James (26 March 2017)
"Avoiding errors in some web sites for calculating dates"



Avoiding errors in some web sites for calculating dates

By James: God Bless

In my analysis of the web site Time and Date, I have found two sets of errors in the web site calculations.

https://www.timeanddate.com/date/durationresult.html?m1=2&d1=1&y1=1900&m2=3&d2=1&y2=1900&ti=on

First a little history. By the time the 1500s AD came there were many calendars in use and all of them had a problem. The events that were, as an example, a spring festival, would over the years back up in time on the calendar to come closer to winter, forcing a periodic reset.

As the studies about a new calendar continued in the 1500s they found the best solution. They decided to define a leap year as a year divisible by 4 and a century leap year divisible by 400. If the century year was not divisible by 400 then it was a non leap year as 1700, 1800, 1900, and 2100 are non leap years, while 2000 was a leap year. This calendar was not accepted by most nations then, as they had their other variations, but eventually they did use the modern Gregorian calendar.

There was also the problem of the backup of the festivals that needed to be adjusted so that Easter came around the equinox. They decided to drop 10 days out of October to allow Easter to line up with the spring equinox. That took care of the backward march of the equinox, which made Easter earlier each year. This was done October 4, 1582, making the next day October 15, 1582. Effectively 10 days were dropped from the calendar that year.

The Gregorian calendar is accurate to 1 day in about 3236 years. This will not always continue into the far future due to the very slow decrease in the earth's rotation and changes in the orbital shape, all part of the interaction of gravitational interaction of the moon and the other planets.

Time and Date is easy to use and gives accurate results only from March 1, 1700, to the present time, or in between non century years before Feb 28, 1700. It will correctly calculate 1800 as a non leap year, but it incorrectly calculates 1700 AD as a leap year, which it is not.

Time and date has another error for October 1582. This has to do with the 10 days there were deleted. This 10 day span is not accounted for.

The only accurate way of determining all dates that span years BC, and through to the present and future, is to use the Julian Date Calendar (JD) which was developed for astronomical observations and hence independent from local and historical calendars. This site can be accessed by this URL

 http://aa.usno.navy.mil/data/docs/JulianDate.php

Some examples of the errors and how to avoid them.

If you were to find out how many days there are in October 1582, Time and Date will give an answer of 31 days, not 21 days.

Testing October 1582 using the JD (Julian Date) calendar goes like this;

Input to JD site, Oct 4, 1582, to get the JD 2 299 159.5
 
Input Oct 15 to get JD 2 299 160.5.   You will see that it is a 1 day span, because of the removal of the 10 days.

JD 2 299 160.5 - 2 299 159.5 = 1 day



Here is the leap year test for February 1, 1700, to March 1, 1700.

Feb 1, 1700 is JD 2 342 003.5 and March 1, 1700  JD 2 342 031.5

JD 2 3342 031.5 - 2 342 003.5 = 28

The difference is 28 days, not including March 1, 1700. 1700 is not a leap year. Century years prior and including 1700 AD that are not divisible by 400 are also not leap years.

When using Time and Date, for Feb 1, 1700 to March 1, 1700, you will be given 29 days, which is incorrect. Note: use March 1, not inclusive, to test the calculation.
If you were trying to understand why some of your calculations for long spans of time were wrong, or were out of place, now you know why, and what you can do about it.