Insights Measuring How Many Days Are in a Year - Comments

[Janus]

Janus submitted a new PF Insights post

Measuring How Many Days Are in a Year

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Great first entry @Janus! This is a topic I never knew could be so deep!

 

[Jeff Rosenbury]

There are so many rational ways to measure a year.

But let's not forget our Muslim readers. Their year is based on how many months have passed. And their months are based on direct observation of the moon. The length of the month can change depending on the weather since clouds interfere with moon sightings. Because of this it is impossible to predict with certainty what the next Muslim year's dates will be. The future is spun out real time.

So anyone who thinks these various astronomical measurements are complex, be glad you're not a Muslim. (Unless you are, in which case the future is as God wills it.)

Humanity has measured time in lots of ways in history. Some of them will seem strange to us living in an era where calendars are common place technology.

 

[QuantumCurt]

This is a very cool topic. I recently read a book by Stephen Jay Gould called "Millenium" (or something like that) which discussed many of these points. The calendar is a formidably complicated beast to tackle when one really gets deep into the topic.

 

[mfb]

To make things worse, the rotation rate of Earth is not constant. The effect can be up to one second per year.
Over longer timescales, the days get longer by about 2.3 milliseconds each century, currently with a lower rate of 1.7 ms as some continental masses still move around related to the last ice age.

To keep atomic clocks in sync with the position of the sun, we frequently need leap seconds, and we will need more and more in the future.

 

[PWiz]

To make things worse, the rotation rate of Earth is not constant. The effect can be up to one second per year.
Over longer timescales, the days get longer by about 2.3 milliseconds each century, currently with a lower rate of 1.7 ms as some continental masses still move around related to the last ice age.

To keep atomic clocks in sync with the position of the sun, we frequently need leap seconds, and we will need more and more in the future.

Well thank god they realized the slowing rotation rate of the Earth in the 60's and changed the SI definition a second.

I guess we just have to wait for the Kilogram, Ampere and Kelvin to get a much needed change in definition to one in terms of (preferably dimensionless) fundamental constants.

 

[mfb]

Well thank god they realized the slowing rotation rate of the Earth in the 60's and changed the SI definition a second.

Well atomic clocks would run more stable than Earth either way. But frequently tuning them would be really messy and make astronomic measurements weird ("and then we have to account for the longer seconds in 1994 to compare the results").

I guess we just have to wait for the Kilogram, Ampere and Kelvin to get a much needed change in definition to one in terms of (preferably dimensionless) fundamental constants.

You need constants with dimensions to fix units. Dimensionless constants (in SI) do not allow to define things like kilograms.

 

[PWiz]

You need constants with dimensions to fix units. Dimensionless constants (in SI) do not allow to define things like kilograms.

Ahh, right, silly me. But incorporation of the fundamental constants in SI definitions is definitely the need of the hour.

 

[Rislam169]

This is very interesting topic.I never knew that and never thought about that.

 

[RJLiberator]

Great post, enjoyable read. Thank you.

 

[amankalra]

Really an interesting topic though I never thought it would have been so much elaborated. I know only the direct 365 days :p

 

[BobG]

"This also means that the position of the Sun with respect to the stars on a given date as seen from the Earth also changes over the years. In the time since the dates for the astrological signs were established, the Sun has moved an entire Zodiac sign. Thus, during the Summer solstice this year, instead of just entering Cancer as the astrological dates suggest, the Sun is just leaving Taurus and entering Gemini. (So if the the Tropic of Cancer had been named today, it would have likely been called the Tropic of Gemini and the Tropic of Capricorn would be the Tropic of Sagittarius)."

So, at the time astrological signs were established, the vernal equinox pointed towards the constellation Aries. And that some point in Aries (the first point of Aries?) could be used to find the direction of the vernal equinox no matter what day of the year it was. And now the direction of the vernal equinox (the first point of Aries) lies in the constellation Pisces?

Man, I can't wait until the direction of the vernal equinox (the first point of Aries) approaches the constellation Aquarius. It will be such a great occasion that we'll all dance and sing songs about it! "It is the dawning of the Age of Aquarius!"

 

[the_emi_guy]

Three historical definitions of "day" are given, but the currently excepted definition is not included i.e.
86,400 SI seconds where the SI second is based on the hyperfine transition frequency of the caesium atom.

