﻿ Calendar History -- Fractions of Years, Etc.
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## Fractions of Years, Etc.

Let's once again review what a synodic day, what is commonly known on earth is simply a day, really is.

### Synodic Day = 24 hours

This is what days are measured by in the solar calendar. This is also called the mean solar day, which is the basis of a calendar day. The Earth rotates a little bit over 360 degrees so that the Sun's point in the sky at NOON when it begins the synodic day is on average the same latitude the next day when a new synodic day begins. It's motion is relative to the noontime point of the Sun. A synodic day is the time it takes the sun to successively pass the meridian (astronomical noon). In a given synodic year, there is one more sidereal day than a synodic day due to the difference of four minutes a day multiplied by 365.24218967. The equivalent number for four minutes turned into a decimalized day is approximately 0.002737909333266.

### Fractions of One Year

If you really want to know where the fraction parts of each year is, you'll have to use the number 365.24218967 and divide whole numbers into it to get results.

As you can see, the Gregorian and Julian calendars have an odd assortment of days in each month. That's the basis of another subject, but for now, we want to figure out where the half of a year mark is on the calendar in relation to what day it is.

Let's start with January 1. You want to find a date on the calendar that is about half the year away from the date. If you instantly said July 1, then read on and we'll see what date is really is.

We take this synodic day figure of 365.24218967 and divide the number 2 into it. We get the answer of 182.621094835. Rounded up to the next whole integer, it's 183, or by dropping the decimal portion, it's 182.

Let's count the number of days away from January 1, naming it day 0, and counting upwards until we reach the day 182 days away. Let's assume that we're using a 365-day calendar, that is, one without a February 29.

We add the number of days in January, 31, to the number 0, and land on February 1 with the number 31, and that means that we have landed on a date 31 days away from January 1.

We add the number of days in February, 28, to the number 31, and get March 1 with the number 59.

We add the number of days in March, 31, to the number 59, and get April 1 with the number 90. So as you can see, we're not a quarter of a year away from January 1 yet, but you can guess that April 2 is.

We add the number of days in April, 30, to the number 90, and get May 1 with the number 120.

We add the number of days in May, 31, to the number 120, and get June 1 with the number 151.

We add the number of days in June, 30, to the number 151, and get July 1 with the number 181. So as you can see, July 1 is not half a year away from January 1.

We add one more day to get July 2 with the number 182, and one more day again to get July 3 with the number 183. Depending on how you round up or down, you can use either date to mark the 1/2 of a year mark on the calendar. Parts of the number of 182.621094835 straddles between the last half of day 182 and the first half of day 183. Since the decimal portion is .5 or above, many would choose day 183 to celebrate the 1/2 year mark as its technically approximately correct using the rounding up or down method.

You can find the 1/2 way point of a year on any calendar by counting up or down 182 days to get the first of two days that mark the 1/2 way point, then, going backwards, day 183 is before day 182, or going forwards, day 183 is after day 182. Even on leap year calendars, you can find the 1/2 way marks, but be careful that if you cross a February 29, that must be counted.

On a non-leap year, of course the calendar is 365 days long, and when you add 365 to January 1, you'll land at another January 11, which is the first half of two dates that correspond to going around the sun once, and a day later is January 2, the second half of two dates. Since 365.24218967 is the synodic year, Most of the one year mark falls on the next January 1, and the rest falls on the early quarter of January 2.

On a leap year, of course the calendar is 366 days long, but when you add 365 to January 1, you'll land at December 31, which is the first half of two dates that correspond to going around the sun once, and a day later is another January 1, the second half of two dates. Since 365.24218967 is the synodic year, Most of the one year mark falls on December 31, and the rest falls on the early quarter of January 1.

### Multiples of One Year

Let's say you want to land on a date exactly two synodic years from the date. Many times, it's the same date as it was two years ago, but sometimes you'll land on a date that's one day later or earlier due to the quirks of the leap year frequency and length of the calendar years.

The .24218967 portion of the synodic year is multiplied by 24 to get the hours, which is 5.81255208. then multiplied by 60 to get the minutes, which is 348.7531248, then multiplied by 60 again to get the seconds, which is 20925.187488. By dropping the whole numbers before the decimal places before you do your multiplying, you get 5 hours, 48 minutes and 45.187488 seconds.

365.24218967 times two is 730.48437934, which is almost on the .5 mark, but isn't.

365.24218967 times three is 1095.72656901, which is close to the .75 mark.

365.24218967 times four is 1460.96875868, which is close to 1461 days. As you can see, every four years, the earth is fast by a fraction of 0.03124132 of a day (or 44.9875008 minutes) every four years, which is why, on the Gregorian calender, we skip three leap years in a 400 year span, as we opt to skip a leap year day on years that are in multiples of 100 that are not multiples of 400. Example. The years 1800, 1900, and 2100 are not or will not be leap years on the Gregorian calendar, but 2000 was a leap year.

### Fractions of a Century

To get a fraction of a century, divide 36,524.218967 by the number 2 to get a 50 year mark (approx 18,262.1094835 days), the number 3 to get a 33 1/3 year mark (approx 12,174.73965566667 days), the number 4 to get a 25 year mark (approx 9,131.05474175 days), and so on as much as you want.

To get a 1/3rd of a decade ago, or 1/30th of a century ago, divide 36,524.218967 by the number 30 to get a 3 1/3 year mark (approx 1,217.473965566667 days)

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