The actual one full cycle of seasons is 365 days 5 hours and 48.75 minutes. Until 1582, the calender used in the western world took the year to be exactly 365 days and 6 hours long. In 1582, corrections were suggested to match the yearlength to the exact full cycle of seasons. The correction suggested would have been:
(A) reducing number of leap days over a cycle of 400 years.
(B) reducing numbers of days in every February.
(C) adding one day to every July.
(D) adding a number of extra days in 1582 to realign the calendar. 
   Please give detailed solution.

Asked by chandubeats21 | 17th May, 2017, 07:12: PM

Expert Answer:

Actually, this calendar and calculation gave birth to leap days and leap years.
According to the Gregorian calendar (which is in use today), the year is intended to be of the same length as the cycle of the seasons. However, the cycle of the seasons, technically known as the tropical year, is approximately 365.2425 days. If the calendar year always consisted of 365 days, it would be short of the tropical year by about 0.2422 days every year. Over a century, the calendar and the seasons would depart by about 24 days!!. To synchronise the calendar and tropical years, leap days are periodically added to the calendar, forming leap years. If a leap day is added every fourth year, the average length of the calendar year is 365.2425 days.
But according to Julian calendar, "every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 were not leap years, but the years 1600 and 2000 were. In this case, the calendar year is longer than the tropical year by about 0.0078 days (almost 12 minutes).
So, adding an extra day to calendar every four years compensates for the fact that a period of 365 days is shorter than a tropical year by almost 6 hours.

Answered by Sivanand Patnaik | 19th May, 2017, 09:41: AM