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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 leap 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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