# True length of sidereal year in 6000 b.c.e.

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## Main Question or Discussion Point

Hi there
Anybody out there able to explain to me how to calculate what the true length of a sidereal year was about 6000 years ago ?
Kind Regards
Edwin.

## Answers and Replies

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phyzguy
As I understand, the length of the sidereal year is quite stable. I was unable to find definitive information about the rate of change. Why do you think it is changing?

Hmm, I guess the answer would depend on what do you mean by "the true length", ie. what precision do you require.
The crude answer would be, that the sidereal year was the same as today, as the Earth's orbit didn't change noticeably on such time scales.

Why do you think it is changing?
As Sun is constantly loosing a tiny fraction of its mass via EM radiation and solar wind, the Earth is slowly drifting away from the Sun, and thus prolonging its orbital period. I am lazy to do it, but the calculation should not be difficult. I guess, the change would be really negligible on the scale of thousands years.
There might be also another factors influencing the Earth's orbit, e.g. interaction with other bodies in the Solar system, or tidal interaction with Sun. But these are probably even more negligible.

As Sun is constantly loosing a tiny fraction of its mass via EM radiation and solar wind, the Earth is slowly drifting away from the Sun, and thus prolonging its orbital period. I am lazy to do it, but the calculation should not be difficult. I guess, the change would be really negligible on the scale of thousands years.
There might be also another factors influencing the Earth's orbit, e.g. interaction with other bodies in the Solar system, or tidal interaction with Sun. But these are probably even more negligible.
Yeah solar tides are weaker than lunar tides which vary the distance of the moon by centimeters a year which at such large scales is practically invariant compared to the current distance. Of course tidal forces are not simple to calculate as the rate of efficiency in the exchange varies but at the very least the tidal effect like the solar mass loss is negligable on short timescales like thousands or even tens of millions of years. The variations due to eccentricity changes might be moresignificant but again 6000b.c.e. is far to recent for that to measurably vary

solar mass loss is negligable on short timescales like thousands or even tens of millions of years
Earth migrates away from the Sun at ~1.5 centimeters per year.
I don't know how reliable this figure is, but on a time scale of 6000 years, it makes only about 90m. So, very negligible change, indeed.

As I understand, the length of the sidereal year is quite stable. I was unable to find definitive information about the rate of change. Why do you think it is changing?
Hi there.
Firstly, thank you for taking the time to reply.
The reason I’m asking the question is because of the following article I read on the Harvard.edu website.
Title: Sidereal Years - Catalogue Uses in Archaeoastronomy
Authors: Barlai, K. & Ecsedy, I.
Journal: Inertial Coordinate System on the Sky, Proceedings of IAU Symposium No. 141 held 17-21 October 1989 in Leningrad, USSR. Edited by J.H. Lieske and V.K. Abalakin. Dordrecht: Kluwer Academic Publishers, p.197, 1989
In that article the author states
“the tropical solar year should have been 365.24244 days in 2000 b.c.e. and the sidereal year determined by successive heliacal rises of Sirius about 365.25059 days at 30 degrees northern latitude.”
Due to that statement and the current sidereal year being 365.25636 days, I wondered how the 365.25059 day value was produced. I mean, that’s quite a discrepancy. Could it have something to do with Sirius ? If so, may I kindly ask once more if that could be explained ?
Kind regards
Edwin

Hmm, I guess the answer would depend on what do you mean by "the true length", ie. what precision do you require.
The crude answer would be, that the sidereal year was the same as today, as the Earth's orbit didn't change noticeably on such time scales.
Thank you for the reply.
Kind regards
Edwin

I don't know how reliable this figure is, but on a time scale of 6000 years, it makes only about 90m. So, very negligible change, indeed.
Thank you for the reply.
Kind regards
Edwin

“the tropical solar year should have been 365.24244 days in 2000 b.c.e. and the sidereal year determined by successive heliacal rises of Sirius about 365.25059 days at 30 degrees northern latitude.”
Due to that statement and the current sidereal year being 365.25636 days, I wondered how the 365.25059 day value was produced. I mean, that’s quite a discrepancy. Could it have something to do with Sirius ? If so, may I kindly ask once more if that could be explained ?
Kind regards
Edwin
If you measure the sidereal year in SI seconds, it is the same now as thousands years ago - based, on previous posts, I made a quick back-of-the-envelope calculation, and the discrepancy would be somewhere on the order of 10-7 seconds, if I am not mistaken. So practically, zero change.

One possible explanation of the discrepancy could be that the sidereal years (now and before) are provided in days. Now, what "kind of" days they used? Do they specify in the article? The value for current sidereal year: 365.25636 days is apparently using ephemeris day, which is fixed to 86 400 SI seconds. Is the ephemeris day used as a unit for the value 365.25059 as well?

