How can the beginning times for Fajr prayer, Ishaa prayer, and Imsak (the start of fasting) be determined in the city of Newcastle, Britain, where the light of dawn extends for long periods before sunrise and the light of twilight extends for long periods after sunset, based on the astronomical division of light into three categories?

Determining the times for prayers and for imsak (abstinence during fasting) is done by the appearance of the Sharia-stipulated signs, not by astronomical divisions. Dawn (Fajr) is when the transversal light appears in the east and ends with sunrise. Maghrib (sunset prayer) is when the sun's disk sets. Isha (night prayer) is when the red twilight disappears. Imsak begins with the entry of the Fajr time and ends with the setting of the sun's disk.