Question about the astronomy

The First and the Last Noon of the solar year don’t coincide. This means solar noon lags by about 6 hours each year and about 24 hours after every 4 years. Days and Nights flip after two years. We update our calendar after 4 years for our own convenience by adding Feb 29. Apparently, we age 365.25 x4 +1 =1462 days in 4 solar years but the actual figure is 1461 days due to the reversing of aforementioned unnoticeable one day. The earth starts its next year (5^th) in the orbit but in reality, we are 24 hrs behind the earth in its orbit around the sun.

This small change in one year reverses not only days and nights but also seasons latently with the passage of time but neither we adjust our clocks for above-mentioned unnoticeable 24 hrs nor we adjust this in our calendar.

365.25x4 already factors in the leap day. You are adding it twice.

The First and the Last Noon of the solar year don’t coincide. This means solar noon lags by about 6 hours each year and about 24 hours after every 4 years. Days and Nights flip after two years. We update our calendar after 4 years for our own convenience by adding Feb 29. Apparently, we age 365.25 x4 +1 =1462 days in 4 solar years but the actual figure is 1461 days due to the reversing of aforementioned unnoticeable one day. The earth starts its next year (5^th) in the orbit but in reality, we are 24 hrs behind the earth in its orbit around the sun.

This small change in one year reverses not only days and nights but also seasons latently with the passage of time but neither we adjust our clocks for above-mentioned unnoticeable 24 hrs nor we adjust this in our calendar.

Year of 365 days would be innacutare for that one day every 4 years.
Without it, 4 years would be 1460 days.
Julian calendar (45 BC) added one day every 4 years, which means 1/4 of a day every year, hence 365.25.
So, by making year to be 365.25 days that one day every 4 years was already added.

But, solar (tropical) year is not 365 days and 6 hours.
Solar year is 365 days 5 hours 48 minutes and 45 seconds.
A bit less than 365 days and 6 hours.

Because of that Julian calendar was making error of 1 day every 128 years.
Pope Gregory XIII introduced Gregorian calendar (1582 AD) with corrections:
Leap years will remain every 4 years, but every 100th year will not be leap year, except every 400th year, which will be.
Gregorian calendar accepted one year to be 365.2425 days.
Error made by Gregorian calendar is 1 day every 3030 years.

Solar (tropical) year is 31 556 925 seconds (365.2421875 days).
Gregorian year is 31 556 952 seconds (365.2425 days), making error of 27 seconds per year, which accumulates to 1 day in 3030 years.
Julian year is 31 557 600 seconds (365.25 days), making error of 675 seconds per year, which accumulates to 1 day in 128 years.

In daily use we accepted 365.25 because it is "close enough" for calculations within lifetime, or within century.

EDIT: All this is for solar day of 86400 seconds.
Sidereal day is a bit shorter and calculations are a bit diferent.

I wrote "about" - doesn't day flip into night after two yaers - we reverse 12 hours in two years and hence 24 hours in 4 years. The solar noon of Feb 28 doesn't coincide with March 01. It takes 4 years for the solar noon of Feb 28 to meet with solar noon of Feb 27 - My question is about this unnoticeable 24 hrs which we lagged in 4 years

The only difference is that Earth doesn't go full 360 degrees for 365 solar noons. It goes 359.7536 degrees.
So, for 4 years goes 1439.0144 instead of 1440.

If time between two solar noons would be exactly 365th part of the year, we would have at 365th solar noon Earth at the same orbital position as last year.
Instead, Earth is for 365th solar noon short by 0.2464 degrees (quarter of 0.9856 degrees).
Second year it is 0.4928 degrees (half of 0.9856), third year for 0.7392 degrees (three quarters of 0.9856) and foruth year is full 0.9856 degrees.
That's why we add one more day to give Earth time to "catch up".

(If year had 360 days it would be 1 degree per day. Since it has a bit more, it is a bit less than one degree per day.)

I wrote "about" - doesn't day flip into night after two yaers - we reverse 12 hours in two years and hence 24 hours in 4 years. The solar noon of Feb 28 doesn't coincide with March 01. It takes 4 years for the solar noon of Feb 28 to meet with solar noon of Feb 27 - My question is about this unnoticeable 24 hrs which we lagged in 4 years

No, in non-leap years, what we call a year is exactly 365 of 24-hour mean-solar-days and in a leap year, what we call a year is exactly 366 of 24-hour mean-solar-days.

See

A Year Is Never 365 Days Long
A tropical year, also known as a solar year, an astronomical year, or an equinoctial year, is, on average, approximately 365 days, 5 hours, 48 minutes and 45 seconds long (365.24219 days).