 

[Edward Oxford]

Well, try this. Figure out the EXACT way that they determine when Easter is each year. And, no, it has little to do with the Vernal Equinox. It has something to do with "The Golden Number" (which has a lot to do with astronomy). This was so confusing that the various churches (Catholic, Anglican, etc.) would print the day Easter falls on for a large number of years in the Common Prayer Book of the ordinary Christian (Easter is by far the most important Christian holiday).

 

[bland]

Excellent post. I'd like to point out that we live in a very special time during the 26,000 precession cycle where we have the brightest star that it's possible to have as the North Star which is very close to the actual north pole, this lasts about 200 years before drifting away.

 

[Jim60]

In the past they must have thought there was only 360 days in a year, that’s probably why we’ve got 360 degrees in a circle?

 

[Drakkith]

In the past they must have thought there was only 360 days in a year, that’s probably why we’ve got 360 degrees in a circle?

Nah, the 360 degrees thing is left over from the Babylonian number system: https://en.wikipedia.org/wiki/Babylonian_numerals

The legacy of sexagesimal still survives to this day, in the form of degrees (360° in a circle or 60° in an angle of an equilateral triangle), minutes, and seconds in trigonometry and the measurement of time, although both of these systems are actually mixed radix.

The Babylonian calendar used lunar months, which vary from 29-30 days each, along with an intercalary month when necessary. The years wouldn't have been 360 days long as far as I can tell.

 

[mfb]

It is quite easy to get the length of a year with a precision of a day over a human lifetime without any dedicated measurements, and getting 365.25 as approximation is possible with very simple astronomical observations. I don't think anyone ever thought a year would be 360 days long. The Babylonians certainly knew it better (see above).
Getting more precise than 365.25 is challenging, and brings up all the complications mentioned in the insights article.

 

[Jim60]

Finding how many days in a year by using the sighting of the crescent moon must have been impossible?

If you count 6 times 29 and 6 times 30, add them together, it comes to 354 days.

That’s 11.25 days less than the accepted figure of 365.25…

Did they know how to add fractions?

It must have been after Newton and Kepler when they finally got it about right?

 

[Drakkith]

Finding how many days in a year by using the sighting of the crescent moon must have been impossible?

If you count 6 times 29 and 6 times 30, add them together, it comes to 354 days.

That’s 11.25 days less than the accepted figure of 365.25…

Did they know how to add fractions?

It must have been after Newton and Kepler when they finally got it about right?

Yes, ancient civilizations knew how to add fractions, and I doubt they split the year up into 6 months of 29 days and 6 months of 30 days. Being 10+ days off in a single year was very, very noticeable to those who watch for these kinds of things.

https://en.wikipedia.org/wiki/Fraction_(mathematics)#History

 

[Jim60]

Why did they use the moon as a clock if they knew the year was 365.25 days long, and more importantly, how did they work it out?
It must have been a remarkable achievement for a Babylonian. What was his name?

 

[Drakkith]

I don't think I can answer any of those, sorry!

 

[Jim60]

Thanks for the reply.
I read somewhere that the Romans used the star Sirius to calculate the days in a year, but it didn’t give the method they used, or I might have forgotten.

 

[mfb]

You can measure the maximal height above the horizon, or the point at the horizon where Sirius goes up/down. You can do the same thing with the sun. Nearly everything that does not depend on the moon or other planets will show the same period of 365.25 days if observed over a few years.

 

[SteamKing]

Finding how many days in a year by using the sighting of the crescent moon must have been impossible?

If you count 6 times 29 and 6 times 30, add them together, it comes to 354 days.

That’s 11.25 days less than the accepted figure of 365.25…

Did they know how to add fractions?

It must have been after Newton and Kepler when they finally got it about right?

The Greeks knew that the year was just a little shorter than 365.25 days. When Julius Caesar came to power in Rome, he instituted a reform of the calendar, since the old Roman lunar calendar had only about 355 days in a year, and the Roman months had gotten badly out of step with the seasons over time.

