Praise be to Allah.
In defining the times of prayer, the astronomers’ calculations do not matter. For determining the time of Fajr, what counts is the appearance of a horizontal line of light on the eastern horizon. The time for Fajr starts when this line becomes clear and distinct, and it ends when the sun rises. The time for Maghrib starts when the disk of the sun has set, and it doesn’t matter if there is still light after the disk of the sun has disappeared. The time for ‘Isha’ begins when the red afterglow of sunset disappears.
The time for fasting begins when the time for Fajr begins, as we have explained above, and the fast ends when the disk of the sun itself has set, even if some of its light remains afterwards.