Astronomy was actually a very important science during the Medieval period, particularly because of the importance of being able to calculate the changing dates of Easter in the Roman Catholic calendar. Easter, or pacha, was one of the most important festivals of the medieval Christian year, and was bound up with the importance of seasonal calculations in a largely agrarian economy. Alongside the expected Church records and monastery annals, it was popular for people to have kept Books of Hours which contained detailed calendars of festivals and saints days. The celebration of saints' days was also important, and in the cases of local saints often served as much as political events as religious. In a society wherein church attendance was often mandated by law, this in fact meant that a medieval population would have, in fact, been incredibly aware of the date.

Part of this can be seen in the rich medieval literary tradition of annals and chronicles which keep very detailed records. Chroniclers such as Thietmar of Merseburg or Regino of Prüm will chronicle events down to the exact day of the month. The Anglo-Saxon Chronicle also records prominent events such as major battles or the deaths of kings with specific dates. The knowledge of the year takes on major importance towards the end of the 10th century. As the year 1000 approaches, growing panic about an approaching Domesday spreads throughout Europe. Some of this is influenced by events, such as the increasing Viking raiding around England in the later years of the tenth century.

Some reading:

Grant (1996), The Foundations of Modern Science in the Middle Ages

Hannam (2011), The Genesis of Science: How the Christian Middle Ages Launched the Scientific Revolution

Huff (2003), The Rise of Early Modern Science: Islam, China, and the West

Lindberg and Shank (eds.) (2013), The Cambridge History of Science, Vol.2: Medieval Science

Holland (2008), Millenium

Duffy (2006), Marking the Hours: English People and their Prayers 1240-1570

Wieck (1988), Time Sanctified: The Book of Hours in Medieval Art and Life

Did the wealthy and or "scientific" community have a knowledge of this much earlier?