failed.