To help him reform the Roman calendar to make it more accurate and keep it in step with the seasons, Caesar used the services of a Greek astronomer from Alexandria, one Sosigenes, as explained in this article:

https://en.wikipedia.org/wiki/Julian_calendar

The reformed Julian calendar established the familiar lengths of the months which we still use and created an extra leap day which is inserted into the calendar every four years, the famous Feb. 29. This made the average length of the Julian year some 365.25 days, and the new Julian calendar was a smashing success, at least for a while.

While the length of the actual year is not exactly 365.25 days, the difference amounts to only a few minutes per year, which is almost completely unnoticeable. However, over time, a few minutes here and a few minutes there add up, so that by the middle of the 16th century A.D., the Julian calendar was falling out of step with the seasons, just like the old Roman calendar had, which vexed Caesar. A new set of calendar reforms was established by Pope Gregory XIII in 1582, which eliminated 10 days from the Julian calendar to re-align the months with the seasons, and further adjusted which years received a leap day.

https://en.wikipedia.org/wiki/Gregorian_calendar

Because this Gregorian calendar was a product of the Pope in Rome, it was adopted immediately only in the countries which were Roman catholic. Protestant countries like England and eastern Orthodox countries like Russia continued to use the Old Style Julian calendar to reckon the years. Eventually, England (including the American colonies) adopted the Gregorian calendar in 1752, and Russia held out until 1918, when the Bolsheviks finally decreed calendar reform in Russia.

 

[SteamKing]

Why did they use the moon as a clock if they knew the year was 365.25 days long, and more importantly, how did they work it out?
It must have been a remarkable achievement for a Babylonian. What was his name?

The Babylonians used the moon as a clock because it was important to their religious practices, not because they wanted to be good astronomers, which they were.

Each of the gods worshipped by the Babylonians was associated with a certain month in their calendar, which is quite a bit more complex than modern calendars at reckoning the days.

https://en.wikipedia.org/wiki/Babylonian_calendar

Time over long periods was reckoned using a lunar-solar cycle, which repeats approximately every 19 years.

Certain religious aspects in current times are still based on the moon, like determining the date of Passover or Easter. For centuries, the method used to determine when Passover was celebrated was kept secret by the rabbis, and various methods were developed to calculate the date of Easter either in the Julian or Gregorian calendars. The mathematician C.F. Gauss developed one such algorithm for calculating the date of Easter early in his career.

https://en.wikipedia.org/wiki/Computus

http://www.staff.science.uu.nl/~gent0113/hovo/downloads/text1_08b.pdf

 

[Jim60]

Thanks very much for all the replies.
Has anyone tried timing the Sun or Sirius to get the length of a year?
If anybody can give me some tips, I’ll give it a go myself.
Getting 365.25... Day’s without any modern equipment like an accurate clock and a precision mounted telescope seems impossible, how did the Romans achieve it?

 

[mfb]

You don't need any timing, apart from counting days.

Find some place with a clear view to the horizon. where the sun rises or sets. On a clear day, observe where it does so, note down your own position and the apparent position on the horizon. Ideally, repeat this a few times to get several data points, and to get a feeling how much this changes over time. Always write down how many days passed since the first data point. In about 4 months, the sun will approach the same position for sunset/sunrise again, but this time going in the opposite direction from day to day. In about a year, the sun will approach the same position again - find the day that is closest to the initial position. If you do it right, you should get something between 363 and 367 days if you live not too close to the equator or the poles. Wait another year (but count days), repeat the measurement. By now you can probably narrow it down to +- 1 day. Multiple measurements and interpolation between the days allows to get more precise. Alternatively, do the observations for a few years and you get a much better precision.

The disk of the sun has an apparent diameter of 1/2 degree, if you measure its position with an uncertainty of 1/2 the sun diameter you get 1/4 degree resolution, which should be of the order of the change within a day.
A building or similar tall structure at the horizon allows to make measurements much more precise than half the sun diameter.

A few years ago I measured my latitude based on the highest angle of the sun. Got it accurate to within half a degree (that is the width of the half-shadow region) with the shadow of a corner of a building, stones, a rope, pen and paper as the only tools (no ruler, no calculator). Observing the location where the sun rises should be much more accurate. Longitude needed a modern clock, of course.

 

[SteamKing]

Thanks very much for all the replies.
Has anyone tried timing the Sun or Sirius to get the length of a year?
If anybody can give me some tips, I’ll give it a go myself.
Getting 365.25... Day’s without any modern equipment like an accurate clock and a precision mounted telescope seems impossible, how did the Romans achieve it?