Another possible explanation (and I think more probable), would be due to proper motion of Sirius. The Sirius system is very close to us, so it might appear to move more "rapidly" on the sky comparing to more distant stars.
the sidereal year determined by successive heliacal rises of Sirius
... during the period between two successive heliacal rises (one year), the Sirius might have changed the apparent position enough to explain the discrepancy. ... ancient Egyptians should have used a more distant star as a reference to anticipate flooding, not Sirius

These are just my suggestions to explain the discrepancy, but I'd like to be corrected by others, if my thoughts are wrong.

If you measure the sidereal year in SI seconds, it is the same now as thousands years ago - based, on previous posts, I made a quick back-of-the-envelope calculation, and the discrepancy would be somewhere on the order of 10-7 seconds, if I am not mistaken. So practically, zero change.

One possible explanation of the discrepancy could be that the sidereal years (now and before) are provided in days. Now, what "kind of" days they used? Do they specify in the article? The value for current sidereal year: 365.25636 days is apparently using ephemeris day, which is fixed to 86 400 SI seconds. Is the ephemeris day used as a unit for the value 365.25059 as well?

Another possible explanation (and I think more probable), would be due to proper motion of Sirius. The Sirius system is very close to us, so it might appear to move more "rapidly" on the sky comparing to more distant stars.

... during the period between two successive heliacal rises (one year), the Sirius might have changed the apparent position enough to explain the discrepancy. ... ancient Egyptians should have used a more distant star as a reference to anticipate flooding, not Sirius

These are just my suggestions to explain the discrepancy, but I'd like to be corrected by others, if my thoughts are wrong.
Hi Lomidrevo, thank you for the reply.
I don't find any mention of ephemeres days in the article. The article I'm quoting from can be found here [http://adsabs.harvard.edu/full/1990IAUS..141..197B].
Kind regards
Edwin.

phyzguy
I would agree with @lomidrevo that the proper motion of Sirius is the most likely cause for the discrepancy. Sirius is relatively close and so has a significant proper motion. Modern astrometry uses distant quasars as references, which are so far away that their parallax and proper motion are basically zero.

I would agree with @lomidrevo that the proper motion of Sirius is the most likely cause for the discrepancy. Sirius is relatively close and so has a significant proper motion. Modern astrometry uses distant quasars as references, which are so far away that their parallax and proper motion are basically zero.
Thank you Phyzguy.

I don't find any mention of ephemeres days in the article. The article I'm quoting from can be found here [http://adsabs.harvard.edu/full/1990IAUS..141..197B].
At the beginning of the article:
On a historic time scale the length of the sidereal year varies and its variation is determined by the proper motion and the precession of the star chosen as time marker.
Bingo!

At the beginning of the article:

Bingo!
Hi there Lomidrevo.
Awesome!!! Could I kindly request a working example of that statement. I would really love to be able to actually calculate the length of a sidereal year going back x-years based upon that statement. How do I do that ? Thank you for spotting that Lomidrevo.
Kind regards
Edwin

I probably don't understand your goal. If you want to know what was the sidereal year x thousands years ago, you already know the answer with super-high precision: it was the same as it is today (measured by taking very distant quasars as reference, see post #12 by @phyzguy). So you don't need to calculate anything.
Contrary, if you measured it by taking a close star as a reference, Sirius for example, which cannot be considered as a fixed background star anymore, you wouldn't get a precise value.

Since the moon is constantly slowing the spin of the Earth and every major Earthquake can have a measurable effect on day length, these things would probably need to be considered when comparing year length using days as units of measure.
There are so many unknowns that any prediction is probably not much more than a guess no matter how much research you do. Recent Earthquakes have caused the earth to spin faster which counters the effect of gravitational braking. Maybe, the people at NASA could make an educated guess about day and year length ten millennium ago, but it would still be a guess.

Since the moon is constantly slowing the spin of the Earth and every major Earthquake can have a measurable effect on day length, these things would probably need to be considered when comparing year length using days as units of measure.
There are so many unknowns that any prediction is probably not much more than a guess no matter how much research you do. Recent Earthquakes have caused the earth to spin faster which counters the effect of gravitational braking. Maybe, the people at NASA could make an educated guess about day and year length ten millennium ago, but it would still be a guess.
My brother actually works for NASA. I will try to remember to ask him, but I suspect he will say the same thing I posted above. He works with microthrusters for cubesats, but has always been passionate about cosmology. I share that passion, but I chose computer science over aerospace engineering.

Since the moon is constantly slowing the spin of the Earth and every major Earthquake can have a measurable effect on day length, these things would probably need to be considered when comparing year length using days as units of measure.
These effects play no role, if you use emphemeris days (SI days) for the measurements. It would make difference if you used solar days.

As Sun is constantly loosing a tiny fraction of its mass via EM radiation and solar wind, the Earth is slowly drifting away from the Sun, and thus prolonging its orbital period. I am lazy to do it, but the calculation should not be difficult. I guess, the change would be really negligible on the scale of thousands years.
There might be also another factors influencing the Earth's orbit, e.g. interaction with other bodies in the Solar system, or tidal interaction with Sun. But these are probably even more negligible.
I am not convinced that interaction with other bodies in Solar System is negligible in medium term.
The direction of Earth orbit apsides oscillates nearly periodically, with periods in the region of 100 000 and 400 000 years - and eccentricity of the orbit also changes over that period. Principally due to perturbations from Jupiter and Saturn.
How much does Earth orbital period change over such 100 000 year cycles of eccentricity?