From: How Long Is a Tropical Year / Solar Year?

So, were a year defined as 365.24219 days the solar days would get out of step with the exact time of the New Year

• only to come into approximate agreement after 4 years
• but still drifting more slowly to be out of step the other way by about one day after 100 years, etc, etc.

In the current Gregorian calendar used since 1582 CE, one year averages 365.2425 days with an error of 27 sec/year (1 day in 3236 years).

For two "better calendars" see Is There A Perfect Calendar? for the "The Revised Julian Calendar" and the "Persian calendar" - who said those "ancients" were primitive.

Instead, Earth is for 365th solar noon short by 0.2464 degrees (quarter of 0.9856 degrees). Second year it is 0.4928 degrees (half of 0.9856), third year for 0.7392 degrees (three quarters of 0.9856) and foruth year is full 0.9856 degrees.

This means sun doesn’t appear in same position in sky on the solar noon of March 01 and so on after the completion of first year of earth in its orbit.

First year: lag by 1/4 of a day,
Second year: lag by 1/2 of a day - Here solar noon of Feb 28 of second year takes its position in the orbit where there was a midnight on Feb 28 of the first year

Third year: lag 3/4 of a day - Here solar noon of Feb 28 of third year takes its position in the orbit where there was a evening on Feb 27 of the first year

Fourth year: lag 1/1 of a day - solar noon of Feb 28 of fourth year takes the position of solar noon of Feb 27 of first year

Solar noon of the first year of Feb 28 is going back till it meet with solar noon on Feb 27 of fourth year

So does this mean day and nigh flip after two year due to the difference of 12 hours if not then everything is fine – just wondering - thanks

Solar noon of the first year of Feb 28 is going back till it meet with solar noon on Feb 27 of fourth year
So does this mean day and nigh flip after two year due to the difference of 12 hours if not then everything is fine – just wondering - thanks

I'm sorry if I'm confusing, let me try to explain it in one more way:

Solar noon on Feb 28 of given year is exactly 365th solar noon after Feb 28th of previous year.
Calendar counts days, not orbital position of Earth.

By counting days, instead of degrees in orbit, calendar makes error and needs correction in order to be useful for tracking seasons.

My explanation will be more clear if you pause the video @ 12:31 in the following link.



Just mark noon and midnight on the said dates. 

My explanation will be more clear if you pause the video @ 12:31 in the following link.



Just mark noon and midnight on the said dates.

Ok, let's assume the difference is 6 hours per year, to make things more obvious.

After 365 days calendar counts one year.
Days are still 86400 seconds each.
Solar noon is still when our meridian is directly facing the Sun.
Seasons shifted by 6 hours.

After 730 days calendar counts two years.
Days are still 86400 seconds each.
Solar noon is still when our meridian is directly facing the Sun.
Seasons shifted by 12 hours.

After 1095 days calendar counts three years.
Days are still 86400 seconds each.
Solar noon is still when our meridian is directly facing the Sun.
Seasons shifted by 18 hours.

After 1460 days calendar counts four years.
Days are still 86400 seconds each.
Solar noon is still when our meridian is directly facing the Sun.
Seasons shifted by 24 hours.

After 4 years we count one period between two solar noons as extra day.
It is irrelevant where in the year we do it.
One extra day compensates for seasons shift.

Without compensation, after 100 years our calendar would, at the beginning of spring, show April 14.
After 100 more years it would show May 9.
(Spring starts when Sun is above Equator and going north. It is based on tilt between Sun, and Earth's axis.)

Soon it would become useless for agriculture, and for few other activities.

EDIT:
I think that Arabic calendar is based on Moon.
Ramadan was in August in 2009 and in 2018 will be in May.
Their year is simply shorter and shifts pretty quickly through seasons.
They don't pay much attention to it.
But when they do business, they use Gregorian calendar.

I also think that Chinese calendar is based on Moon.
In 2016 Chinese new year was on Feb 9, in 2018 is on Feb 16.
They every several years add one month, so their year shifts only back and forth, not through all four seasons.
For business they also use Gregorian calendar.

All together we count hours based on time between two solar noons and days and hours can't shift from each other.

You are right. I just confused with the arrow in diagram. I appreciate your replies. Thank you again.