It wasn't the Romans who did. It was the Greeks among others who made the observations necessary.

Hipparchus of Nicaea was the premier astronomer of his time, insisting that Greek astronomy be done just as precisely and meticulously as the Babylonians did.

https://en.wikipedia.org/wiki/Hipparchus

Hipparchus had access only to simple tools and instruments. The length of the year was made by observing the equinoxes.

 

[Jim60]

Would it be easier to start counting the days from March 20th the spring equinox, as the Sun would rise in the east and set in the west on that day?
After that day the Sun would start rising more northerly until about June 19th, then after that day the Sun would start to rise more easterly again.
Eventually the Sun would be back to where it started on about September 22nd
After September 22nd the Sun would start to rise more southerly until around December 21st.Then the Sun would return to where it started on March 20th 365.25 days later.
Hope this waffle can be understood.
Have I missed something?

 

[SteamKing]

Would it be easier to start counting the days from March 20th the spring equinox, as the Sun would rise in the east and set in the west on that day?

As far as I know, the sun rises in the east and sets in the west every day.

After that day the Sun would start rising more northerly until about June 19th, then after that day the Sun would start to rise more easterly again.
Eventually the Sun would be back to where it started on about September 22nd
After September 22nd the Sun would start to rise more southerly until around December 21st.Then the Sun would return to where it started on March 20th 365.25 days later.
Hope this waffle can be understood.
Have I missed something?

Hipparchus and other Greek astronomers used a device called an equatorial ring to determine when the equinoxes occurred:

https://en.wikipedia.org/wiki/Equatorial_ring

 

[mfb]

Would it be easier to start counting the days from March 20th the spring equinox, as the Sun would rise in the east and set in the west on that day?

There is nothing special about a sunrise exactly east and sunset exactly west - unless you use something like the equatorial ring, but that needs alignment before (and then you could also use it for different days, with different alignment).
A precision of an hour is great, that gives 365.25 within a single year, with "2" as significant figure already. 10 years and you start noting that 365.24 is a better approximation.

 

[Jim60]

If we take the Suns position on the horizon as true east on March 20th, how many degrees does the Sun move north and south of east in total over the year?
The reason for asking this, is because you would need a fairly wide horizon east without any obstructions.
It would also be helpful in designing something to mark the position of each Sun rise.

 

[Jim60]

That equatorial ring looks like it does the same job as the equatorial mount on a telescope, where it compensates for the 23 degrees tilt of the Earth?
I presume you would check the Suns position with that while it’s on the meridian at mid day?

 

[Drakkith]

That equatorial ring looks like it does the same job as the equatorial mount on a telescope, where it compensates for the 23 degrees tilt of the Earth?
I presume you would check the Suns position with that while it’s on the meridian at mid day?

No, I think you can check it at any time of the daytime. If oriented correctly, the bottom of the ring looks like it should in shadow for the entirety of the day.

 

[Jim60]

Yes you could. The shadow would move steadily clockwise from sunrise till sunset.
Great skill would be needed in setting it up though; the location would have to be ideal.

 

[Drakkith]

Orienting it would be a delicate process, but offhand I would think you could set one up just about anywhere.

 

[Jim60]

Checking how many days from equinox to equinox using this site, I’m puzzled that the time varies from year to year.

http://aa.usno.navy.mil/data/docs/EarthSeasons.php

This year’s equinox fell on March the 20th at 4 hours 30 minutes UTC, and next years equinox falls on March 20th at 10 hours 29 minutes UTC, a difference of 365.25 – 365.249 = 1 minute less than it should be.
Either I can’t do simple maths, or there is something else that I would have to take into account if wanted to find out how many days from equinox to equinox.

 

[mfb]

It should not be 365.25.

Independent of that, there are smaller variations, some regular, some not.

If we take the Suns position on the horizon as true east on March 20th, how many degrees does the Sun move north and south of east in total over the year?

It depends on your location. If I did not make a mistake, those are the angles (in degree) for different latitude, with 23.5 degrees tilt of Earth:
66: 157 <- but hard to observe as the sun barely makes it above the horizon at winter solstice where most of that change happens.
60: 106
50: 77
40: 63
30: 55
20: 50
10: 48
0: 47 <- much easier to observe thanks to nearly vertical sunrise/set

 

[Jim60]

Is this the Solar Azimuth Angle degrees clockwise from north?

