When I was at school in the 1960s and 1970s we were taught the Anglo-Saxon's were defeated in 1066 and the middle ages ended in 1485. However, the past is not that simple. The British Library are currently hosting an exhibition of manuscripts called Anglo-Saxon Kingdoms Art, Word and War (https://www.bl.uk/anglo-saxons). Although most of the surviving manuscripts are royal charters and ecclesiastical in nature there are a few scientific items that have survived. Harley MS2506 is an astronomical compilation from about 990 CE with added illustrations from the 11th century. This work in Latin draws on Pliny the Elder and Marcus Cicero but the drawings are Anglo-Saxon. The phases of the Moon are drawn only in outline and show no details of the Lunar surface.
The 11th century manuscript MS Tiberius B contains map of the known world. This is sometimes known as the Cotton map. It shows Great Britain in some detail as well as the Scottish islands. Of course it was well known at this time that the Earth was spherical not flat and Bede in his work "The Reckoning of Time" wrote that "the roundness of the Earth, for not without reason is it called 'the orb of the world' on the pages of Holy Scripture and of ordinary literature. It is, in fact, set like a sphere in the middle of the whole universe."
When Isidore of Seville was not busying himself hunting for witches or producing racist literature and anti-jewish tracts he tried to compile a book of containing everything there was to know. "De Natura Rerum" or On the nature of things that was dedicated to the Visogothic King Sisebut in 612 or 613 CE. Isidor took much of his text from Lucretius (99 to 55 BCE) and his set of six didactic poems also called De Natura Rerum. Isidor's work was hardly original and was intended to be a summation of everything known about the natural world up to that point. Isidore included a map of the Universe with the Earth at its centre. Venus is called Lucifer and Vesper could be either Mars or Venus in the evening sky and Jupiter is called Fofton.
It is clear that there has been few scientific advances in the Anglo-Saxon period (in fact the Anglo-Saxons did not even have a word for the natural sciences). The Anglo-Saxons did not go away with the Norman conquest in 1066 their ideas, art and culture endured and shaped people's behaviour for many centuries. In Shakespeare's time the vast majority of people believed that the Earth was the centre of the Universe and some still believed that the Earth was flat. Astrology still was held in high regard and it is clear that people thought illness could result from an unfavourable alignment of the planets. Shakespeare was writing in a time when the old beliefs were being replaced by science, logic and reason and his works are a reflection of the time in which they were written. But science and religion need not be enemies. In the 20th century Albert Einstein wrote "Science without religion is lame. Religion without science is blind ". Einstein also wrote that "Everyone who is seriously involved in the pursuit of science becomes convinced that a spirit is manifest in the laws of the universe – a spirit vastly superior to that of man". In Shakespeare's time such views would have got a scientist in serious trouble with the church but thankfully today we live in a more enlightened age.