I probably don't understand your goal. If you want to know what was the sidereal year x thousands years ago, you already know the answer with super-high precision: it was the same as it is today (measured by taking very distant quasars as reference, see post #12 by @phyzguy). So you don't need to calculate anything.
Contrary, if you measured it by taking a close star as a reference, Sirius for example, which cannot be considered as a fixed background star anymore, you wouldn't get a precise value.
I guess my confusion with the matter revolves around how the sidereal year is determined. As I understand it, it takes 365.256363004 ephemeris days (Earth rotations) of 86400 seconds each for Earth to orbit the Sun. An ephemeris day is an imaginary value though because it takes Earth (a) 86164.098903691 seconds of mean solar time to complete a rotation around its axis (stellar day) ... (b) 86164.090530832 seconds of mean solar time to complete a rotation upon its axis (sidereal day). According to Wikipedia
"Atomic clocks show that a modern-day is longer by about 1.7 milliseconds than a century ago, slowly increasing the rate at which UTC is adjusted by leap seconds. Analysis of historical astronomical records shows a slowing trend of about 2.3 milliseconds per century since the 8th century B.C.E."
If the length of the year is determined by the amount of rotations it takes Earth to complete around its axis in one orbit of the Sun, and that rotation time is increasing, then how can one say the length of the year hasn't changed over the passage of time ?
I think that's probably the source of my confusion here ... so far ... I mean, I get it, "freeze" the length of the day (a rotation) at 86400 seconds and the length of the year will never change .... but that's not what's actually happening because the length of a rotation is changing and has been changing over the passage of time.
How does one make sense of these things ?
Kind regards
Edwin

My brother actually works for NASA. I will try to remember to ask him, but I suspect he will say the same thing I posted above. He works with microthrusters for cubesats, but has always been passionate about cosmology. I share that passion, but I chose computer science over aerospace engineering.
Hi ChrisKnight. That's very kind of you, but I don't think that's necessary. I'm just trying to get my head around ... well ... you can tell by the thread. Somebody will put me straight soon enough ... I hope.
Kind regards
Edwin

If the length of the year is determined by the amount of rotations it takes Earth to complete around its axis in one orbit of the Sun, and that rotation time is increasing, then how can one say the length of the year hasn't changed over the passage of time ?
I think that's probably the source of my confusion here ... so far ... I mean, I get it, "freeze" the length of the day (a rotation) at 86400 seconds and the length of the year will never change .... but that's not what's actually happening because the length of a rotation is changing and has been changing over the passage of time.
You are right, the value you get depends on the choice of units. If your units are changing over time, like solar days for example, than it is no surprise that the value of the sidereal year will be changing as well (although 1.7 milliseconds per day per century is not that bad on timescales we discussed so far). However, if you chose a fixed time units (SI seconds, or SI days), the sidereal year is pretty stable (on the scales we discussed). This is more sensible to me, to chose fixed units.
No matter of the time units, note that you also have to chose a very distant stars as a reference, in order to not produce additional discrepancy caused by proper motion, as we seen in case of Sirius. That was the original storyline of this thread.

How much does Earth orbital period change over such 100 000 year cycles of eccentricity?
According to wikipedia, it doesn't change with these cycles:
Eccentricity varies primarily due to the gravitational pull of Jupiter and Saturn. However, the semi-major axis of the orbital ellipse remains unchanged; according to perturbation theory, which computes the evolution of the orbit, the semi-major axis is invariant. The orbital period (the length of a sidereal year) is also invariant, because according to Kepler's third law, it is determined by the semi-major axis.

I am not convinced that interaction with other bodies in Solar System is negligible in medium term.
The direction of Earth orbit apsides oscillates nearly periodically, with periods in the region of 100 000 and 400 000 years - and eccentricity of the orbit also changes over that period. Principally due to perturbations from Jupiter and Saturn.
How much does Earth orbital period change over such 100 000 year cycles of eccentricity?
You are right, the value you get depends on the choice of units. If your units are changing over time, like solar days for example, than it is no surprise that the value of the sidereal year will be changing as well (although 1.7 milliseconds per day per century is not that bad on timescales we discussed so far). However, if you chose a fixed time units (SI seconds, or SI days), the sidereal year is pretty stable (on the scales we discussed). This is more sensible to me, to chose fixed units.
No matter of the time units, note that you also have to chose a very distant stars as a reference, in order to not produce additional discrepancy caused by proper motion, as we seen in case of Sirius. That was the original storyline of this thread.
Thank you Lomidrevo. So sticking to the original storyline, if I wanted to calculate what the length of a stellar year was 6000 years ago using Sirius as a point of reference, how would I go about doing that ? Just asking the question is making me shrink in my seat.
Kind regards
Edwin