Leap-time (leap days and years and accumulations)
"Tyler Nally" (tnally@iquest.net)
Fri, 6 Aug 1999 14:11:01 -0500
Bro Tyler (me) scribeth...
>Leap days are given once every four years because of the accumulation of
>extra time over the course of four years of the earths space travel around
>the sun. That's why we get an *extra* day every 4th year (if the year is
>divisble by 4 evenly with no remainder).
NOTE: If you don't want your head to hurt because of all of the
math and science to follow, please close this e-mail and
don't give it any attention.... but you might learn something
in the process.
If I remember my science correctly.... the amount of time for the earth to
spin around once on it's axis (a solar day ... a.k.a. sidereal day) is ...
23 hours 56 minutes 4 seconds. My New American Heritage dictionary
describes it as such...
The time required for one complete rotation of the earth in
reference to any star or the vernal equinox at the meridian,
is equal to 23 hours 56 minutes 4.09 seconds
My New American Heritage dictionary explains a sidereal year this way...
The time required for a complete revolution of the earth
about the sun, relative to the fixed stars, or 365 days 6 hours
9 minutes 9.54 seconds.
So getting a calculator out, I convert a sidereal year and a sidereal
day into decimal format ...
1 sidereal year = 365 days 6 h 9m 9.54s = 365.25636 days
1 sidereal day = 23h 56m 4.09s = 0.99727 days
So... I'll bet that ya'll didn't know that by the time it takes for
the earth to travel completely around the sun is a number that ya'll
won't hardly believe.
365.25636 days / 0.99727 days = 366.2562
... we actually gain a day *in time* during a sidereal year.
What's wrong with that! Nothing! The math simply tells you something
that your teachers didn't, which is that there is really 366.25 "star
days" in a year, and that the effect of the rotation around the sun
is to subtract an effective day (it could have been to add a day, but
I guess the effective swirl of mass in the solar system was generally
in the same direction). This ultimately means that our *24 hour* days
piled end-on-end are equivalent to 366.25 *solar/star/sidereal* days.
With an extra quarter of a day (.25 of a rotation) left over to accumulate.
So, we have about a quarter of a day at the end of each trip around the
sun that we reward ourselves with an extra day (leap day) on every fouth
year. But because the extra days accumulation isn't even (as it's truly
.2562 days instead of .25) there's still a remainder at the end of four
years. After four years, 4 X .2562 days, we get a leap day of the
accumulations of a extra 24 hour period of time. But it's not exactly 1
day even, but 1.0248 days. Or 1 day 35 minutes 42.72 minutes. It takes
40.32258064516 *leap days* of accumulations to give us an extra day (which
is about 160+ years of time being elapsed) to which even that isn't a whole
day but about a third of a day more.... than what has been accumulated.
By the time you add a day here on the normal leap years and on years
evenly divisible by 400, and not have a leap year on the years on the
even "100" mark (to give back the days accumulated), it all evens out
pretty well.
To me, this stresses how hard it would have been for anyone to
keep track of which day is *the seventh* day to rest as we take
and lose days all the time. A few days here, a few days there...
give some, take some, lose some, earn some... all the while ......
my head is now dizzy and I got to stop this nonsense.
Bro "math geekbert" Tyler
--
Bro Tyler Nally
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