In his play A Winter's Tale Shakespeare writes of the Isle of Delphos and the oracle in Apollo's Temple (Act II, Scenes 1 &3 and Act III, Scene 2). He also writes of Bohemia having a sea coast so perhaps we should not take Shakespeare's geography too seriously. Delphi is actually on the side of Mount Parnassus about 10 miles away from the village of Arachova and by no stretch of the imagination an island! However, the oracle of Delphi was well known in the ancient world and was considered by the ancient Greeks to the centre of the world. More specifically the Omphalos Stone at the Temple of Apollo was the exact centre of the world. The Omphalos Stone is divided into twelve to show the 12 settlements or divisions of the ancient world which corresponded to the twelve signs of the zodiac. Tudor play audiences would have been familiar with the oracle and the three main Delphic maxims including "Know Thyself" which was carved into the temple walls. The other two are "Nothing in Excess" and "Be Careful What You Promise". Know Thyself and the phrase "As Above So Below" (from the emerald tablets of Hermes Trismegistus thought to date from the 6th or 7th century CE ) form part of the basis of the Hermetic tradition which was important in the Tudor period. What happens high above in the heavens affects what happens down below on the Earth. Even in Isaac Newton's time this ancient philosophy was still well regarded.
When the heavens are ordered and harmonious there will be harmony and peace on Earth. When the heavens are disordered (new stars, eclipses, comets) there will be turmoil on Earth. This world view was widely held in Shakespeare's time and is reflected in his plays. Personally I have never found Winter's Tale a very satisfactory play. Its a curate's egg and only good in parts. Whilst it offers the possibility of redemption and putting the past right the idea of a statue coming to life is rather odd as is "exit pursued by a bear"! The unjustified death of Mamillus also casts a shadow over the play which is not redeemed at the end.
Finally in addition to Delphic wisdom another idea which held sway in the Tudor era was the Pygthorean concept of the music of the spheres. In the late 1960s several German musicians tried to recreate the music of the spheres and groups like cluster (later known as Kluster) and Amon Duul created a genre of music called Kosmic Music which was dubbed Kraut Rock by the late DJ John Peel. A few days ago I received a new CD of Kosmic Music from the Dusseldorf based band Vibravoid called Vibrations from the Cosmic Void. This music really does sound like it comes from outer space with the spacey sounds representing the passage of the planets and stars in the night sky.