I confused you because I interpreted w/o diagram so here is correct version if you want to have a look

First year: Noon on Feb 28

Second year: Noon of Feb 28 coincides with Morning of Feb 28 of first year

Third year: Noon of Feb 28 coincides with Evening of Feb 27 of first year

Fourth year: Noon of Feb 28 coincides with noon Feb 27 of first year

one more question: do you think will this 6 hrs lagging in each year change the position of the sun in sky

I think flip happens if we follow the red arrow as a reference point on the globe in diagram right from the start point

Red arrow is on the solar noon on March 01 right at the start point
Red arrow is on the morning of March 01 after the completion of one year due to 6-hour extra rotation
Red arrow is on midnight of March 01 after the completion of the second year due to 12 hour extra rotation

This means the reference point of solar noon changes to midnight at the same start point in the orbit of earth in two consecutive years

one more question: do you think will this 6 hrs lagging in each year change the position of the sun in sky

Throughout the year Sun position does change.
Actually, what changes is altitude of complete Sun's apparent trajectory, which means altitude of solar noon changes too.

Winter starts when solar noon is lowest, summer starts when solar noon is highest, and spring and autumn start when solar noon is exactly in the middle.
Without correction, our calendar would slowly shift more and more every year and on same dates we would have different solar noon heights.
(In other words, on same solar noon heights our calendar would count different dates.)

But the change in the position of sun in the sky on the same date (e.g. March 01)) is so big that we can’t ignore. It will be easy if you follow the red line again on the globe from the start point (March 01) in the video. We have

Solar Noon on March 01, of the first year - start
Morning on March 01, of the second year but our clock will show noon (1200) - after completion of first year
Midnight on March 01, of the third year but our clock show noon (1200) - after completion of second yaer
Solar Noon on March 01, of the fourth year but our clock will show noon (1200) - after completion of third year

Should we have to adjust our clocks?

I meant if the clocks are synchronized (24 hour Noon to Noon) with the red line on the globe in above post

sorry i mess up with above - if the clocks are synchronized (24 hour Noon to Noon) with the red line on the globe then it doesn't show 1200 on solar noon on the March 01 except from the start point

there will be 0600 on the clock on the solar noon of March 01 of the first year
there will be 2400 on the clock on the solar noon of March 01 of the second year

sorry i mess up with above - if the clocks are synchronized (24 hour Noon to Noon) with the red line on the globe then it doesn't show 1200 on solar noon on the March 01 except from the start point

there will be 0600 on the clock on the solar noon of March 01 of the first year
there will be 2400 on the clock on the solar noon of March 01 of the second year

Red line in the above video, at 13:40, is not on the globe.
Full rotation of the globe is within each of the small rectangles lined along the orbital path.

The line is on the orbital path in the position of March 1 of the first year.
It is not even where any season begins, but where it was convenient for us to add that one extra day.

Here is full detail for those who confused with all of above.

Click the following video




Take any reference point in the orbit, say start point “P” in the diagram mentioned in the video @11:54. The reference point on the earth / glob is a red line (24 hrs. Noon to Noon).

Observe the earth at the said reference point "P" for four consecutive years.


Red line indicate solar noon (clock shows 1200) when the earth is at “P” at START

Earth returns to its original position after the completion of first revolution
Red line indicate Evening (clock shows 1800) but we have solar noon

Earth returns to “P” after the completion of second revolution
Red line indicate Midnight (clock shows 2400) but we have solar noon

Earth returns to its original position after the completion of third revolution
Red line indicate Morning (clock shows 0600) but we have solar noon

Earth returns to “P” after the completion of fourth revolution
Red line indicate Noon (clock shows 1200) - back on track

Here is full detail for those who confused with all of above.

Click the following video




Take any reference point in the orbit, say start point “P” in the diagram mentioned in the video @11:54. The reference point on the earth / glob is a red line (24 hrs. Noon to Noon).

Observe the earth at the said reference point "P" for four consecutive years.


Red line indicate solar noon (clock shows 1200) when the earth is at “P” at START

Earth returns to its original position after the completion of first revolution
Red line indicate Evening (clock shows 1800) but we have solar noon

Earth returns to “P” after the completion of second revolution
Red line indicate Midnight (clock shows 2400) but we have solar noon

Earth returns to its original position after the completion of third revolution
Red line indicate Morning (clock shows 0600) but we have solar noon

Earth returns to “P” after the completion of fourth revolution
Red line indicate Noon (clock shows 1200) - back on track

Next to the red line, on the right side we have white gap.
At red line Earth returned to original position, but not to original orientation towards the Sun.
Original orientation Earth had on the other side of the white gap, at the end of Feb 28.

That is why our counting of next year begins at Mar 1 in the second line on diagram at 13:40.
Mar 1 of the second line (and our next year) begins for the gap earlier than red line.

That is because we count whole days for our calendar.
Whole number of intervals between two solar noons.
(Actually between two solar midnights at Grinich, but it is same moment as solar noon at longitude 180, because that longitude is facing Sun directly.)

