Leap-128 Based years
More accurate leap year rules based on a earth solar calendar.
By Michael Chungkun Chen
Copyright © July 18, 2002 All Rights Reserved.
Permission to use ideas and equations are freely granted as long as the original author is acknoledged.
While programming a calendar structure, I found a reason to suspect that the gregorian rules,
no leap year every 100 years unless the year is divisible by 400, was flawed. We would have
an one day discreprancy every 3320 years. In the life span of a person this is not a big deal.
We would never have to worry about this personally, but this will be a problem in the future
unless we adopt a non earth solar year. Even if we do begin to populate other planetary bodies,
We may still retain our earth-solar years, for birthdays and anniverseries if nothing else.
I propose a different method for leap year corrections which may be simpler. We have an extra
day every four years, unless the year is divisible by 128. And every 88642 years we have a special
leap year ourside our normal 4 year leap year interval. And every 11912250000 years we skip
the leap year. Correction factors may be added in the future when if necessary.
As you can see from the data below, this new method has a higher precision, and forgoes the
quadcentenial adjustments the Gregorian corrections required. A simple 128
no leep year rule
would be easy to remember, and 88642 years from now, we would only be off by one
day.
| Number of seconds in a year | 31556925.9747 | ||||||||||||
| Precise Days in a year | 365.2421987813 | ||||||||||||
| Years | 1176000 | 128 | 88642 | 11912250000 | 2002 | 2048 | 2100 | 2200 | 2500 | 3000 | 3320 | 2600 | 2700 |
| Accurate Days | 429524825.8 | 46751.00144 | 32375798.98 | 4.35086E+12 | 731214.882 | 748016.0231 | 767008.6174 | 803532.8373 | 913105.497 | 1095726.596 | 1212604.1 | 949629.7168 | 986153.9367 |
| Non Leaped Days | 429240000 | 46720 | 32354330 | 4.34797E+12 | 730730 | 747520 | 766500 | 803000 | 912500 | 1095000 | 1211800 | 949000 | 985500 |
| Missing Days | 284825.7667 | 31.001444 | 21468.98437 | 2885132432 | 484.8819601 | 496.023104 | 508.6174406 | 532.8373187 | 605.4969531 | 726.5963437 | 804.0999537 | 629.7168312 | 653.9367094 |
| Julian Correction | 294000 | 32 | 22160.5 | 2978062500 | 500.5 | 512 | 525 | 550 | 625 | 750 | 830 | 650 | 675 |
| Gregorian Correction | 285180 | 31.04 | 21495.685 | 2888720625 | 485.485 | 496.64 | 509.25 | 533.5 | 606.25 | 727.5 | 805.1 | 630.5 | 654.75 |
| Michael's Correction | 284825.7667 | 31.001444 | 21468.98437 | 2885132432 | 484.8819601 | 496.023104 | 508.6174406 | 532.8373187 | 605.4969531 | 726.5963437 | 804.0999537 | 629.7168312 | 653.9367094 |
| Error in Julian Correction | -9174.23325 | -0.998556 | -691.5156324 | -92930068.06 | -15.61803994 | -15.976896 | -16.38255938 | -17.16268125 | -19.50304688 | -23.40365625 | -25.90004625 | -20.28316875 | -21.06329063 |
| Error in Gregorian Correction | -354.2332501 | -0.038556 | -26.70063244 | -3588193.055 | -0.603039938 | -0.616896 | -0.632559375 | -0.66268125 | -0.753046875 | -0.90365625 | -1.00004625 | -0.78316875 | -0.813290625 |
| Error in Michael's Correction | -3.18396E-08 | -5.08038E-13 | -1.88084E-09 | 1.52588E-05 | 1.11413E-11 | -8.12861E-12 | -5.01927E-11 | -4.14957E-11 | -1.54614E-11 | 2.80806E-11 | 5.59339E-11 | -6.70752E-12 | 2.04636E-12 |
| Convienent conversion times | |||||||||||||
| Based on the following chart, I've determined that the next convienent conversion time would be | |||||||||||||
| the year 2048, where we would ignore the leap year, and have a 365 day year. From that year | |||||||||||||
| forward, we would only need to skip the leap year every 128 years. And have a special leap year | |||||||||||||
| every 88642 years. | |||||||||||||
| Year | Greg's Correction | Michael's Correction | |||||||||||
| 100 | 1 | 0 | |||||||||||
| 128 | 1 | 1 | |||||||||||
| 200 | 2 | 1 | |||||||||||
| 256 | 2 | 2 | |||||||||||
| 300 | 3 | 2 | |||||||||||
| 384 | 3 | 3 | |||||||||||
| 400 | 3 | 3 | |||||||||||
| 500 | 4 | 3 | |||||||||||
| 512 | 4 | 4 | |||||||||||
| 600 | 5 | 4 | |||||||||||
| 640 | 5 | 5 | |||||||||||
| 700 | 6 | 5 | |||||||||||
| 768 | 6 | 6 | |||||||||||
| 800 | 6 | 6 | |||||||||||
| 896 | 6 | 7 | |||||||||||
| 900 | 7 | 7 | |||||||||||
| 1000 | 8 | 7 | |||||||||||
| 1024 | 8 | 8 | |||||||||||
| 1100 | 9 | 8 | |||||||||||
| 1152 | 9 | 9 | |||||||||||
| 1200 | 9 | 9 | |||||||||||
| 1280 | 9 | 10 | |||||||||||
| 1300 | 10 | 10 | |||||||||||
| 1400 | 11 | 10 | |||||||||||
| 1408 | 11 | 11 | |||||||||||
| 1500 | 12 | 11 | |||||||||||
| 1536 | 12 | 12 | |||||||||||
| 1600 | 12 | 12 | |||||||||||
| 1664 | 12 | 13 | |||||||||||
| 1700 | 13 | 13 | |||||||||||
| 1792 | 13 | 14 | |||||||||||
| 1800 | 14 | 14 | |||||||||||
| 1900 | 15 | 14 | |||||||||||
| 1920 | 15 | 15 | |||||||||||
| 2000 | 15 | 15 | |||||||||||
| 2048 | 15 | 16 | |||||||||||
| 2100 | 16 | 16 | |||||||||||
| 2176 | 16 | 17 | |||||||||||
| 2200 | 17 | 17 | |||||||||||
| 2300 | 18 | 17 | |||||||||||
| 2304 | 18 | 18 | |||||||||||
| 2400 | 18 | 18 | |||||||||||
| 2432 | 18 | 19 | |||||||||||
| 2500 | 19 | 19 | |||||||||||
| 2560 | 19 | 20 | |||||||||||
| 2600 | 20 | 20 | |||||||||||
| 2688 | 20 | 21 | |||||||||||
| 2700 | 21 | 21 | |||||||||||
| 2800 | 21 | 21 | |||||||||||
| 2816 | 21 | 22 | |||||||||||
| 2900 | 22 | 22 | |||||||||||
| 2944 | 22 | 23 | |||||||||||
| 3000 | 23 | 23 | |||||||||||
| 3072 | 23 | 24 | |||||||||||
| 3100 | 24 | 24 | |||||||||||
| 3200 | 24 | 25 | |||||||||||
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