The 'Gregarian' Calendar

Two-digit calendar-years aren't the only trouble at the Y-2K millennium: The Gregorian Calendar needs a 6000th-rule, And, We may have one-too-many leap years if it doesn't get it ...

The Gregorian calendar in use today is based on the tropical year, 365.242192 24-hr days or that is 31556925.4 sec. (A.D. 2000), which keeps the equinoxes in place and yearly hot and cold seasons in their places. It is slightly shorter, by 1223.5 seconds, than the sidereal year which keeps the sun in line with the fixed stars, as presumed in the ancient, archaic calendars (*): When converting the ancient calendars we must ratiocinate their sidereal count to our tropical to know when -what day in what season- an event occurred. However, the Gregorian calendar was only accurate to a millennium: Beyond that, it is off by a day per three millennia; And given its purpose to span the Biblical Testament Era, it is now off by about a day ... But, however, the Earth's rotation slows by 5-to-6 msec-per-year per year, or 60-to-70 μ-day-per-year per millennium, so that, four-to-five millennia ago his calendar-rate "was" accurate. (The slowing is equivalent to 6.5-8.0 mm-per-day per year, at the equator; amounting to one full Earth-rotation since Adam in Eden.)

* (A gappy notion: The difference accounts for a 25793.3333-year nutation "great year", but stars move independently, the nearer relative to the sun itself moving some 220km/s, gliding along the galaxy arm, up and down its sleeves, the farther orbiting the galaxy some 220Myr, and, that, relative to distant galaxies moving about the cosmos ... and yet, Scholarly references are slim for the solar-system orbitation gyrations due to the major planets, nearby stars, and occasional passing rogue stars, as well as unseen Pluton.)

* (And further various calendars were in use in their attempts to count and match years, months, days, conveniently, for their users even in common: the basic lunar calendar 12-moons-per-year, the Hwt 360-day-year, the Biblical 364-day-year, the revised-Hwt 365-day-civic-year, the adjusted 365.25-day-year...)

The rate, of the Gregorian calendar is 365 days per year plus a day more every leap year being every fourth but not hundredth but including the four-hundredth,-- that is, 365 + (1/4) - (1/100) + (1/400) = 365.2425 ... most-accurate ca. 2600 B.C., but too long by 0.0003 today and would have been closer with a five-hundredth: but his plan was to extend it by alternately adding and subtracting ever tinier fractions .... So, A.D. 1992, 1996, 2000 are all leap years, A.D. 2000 being included as it is the fifth four-hundredth.

(Note the semiofficial Orthodox calendar used in Greece replaced the 400th-rule by more-accurate, 200th-or-600th-modulo-900.)

We can extend his calendar a few millennia from the present by excluding every two-thousandth and including every five-thousandth: that is, ...-(1/2000) + (1/5000) = 365.2522; and were it not for the Earth slowing, this would last a hundred times longer-still. (Note that although two-thousand does not factor five-thousand, neither does four-hundred, but all meet again at ten-thousand which is then ruled by the lattest, the but-five-thousandth.) But by that slowing, that five-thousandth rule, in 3000 years, will need be dropped ....

And yet, exclusion of the 2000th, raises the question of our A.D.-2000 leap year, as Gregory didn't leap earlier in B.C. to offset for A.D. 0 that didn't exist: It wasn't leaped, And A.D. 2000 shouldn't, on a contemporary-version calendar: We're more than half way.

For end-to-end accuracy though, the averaged-tropical year, 365.24235 days, over the past six millennia, is now 0.9 day off ... and ... though 1 B.C. was not a leap year in Gregory's formula-sense, neither was it a full deletion but a three-year-skipped-leap ... leaving us 0.15 day off ... Basically right-on ... So ...

The other alternative is to modify the Gregorian formula minimally by assuming his calendar is most accurate in the middle, 170 B.C., and leaving extreme millennia longer or shorter:-- The extension for this is simply to exclude every sixth millennial year: 365+(1/4)-(1/100)+(1/400)-(1/6000)=365.242333..., most accurate ca 240 B.C.-A.D. 80, And, as 1 B.C. was not a leap year, we needn't change soon ... for serendipitous calendric accuracy despite the fact Gregory XIII was not aware of the moon's drag on the Earth's spin ....

Other calendar options:

Had we not been so accustomed to decadal arithmetic we could have chosen a fast, binary, series: 365 + (1/4) - (1/128) = 365.24219.

Any calendar vacillates a few days over millennia because of the compounded inclusions and exclusions of leap years .... A more-stable calendar tight to about half a day could periodically stall its leap, to its fifth year every sixth a rounded half-jubilee except in every fourth century of the prior millennia but in the fifth of the B.C.-A.D. millennium and now hereafter ... (meaning we would change now).

Year A.D. 2000:

But, The Gregorian Calendar itself uses Julian dates prior to A.D. 1582 or whenever locally adopted, so our concern really, is, for the present era and succeeding A.D. 2000;--

The Gregorian calendar includes it as a leap year, but our 'Gregarian' extension contends it .... It may seem a little late for switching, since the calendar has been in service since A.D. 1582, adopted in various years, but not impossibly: a switch affects only dates after A.D. 2000, not those ca 1 B.C. (which is a story about a birthday, March 25th, 5 B.C.) .... The obvious best answer is to go back to the early routine of declaring a leap-year adjustment as-needed, (or 26 leap-seconds per year), but until we do, we have the 6000th-rule:

Our 'Gregarian' Calendar, is, the 6000th-year-exclusion rule to a fully-retroactivated-Gregorian: at the '6K'-average calendar-rate.

Further and-prior adjustments: Cosmic expansion effects. [2013]

A new-theory variable is noticeable in the orbital revolution of Earth about our sun--It would appear that the expanding cosmos -in the expanding-space version of the theory- being essentially isotropic, raises the orbital radius of every process, moons, planets, stars, galaxies, supergalactic clusters, atoms and nuclei (but with quantum fallback heating): Any orbit or orbital in free-space, being a balance of angular momentum and central holding force, the expansion of space-itself 'gently' lifts the orbitation away from its center, whereto it has excess linear velocity, than the directly-higher orbitation, which carries it yet equally further: a rate of recession twice the cosmic expansion velocity... whence Earth's orbit ca 4.6 Ga, 2/3 of the age of the cosmos today, was (2/3)² of today's 93 million miles ~ 41 million miles, closer than Venus today, and so orbiting faster in a shorter period of (2/3)³ ~ 0.2963 today's-year ~ 108 days... At six millennia ago this would have been (1-(6000 yr / 13.82 Ga))³, ~ 8.68@-7 shy ~ 27.4 sec. shorter than 365.2425 days ~ 365.2422 days/year which just happens to be the same as our present year except our day itself is longer as the Earth rotation has slowed the same tidally torqued by the moon and sun...

N.B. In the subsequent slower expansion of the cosmos, VHubble ≈ D / Tcosmos ≈ c at 13.82@9 light-years so far, Earth will recede farther but slower, beyond Mars' present orbit: (4/3)² over the next-4.6 Gyr vs. (3/2)² in its previous-4.6 Ga...

Alternatively, in the exploding-energy version of the theory, all processes would be gaining potential energy, which is mass-energy, rest-mass in the case of particles, and increasing gravitational attraction and so shrinking orbits over eons... (Or it may be a combination...)

(Note, As twin planets with Venus, the two started in-between ca 0.38 AU...)

A premise discovery under the title,

Grand-Admiral Petry
'Majestic Service in a Solar System'
Nuclear Emergency Management

1996, 2004, 2006, 2013