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View Full Version : When will we need to correct the Gregorian calendar?



parallaxicality
2009-Apr-19, 02:15 PM
My incredibly bad calculations suggest that the extra day needed to account for the annual loss of 26 seconds on the tropical year will need to be added by the end of 4906 AD. Assuming that is correct, and assuming we did, and assuming we maintained the correction every 3323 (?) years, when would we need to make another adjustment?

grant hutchison
2009-Apr-19, 07:56 PM
Um. 8229 AD. Is this a trick question? :)

Grant Hutchison

parallaxicality
2009-Apr-19, 08:13 PM
No, just badly phrased. What I meant was, first off, were my calculations correct and second, if we did adjust for the 26-second shortfall, how accurate would the calendar then be, assuming the affects of such things as leap seconds?

grant hutchison
2009-Apr-19, 08:19 PM
I think the answer is probably that your calculations are correct (depending on which value for a tropical year you've chosen), but not entirely relevant.
Trouble is, the length of the tropical year is changing, and the rotation rate of the Earth is changing, and over millennia into the future we can't predict exactly how many fractional solar days there will be in a tropical year, and so can't predict accurately when a one-day calendrical debt will eventually accumulate.
There are various suggestions for how we might adjust the calendar (skipping the leap year in 4000 AD is one) but they're all necessarily a bit speculative.

Grant Hutchison

grant hutchison
2009-Apr-19, 10:23 PM
Ah, here we go. Jean Meeus wrote about this in Section 6.3 of More Mathematical Astronomy Morsels.
He points out that the tropical year is the time for the sun's mean longitude to increase by 360 degrees, which is not quite the same thing as the time between one March equinox and the next (which Meeus calls the E-E year). Both years are variable in length, with the tropical year currently decreasing and the E-E year increasing. At J2000.0, the tropical year was 365.242190 days, while the E-E year was 365.242375 days, closer to the mean Gregorian calendar year of 365.2425 days. The E-E year hangs around close to the Gregorian year for the next few millennia, so (according to Meeus) the accumulated mismatch between calendar and equinox would amount to only 0.26 days between 2000 and 8000 CE.
However, the Earth's rotation is slowing, with a cumulative mismatch between Dynamic Time and Universal Time (all those leap seconds). That effect, superimposed on the pretty small mismatch between the E-E year and the mean Gregorian year, means that (according to Meeus) we will have accumulated a one-day mismatch between equinox and calendar by about 7200 CE (but with a strong dependence on the rate of slowing of Earth's rotation during that time).

Grant Hutchison

parallaxicality
2009-Apr-20, 11:41 AM
Wow. That's just, wow.

I got nuthin'.

grant hutchison
2009-Apr-20, 10:08 PM
I got nuthin'.Is that in a good way, or a bad way? :)

Grant Hutchison

parallaxicality
2009-Apr-22, 06:33 PM
There are times when I have to recognise the fact that I never got science in high school.