# The Naked Scientists Forum

### Author Topic: 365 days in a year  (Read 10050 times)

#### paul.fr

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##### 365 days in a year
« on: 23/04/2007 01:21:10 »
A year has 52 weeks, a week has 7 days. But that does not equal 365! Why?

#### another_someone

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##### 365 days in a year
« Reply #1 on: 23/04/2007 01:46:33 »
The week is a relatively arbitrary unit.

In fact, there are not exactly 365 days in a year, which is why we need leap years, and even leap seconds - the Sun and Earth do not behave accruing to our nice neat calanders.

A week is approximately 1/4 of a lunar month (even that is not exact, because a lunar month is a little over 29 days, not 28 days that would constitute 4 weeks).  The moon is not synchronous with the year, which is why cultures which use purely lunar calanders (such as the Jewish and Islamic calanders) will drift relative to the solar calender (the Jewish calender will then make a correction every few years by inserting a leap month, but the Islamic calender just continues to drift), and it is also why Easter is a moveable holiday.

#### DoctorBeaver

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##### 365 days in a year
« Reply #2 on: 23/04/2007 09:42:00 »
And also why the Chinese New Year is on a different date each year

#### Ben6789

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##### 365 days in a year
« Reply #3 on: 24/04/2007 16:44:12 »
technically it's 365 1/4 days..

#### paul.fr

• Guest
##### 365 days in a year
« Reply #4 on: 24/04/2007 16:45:15 »
technically it's 365 1/4 days..

if you're going to get technical....im off

#### another_someone

• Guest
##### 365 days in a year
« Reply #5 on: 24/04/2007 17:28:38 »
technically it's 365 1/4 days..

I see you will be getting the date wrong in the year 2100 (which is not a leap year).  Neither was 1900 a leap year.  Luckily for people like you, 2000 was a leap year - so you did not get that wrong.

Do remind me never to ask you to write a date routine for a computer program

#### DrDick

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• Posts: 162
##### 365 days in a year
« Reply #6 on: 24/04/2007 17:30:12 »
To get super-technical, it's 365.2425 days long (according to the Gregorian calendar.  That's why we lose a leap-day every 100 years (except every 400 years).

AD 1604-1696 - leap year every 4 yrs
AD 1700 - no leap year
AD 1704-1796 - leap year every 4 yrs
AD 1800 - no leap year
AD 1804-1896 - leap year every 4 yrs
AD 1900 - no leap year
AD 1904-1996 - leap year every 4 yrs
AD 2000 - leap year (this is the exception to the every 100 yrs rule)
AD 2004-2096 - leap year every 4 yrs
AD 2100 - no leap year
etc.

Dick

#### another_someone

• Guest
##### 365 days in a year
« Reply #7 on: 24/04/2007 17:34:16 »
http://en.wikipedia.org/wiki/Tropical_year
Quote
The motion of the Earth in its orbit (and therefore the apparent motion of the Sun among the stars) is not completely regular. This is due to gravitational perturbations by the Moon and planets. Therefore the time between successive passages of a specific point on the ecliptic will vary. Moreover, the speed of the Earth in its orbit varies (because the orbit is elliptical rather than circular). Furthermore, the position of the equinox on the orbit changes due to precession. As a consequence (explained below) the length of a tropical year depends on the specific point that you select on the ecliptic (as measured from, and moving together with, the equinox) that the Sun should return to.

Therefore astronomers defined a mean tropical year, that is an average over all points on the ecliptic; it has a length of about 365.24219 SI days. Besides this, tropical years have been defined for specific points on the ecliptic: in particular the vernal equinox year, that start and ends when the Sun is at the vernal equinox. Its length is about 365.2424 days.

