ABSTRACT
Astronomers also counted how many moons and days were observed in the cycles of their seasons. Such measurements inspired disparate cultures to design calendars in different ways. Let Ts denotes the time duration of one revolution of the Earth around the Sun, more commonly known as a year. Let Te denotes the time duration of one complete rotation of the Earth, more commonly known as a day. e exact values of Ts and Te are of course constantly varying, since the orbits of the stars and planets in the universe are themselves continually changing. Every galaxy exerts gravity on every other galaxy, and all the stars and planets in each galaxy exert gravity on each other. However, from the mea-
surements made of Ts and Te, we estimate the ratio Ts/Te to be today ~365.242199. It is convenient, therefore, to make a year last 365 days, as did the ancient Egyptians. e problem that arises, both for keeping track of history, and for making predictions about the future, is that a er some time, this seemingly small discrepancy, equal to 0.242199, becomes a large and inconvenient error. Since, 0.242199 is almost 6 h, or one-fourth of a day, one simple solution is to add one extra day for every 4 years. Indeed, in the year 237 BC, the ruler of Egypt, Ptolemy III exactly proposed this modication to the Egyptian calendar. is proposal met some resistance in Egypt, but a few years later, Julius Caesar adopted the practice, and for this reason, this calendar became known as the Julian calendar.†
A day with one extra day is called a leap year. e Julian calendar assumes that a year is exactly 365.25 days long, which is, still, slightly greater than 365.242199. So now, we have an error in the opposite direction, albeit smaller. One solution to this new problem is the Gregorian calendar, named a er Pope Gregory XIII, who was responsible for its adoption. In the Gregorian calendar, leap years are dened as those divisible by four, except not those divisible by 100, except not those divisible by 400. With this rule, a year becomes 365 + 1/4 − 1/100 + 1/400 = 365.2425 days long, a much better approximation.
