Year 2000

Date: 07/13/99 at 15:24:15
From: Ben Ewing
Subject: Why isn't Y2k a leap year?

Why isn't the year 2000 a leap year? Since every year is 365.26 days 
long, wouldn't every 100 years be a double leap year? Does it have to 
do with some weird mathamatical process?  Thanks.

Date: 07/13/99 at 17:07:36
From: Doctor Rick
Subject: Re: Why isn't Y2k a leap year?

Hi, Ben.

I don't know where you got your information, but 2000 _will_ be a leap 
year. The years 1900 and 1800 and 1700 were not leap years, but 1600 
was, and 2000 will be.

Here is an interesting Web site with information about the Gregorian
calendar (which we use now) and its leap-year rule, which I quote:

  The Julian and the Gregorian Calendars, by Peter Meyer
  http://www.magnet.ch/serendipity/hermetic/cal_stud/cal_art.htm   

"In the Gregorian Calendar a year is a leap year if either (i) it is
divisible by 4 but not by 100 or (ii) it is divisible by 400. In other
words, a year which is divisible by 4 is a leap year unless it is 
divisible by 100 but not by 400 (in which case it is not a leap 
year). Thus the years 1600 and 2000 are leap years, but 1700, 1800, 
1900 and 2100 are not."

This Web site also differs with you about the length of a year, 
stating: "The mean solar year during the last 2000 years is 365.242 
days (to three decimal places)." It is because this figure is slightly 
_less_ than 365 1/4 days (not greater, as you stated) that it is 
necessary to _omit_ occasional leap days (rather than add any).

To be precise, 3 days are omitted every 400 years. The average length 
of a calendar year is thus 365.25 - 3/400 = 365 - 0.0075 = 365.2425, 
which matches the astronomical figure given above pretty well.

If the year were 365.26 days long, your calculation would be correct, 
we would need to insert an extra leap day every 100 years.

The calculations I've described don't seem too weird to me, but the 
matter of defining exactly what a year is turns out to be pretty 
complicated, as you will see from this Web site.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/   

Date: 07/18/99 at 13:33:28
From: Ben Ewing
Subject: Re: Why isn't Y2k a leap year?

Thanks, I am skilled in Math and I didn't really mean wierd, sorry 
'bout that. I always thought years were 365.26 so it's good to know 
that they are 365.242.  Thanks again.

Ben

Date: 07/19/99 at 09:14:50
From: Doctor Rick
Subject: Re: Why isn't Y2k a leap year?

Hi again, Ben.

I took no offense at the word "weird"; in fact I wanted to acknowledge 
that the definitions of year and day do get pretty complex and even 
weird - though they make sense when you get to know them. 

I did a quick Web search to verify my hunch about your figure for the 
length of a year. One site I found has a long list of definitions of 
various astronomical periods:

PREDICTABLE PERIODIC EVENTS (Jan Curtis, Alaska Climate Research Ctr.)
http://climate.gi.alaska.edu/Curtis/astro1.html   

I will quote the relevant sections:

"Earth's Tropical year 365.24219 Days

"Interval for Earth to return to same equinox. This explains why leap 
years exist. Leap years also occur only in years when centuries are 
evenly divisible by four (e.g., 1600, 2000, 2400, etc.). The 
Gregorian calendar therefore is equal to 365 days 5 hours 49 minutes 
12 seconds.

"Earth's Sidereal year 365.25636 Days

"Interval for Earth to return to same fixed star.

"Earth's Anomalistic year 365.25964 Days

"Interval for Earth to orbit the Sun as measured from its closest 
point (perihelion) to its return back. This period is slightly less 
than five minutes longer than the sidereal year because the position 
of the perihelion point moves along the Earth's orbit by about 1.1 
minutes of arc yearly. During this current epoch, the Earth is closest 
the Sun just after the new year. It will take about 12,500 years for 
this date to advance six months."

In other words, the length of a year depends on whether you are 
measuring the time for the earth to return to the same place in orbit 
relative to the stars (sidereal year), or relative to the direction of 
the earth's tilt (tropical year), or relative to the perihelion of the 
earth's orbit (anomalistic year). The figure relevant to the calendar 
is the tropical year, because it relates to the seasons. The figure 
you know is correct, but it's one of the other kinds of "year."

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/