If that’s the case my sunrise on the 20/3/2016 was 6.07am LST, and the Suns azimuth angle at that time was about 88.45 degrees north/east.

On 19/6/2016 the Sunrise will occur at 3.06am LST, and the Suns azimuth angle at that time will be about 40.18 degrees north/east.

On 22/9/2016 the Sunrise will occur at 5.51am LST, and the Suns azimuth angle at that time will be about 88.96 degrees north/east.

On 21/12/2016 the Sunrise will occur at 8.46am LST, and the Suns azimuth angle at that time will be about 134.88 degrees south/east.

On 20/3/2017 the Sunrise will occur at 6.08am LST, and the Suns azimuth angle at that time will be about 89.75 degrees north/east.

So sunrise would move about 40.18 degrees north/east to 134.88 degrees south/east.

That would mean you would need a total angle of about 90 degrees clear view of the horizon.

Is this correct or have got it wrong?

 

[Jim60]

Did you notice on that site that the Solstices, Equinoxes and Perihelion to Perihelion varied quite a lot from the norm?

 

[anorlunda]

Very interesting topic indeed. Thank you Janus.

Reading that gives one a bit of sympathy for those who allowed the Y2K bug to exist. Doing date and time correctly in software is pretty difficult. Most programmers were not up to dealing with the complexity and they gave up in disgust. Even those who were up to it had multiple definitions to choose from.

One might expect that a standard time/date library would have been developed even in the days before open source. But (at least) two families of versions would be needed, a scientific family, and a human family. The scientific versions (UTC is one such) would be used for stuff like astronomy. (The Insights article reminds us that there are multiple versions of that.) The human versions would be used for stuff like when does the next train arrive, how much to budget for today's hourly wages (23, 24, or 25 hours?), and how much electric energy will be consumed tomorrow (depends on the day of the week and holidays). Obviously, the human versions would need geographical and cultural instantiations.

Then consider the type conversion problems as real life time/date data collected came from incompatible versions. How many versions of DAYSDIFF(TIMEDATE1,TIMEDATE2) would we need to cover all the combinations of definitions?

Even today, if an open source library exists that is able to deal with all the scientific and human definitions of date/time (past and present), I'm not aware of it.

So thanks again Janus for reminding us that "What time is it?" is a question whose answer we can never find universal agreement. Not in the past; not now; not in the future.

 

[Jim60]

I’ve notice most astronomical events have a Julian Day for a time; it starts from noon January 1st 4713 BC.
For example this years Perihelion occurred on January 2nd 2016 at 22 hours 49 minutes, or 2457390.4506944400 JD (Julian Day).
That’s if you believe that site I mentioned on page 2.

 

[Jim60]

I should have put UTC after minutes, silly me.

 

[mfb]

That would mean you would need a total angle of about 90 degrees clear view of the horizon.

Only if you want to observe the sunrise every day in the year, which is not necessary.

 

[Jim60]

Only if you want to observe the sunrise every day in the year, which is not necessary.

You make sound easy?
Has anyone on this forum attempted to count the days in a year using this method, or any other way for that matter, just to see if it could be done?

 

[Vanadium 50]

Has anyone on this forum attempted to count the days in a year using this method, or any other way for that matter,

Here's another way: I plot the mileage my car gets and fit it to a sinusoid plus a constant. The year is 363.2 +/- 1.2 days long.

 

[jim mcnamara]

Time lapse exposures of the analemma:

https://www.google.com/imgres?imgur...ved=0ahUKEwi62ISM56fMAhUL9WMKHeG4CGIQ9QEIIzAA

 

[mfb]

You make sound easy?

It is easy.
Manhattan has great reference points and good horizon sight with the street layout, the effect is quite famous there. Note how "full sun" has a deviation of at most one day. The same thing can be done with any other reference point close to the horizon.

Getting 365 days with a bit of care is easy, and getting 365.25 with a longer measurement time is not hard either.

 

[Jim60]

I’m getting confused here, what year are we actually measuring? Is it the sidereal year, or the Tropical year?