How did the early Muslims determine the times of prayer, especially for Isha and Fajr, and were they approximate?

The early Muslims used to know the times of prayer by observing the shadow at Dhuhr (noon) and Asr (afternoon), by the sunset for Maghrib (sunset prayer), by the disappearance of the red twilight for Isha (night prayer), and by the true dawn for Fajr (dawn prayer). People have come to rely on the Gregorian calendar to know prayer times, which has led many to be ignorant of how to determine the times without the calendar. And Allah knows best.