Next year ends for the gap earlier than own beginning, and two gaps earlier than Earth's original postition.
Third year begins two gaps before original position, and ends three gaps before it.
Fourth year begins three gaps before red line, and ends four gaps before original position (red line).
Since four gaps are (almost) one day, we add Feb 29 to bridge the four gaps.
That way fifth year begins at read line again and for this purpose we can call it first year again.

Note that every beginning and end are at solar noon.
Our calendar year didn't begin and end at read line.
Tropical (solar) year did, but that is not what our calendar counted.

Our calendar counted days from beginning of Mar 1, to end of Feb 28, not the time from red line to red line.

Here is full detail for those who confused with all of above.

Click the following video



Take any reference point in the orbit, say start point “P” in the diagram mentioned in the video @11:54. The reference point on the earth / glob is a red line (24 hrs. Noon to Noon).

Observe the earth at the said reference point "P" for four consecutive years.

Red line indicate solar noon (clock shows 1200) when the earth is at “P” at START

Earth returns to its original position after the completion of first revolution
Red line indicate Evening (clock shows 1800) but we have solar noon

Earth returns to “P” after the completion of second revolution
Red line indicate Midnight (clock shows 2400) but we have solar noon

Earth returns to its original position after the completion of third revolution
Red line indicate Morning (clock shows 0600) but we have solar noon

Earth returns to “P” after the completion of fourth revolution
Red line indicate Noon (clock shows 1200) - back on track

You appear to be assuming that the red line corresponds to a local solar noon. It doesn't - it indicates a point in the earth's orbit around the sun. For a given point on earth this will only match the same sun position every four years.

An extra day of the leap year is already counted when earth completes its fourth revolution in its orbit. Have you noticed the flip of a day into the night after two years if yes then does it create one full day after 4 years? My question is about this unnoticeable 24 hours. This reverses us one full day after 4 years.

I know my communication skill is not good as all yours, therefore, I thank you all for your patience and volunteering replies.

Without 29th of February one year would be exactly 365 days, or 31 536 000 seconds.
For Earth to complete one exact revolution around Sun it takes 1.0006635 such years.

To synchronize our calendar with orbital position we make one average year to be 365.2425 days.
But we count only whole days in single year, so to change average we make some years have different number of days.

An extra day of the leap year is already counted when earth completes its fourth revolution in its orbit. Have you noticed the flip of a day into the night after two years if yes then does it create one full day after 4 years? My question is about this unnoticeable 24 hours. This reverses us one full day after 4 years.

It's not clear to me where you're seeing a problem. For a given point on the earth's orbit, if it is solar noon at a particular place then two complete orbits later it would be solar midnight at the same place. Two further complete orbits later would take it forward to solar noon and in effect a day would have been gained. The calendar must be adjusted for this extra day so a leap day is inserted.

doesn't a leap day is adjusted itself in the extra rotation of earth towards the start point after the completion of Feb 28.

Also, do you think would I be able to see a star (a reference point in the sky) every night from a fixed spot on earth for 4 consecutive years if you have noticed the changing of days into the nights after two years?

I mean, do you think would I be able to see a star (a reference point in the sky) every night from a fixed spot on earth at the same position in the sky for 4 consecutive years due to the change of position of the earth in its orbit?

I thought a leap day adjusted itself but I was thinking wrong - Cleared now - Thank you both so much

I thought a leap day adjusted itself but I was thinking wrong - Cleared now - Thank you both so much

You're very welcome. Glad to help.

I thought a leap day adjusted itself but I was thinking wrong - Cleared now - Thank you both so much

I'm sorry for not being clear enough the first or second time.
At first I was not smart enough to understand why do you ask and what you don't understand.

About the star:

At the same date at midnight you see one set of stars every year. Sky map is the same.
Six months later at midnight you see completely different set of stars, because at noon the Sun is
between you and those first stars (can't see stars at day), and at midnight Earth is facing opposite way.

For example in June dominant in the sky is Summer Triangle, and in December dominant is Winter Hexagon.
(Winter Triangle also exists and I don't know if it is part of Winter Hexagon, or is composed of other, different stars.)
Besides astronomers, the people who knew the most about stars were old navigators.

Also, might help to google for difference between Solar day and Sidereal day.

No, you are smart but my communication was vague. Also, I didn’t do my homework properly. I thought

1- leap day and the day I observed during flipping (day into night on the face of the earth after 2yaers) are two different days. 2- The said flipping might affect the measurement of rotation of earth w.r.t star

I appreciate your replies. You are Great

Many Thanks