The whole formula is. 12742π/(23+(56/60)+(4/3600))*cos(L) L= Latitude which is either something like 9.183611 or 9°11'01 If it's style 1. Then it just uses it but if it's style 2. Then it goes degrees, minutes and seconds to pronounce 9°11'01. 9 degrees 11 minutes 1 second °+(M/60)+(S/3600) ° = degrees M = Minutes S = Seconds Then use that number in the first formula. Circumference at equator*Cos(L)= Length of circumference at that latitude divided by time which is exactly 23H 56M 4S To get the exact hour you need minutes over 60 plus seconds of seconds in an hour which is 3600 plus the hour which is 23 The diameter of the earth is 12742KM to the nearest KM and multiplied by π you get the circumference at the equator and you can convert to other units because using that formula will be KM/H to get Miles/H you divide it by exactly 1.609344 and those units per second instead of per hour you divide by 3600 and you get that. This long and complex explanation came from a NASA short document when I googled just the formula and expanded the precision here's the short document made by NASA when I searched "earth's rotational speed decreases towards the equator formula." The document that google pinned to the top was "At the equator, the circumference of the Earth is 40,070 kilometers, and the day is 24 hours long so the speed is 1670 kilometers/hour ( 1037 miles/hr). This decreases by the cosine of your latitude so that at a latitude of 45 degrees, cos(45) = . 707 and the speed is . 707 x 1670 = 1180 kilometers/hr." Source: Gsfc.NASA.gov It goes to show when you see something nice and short you can make it long and more precise based off of your insane maths.
