I think there is a problem with your math. 100 miles = 528,000' x 3.1416 x 2 = 1,658,764.8' / 360 = 4,607.68' / 60 = 76.8' per minute of arc at 100 miles.
? confused ? How is it wrong? 100 miles, 5280 feet a mile (528,000), x Pi (3.1416) x 2 gives you the circumference. Divide the circumference by 360 then divide that by 60 to get the arc minute.