An additional complication: We can measure time either in "days of fixed length": SI days of 86,400 SI seconds, defined by atomic clocks or dynamical days defined by the motion of the Moon and planets; or in mean solar days, defined by the rotation of the Earth with respect to the Sun. The duration of the mean solar day, as measured by clocks, is steadily getting longer (or conversely, clock days are steadily getting shorter, as measured by a sundial). One must use the mean solar day because the length of each solar day varies regularly during the year, as the equation of time shows.

As explained at Error in Statement of Tropical Year, using the value of the "mean tropical year" to refer to the vernal equinox year defined above is, strictly speaking, an error. The words "tropical year" in astronomical jargon refer only to the mean tropical year, Newcomb-style, of 365.24219 SI days. The vernal equinox year of 365.2424 mean solar days is also important, because it is the basis of most solar calendars, but it is not the "tropical year" of modern astronomers.

The number of mean solar days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more. This long-term stability is pure chance, because in our era the slowdown of the rotation, the acceleration of the mean orbital motion, and the effect at the vernal equinox of rotation and shape changes in the Earth's orbit, happen to almost cancel out.

In contrast, the mean tropical year, measured in SI days, is getting shorter. It was 365.2423 SI days at about AD 200, and is currently near 365.2422 SI days.

http://en.wikipedia.org/wiki/Sidereal_year
Quote
The sidereal year is the time taken for the Sun to return to the same position with respect to the stars of the celestial sphere. It is the orbital period of Earth, equal to 365.25636042 mean solar days (that is 366.25636042 earth rotations or sidereal days). (A true cycle will always compare two objects that differ mathematically by exactly 1). The sidereal year is 20 minutes and 24 seconds longer than the tropical year.

The Sun and the stars cannot be seen at the same time; if one looks every dawn at the eastern sky, the last stars seen appearing are not always the same. In a week or two an upward shift can be noted. As an example, in July in the Northern Hemisphere, Orion cannot be seen in the dawn sky, but in August it becomes visible. In a year, all the constellations rotate through the entire sky.

If one looks regularly at the sky before dawn, this motion is much more noticeable and easier to measure than the north/south shift of the sunrise point in the horizon, which defines the tropical year on which the Gregorian calendar is based. This is the reason many cultures started their year on the first day a particular special star, (Sirius, for instance), could be seen in the East at dawn. In Hesiod's Works and Days, the times of the year for sowing, harvest, and so on are given by reference to the first visibility of stars.

Up to the time of Hipparchus, the years measured by the stars were thought to be exactly as long as the tropical years. In fact, sidereal years are very slightly longer than tropical years. The difference is caused by the precession of the equinoxes. One sidereal year is roughly equal to 1 + 1/26000 or 1.000039 tropical years.

If one wants to be truly technical about it.

#### DrDick

• Sr. Member
• Posts: 162
##### 365 days in a year
« Reply #8 on: 24/04/2007 17:46:27 »
Yes, I think that would be super-duper technical.

Dick

#### Ben6789

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##### 365 days in a year
« Reply #9 on: 25/04/2007 16:44:10 »
*whoosh*

Hear that? That's that post going right over my head.

#### another_someone

• Guest
##### 365 days in a year
« Reply #10 on: 25/04/2007 17:32:19 »
*whoosh*

Hear that? That's that post going right over my head.

OK, in a nutshell.

Because of the pull of the moon, and the various planets, upon the Earth, no two years are exactly the same length (the differences are very slight - maybe in fractions of a second, but they are real).  There are ofcourse longer term variations in the number of days in the year, but some of this is down to the fact that the days themselves are getting longer.

Then there is the difference between how you measure the year.  If you measure the position of the Sun above the horizon (e.g. midday when the Sun reaches its most northerly position in the sky), you will get one measure; but if you measure how the Sun is positioned relative to the background stars, you get another measure of a year (about 20 minutes and 24 seconds longer than if you measure the year by the position of the Sun above the horizon).
« Last Edit: 25/04/2007 17:34:19 by another_someone »

#### Ben6789

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##### 365 days in a year
« Reply #11 on: 25/04/2007 20:09:09 »