In 1583, Dee met the impoverished yet popular Polish nobleman Albert Łaski, who, after overstaying his welcome at court, invited Dee to accompany him back to Poland. With some prompting by the "angels" (again through Kelley) and by dint of his worsening status at court, Dee decided to do so. He, Kelley, and their families left in September 1583, but Łaski proved to be bankrupt and out of favour in his own country. Dee and Kelley began a nomadic life in Central Europe, meanwhile continuing their spiritual conferences, which Dee detailed in his diaries and almanacs. They had audiences with Emperor Rudolf II in Prague Castle and King Stephen Bathory of Poland, whom they attempted to convince of the importance of angelic communication. The Bathory meeting took place at the Niepołomice Castle (near Kraków, then capital of Poland) and was later analysed by Polish historians (Ryszard Zieliński, Roman Żelewski, Roman Bugaj) and writers (Waldemar Łysiak). While Dee was generally seen as a man of deep knowledge, he was mistrusted for his connection with the English monarch, Elizabeth I, for whom some thought (and still do) that Dee was a spy. The Polish king, a devout Catholic and cautious of supernatural media, began their meeting(s) by affirming that prophetic revelations must match the teachings of Christ, the mission of the Holy Catholic Church, and the approval of the Pope.
Dee was a friend of Tycho Brahe and familiar with the work (translated into English by his ward and assistant, Thomas Digges) of Nicolaus Copernicus. Many of his astronomical calculations were based on Copernican assumptions, although he never openly espoused the heliocentric theory. Dee applied Copernican theory to the problem of calendar reform. In 1583, he was asked to advise the Queen on the new Gregorian calendar promulgated by Pope Gregory XIII from October 1582. He advised that England accept it, albeit with seven specific amendments. The first was that the adjustment should not be the ten days that would restore the calendar to the time of the Council of Nicaea in 325 AD, but by eleven, which would restore it to the birth of Christ. Another proposal of Dee's was to align the civil and liturgical years and have them both start on 1 January. Perhaps predictably, England chose to spurn suggestions that had papist origins, despite any merit they may have had.