apparent day mean solar day common day
sidereal day tropical year shake
millennium figure out calendar re-use

Time megaConverter #4

Introduction and Overview
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Units of time have not been particularly fixed over the years because the primary gauge of time, earth's rotation and revolution, is not fixed. A mean (average) solar year today is 365.2422 days, but the earth's rotation is continually slowing. Every so often, the world's governments have to add a leap second to the master clocks, just to make up the extra time. Millions of years ago, the year was over 400 days long. Millions of years from now, it will be much shorter than it is now. At some point we will either have to change the length of the second or change the way we measure a day.

That is not the only concern. The earth's rotation and revolution are not constant. Occasionally it will speed up or slow down. These changes usually cancel each other out and we never notice them.

The main problem has come with defining a calendar that handles these changes and also takes care of the fact that a year is not an even number of days. The Gregorian calendar was designed to correct this. So now we have leap years, except in century years, excluding those century years divisible by 400 when we do have leap years. Another problem is that the year is not evenly divisible by a week, which is why we need a new calendar every year.

You can figure out when the current year's calendar will next be useful or which previous calendar will work for the current year by using the following table:

If calendar year is... Re-use calendar...
A leap year in 28 yrs or from 28 yrs past
1yr after leap year in 6 yrs or from 11 yrs past
2yrs after leap year in 11 yrs or from 11 yrs past
3yrs after leap year in 11 yrs or from 6 yrs past
* Be careful in century years [read the intro] because the missing leap year may throw the formula off. Consider this: 1980 was a leap year. The 1981calendar was the same as in 1970 and again in 1987. 1982 was the same in 1971 and 1993. 1983 was the same in 1977 and 1994.

For the most comprehensive treatment of measurements, find "NTC's Encyclopedia of International Weights & Measures" by William D. Johnstone at your local library.

Glossary of Conversions:

apparent day
One apparent day is the time it takes for the earth to rotate such that the sun is at the same relative position the following day. Also known as the solar day.

mean solar day
One mean solar day is slightly greater than an apparent day because the apparent day varies in length due to the eccentricity of the earth's orbit around the sun.

common day
One common day is the calendar time that passes from midnight to midnight.

sidereal day
One sidereal day is the time it takes for the earth to rotate such that a fixed star is in the same relative position the following day. Also know as the exact day.

tropical year
One tropical year is the time it takes for the earth to make one complete revolution around the sun... a solar year. The spring equinox is precisely one tropical year from the next spring equinox. This is why there was so much effort placed on creating a workable calendar. Without a correction method like a leap year, the spring equinox kept getting later and later in the calendar year.

A shake, from "a shake of a lamb's tail," is an extremely short period of time sometimes used in physical measurements.

The years AD did not start in the year 0 but in the year 1. Therefore the third millennium AD will not start until the year 2001 which is when the 21st century will officially begin.

Note: Because of round-off errors, converting from very large units to very small units or vice-versa may not be accurate (or practical). Conversion factors can be found by converting a quantity of 1 unit to another unit several steps above or below the first. You may need to string several conversion factors together to find the factor from a very large unit to a very small unit, and then you can use a calculator with sufficient digits to find your answer.