So, does anyone have any idea how accurate the sunpos macro is for historic
or prehistoric dates?  I am specifically interested in how much error to
expect in the sun's position during the first thirty minutes after sunrise
on the morning of the Winter Solstice, say during year -3000 at the


Also, is there a handy way to determine on which day the solstice occurred
during that year?

I'm hoping to be able to illustrate, with a nice POV-Ray animation, the
exceptional service life of Newgrange during a presentation for my civil
engineering practice course.

Thanks in advance for your help,
-David Wagner

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waggy <hon### [at] handbasketorg> wrote:
> So, does anyone have any idea how accurate the sunpos macro is for historic
> or prehistoric dates?

  I don't have any idea which calendar system sunpos.inc uses, but
assuming it's the gregorian calendar, that's actually not very accurate
when we are talking about thousands of years.
  The gregorian calendar has an error of 1 day each 3300 years (I don't
remember if it was 1 day too long or too short).
  Besides that, if it doesn't take into account the slowdown of the
Earth, it will err by some seconds when speaking about thousands of
years.

-- 
                                                          - Warp

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Warp  wrote in message <45c59d2b@news.povray.org>:
>   Besides that, if it doesn't take into account the slowdown of the
> Earth, it will err by some seconds when speaking about thousands of
> years.

AFAIK, the best available model for the rotation of Earth is (or was)
SMART97, which once was freely downloadable on the FTP site of the Bureau
des Longitudes, and which, fortunately, I still have on a very old backup
CD.

The paragraph about precision is:

# The accuracy of SMART97 has been determined by comparing the analytical 
# solutions of the three Euler angles with a numerical integration computed
# using DE403/LE403. Over 20000 days, between 1968 and 2023, the differences
# are smaller than 2.20 microarcseconds for psi, 0.65 microarcsecond for
# omega, and 2.10 microarcseconds for phi. From the three Euler angles and
# the variations of the ecliptic given by VSOP87, the quantities p, epsilon,
# chi and the sidereal time are computed at the same level of precision.

I can not recall where I found this info, but I seem to recall something
about an error of several degrees on the position of an eclipse during the
Roman Empire.

I believe there is little hope to have accurate data about the position of
the Earth beyond a couple of centuries.

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"Nicolas George" <nicolas$george@salle-s.org> schreef in bericht 
news:45c5ae8a$1@news.povray.org...
>
> I believe there is little hope to have accurate data about the position of
> the Earth beyond a couple of centuries.

However, I seem to remember that this has precisely been done for 
Stonehenge. But where to find the info??

Thomas

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Nicolas George <nicolas$george@salle-s.org> wrote:
> I believe there is little hope to have accurate data about the position of
> the Earth beyond a couple of centuries.

  I think that mathematical interpolation of the movements of the Earth
should give pretty accurate values for tens of thousands of years.
  The problem with current calendars is that they are linear while the
rotation of the Earth is not constant (which would require a non-linear
calendar system). Linear calendars are acceptably accurate for only a
few thousand years. If you want a calendar which is accurate to a fraction
of a second for tens of thousands of years, you have to use a non-linear
timeline (because of the slowdown of the Earth).

-- 
                                                          - Warp

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Warp  wrote in message <45c5ef88@news.povray.org>:
>   I think that mathematical interpolation of the movements of the Earth
> should give pretty accurate values for tens of thousands of years.

Except that it it not possible to interpolate, only to extrapolate, which is
much less accurate.

>   The problem with current calendars is that they are linear while the
> rotation of the Earth is not constant (which would require a non-linear
> calendar system). Linear calendars are acceptably accurate for only a
> few thousand years. If you want a calendar which is accurate to a fraction
> of a second for tens of thousands of years, you have to use a non-linear
> timeline (because of the slowdown of the Earth).

The computation system I was referring to, SMART97, is not linear at all. It
uses Poisson series, with thousands of terms.

The movement of Earth on its axis is just too complex to be computed
accurately over large periods of time.

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In article <web.45c55920e46e4f74442464bf0@news.povray.org>,
 "waggy" <hon### [at] handbasketorg> wrote:

> So, does anyone have any idea how accurate the sunpos macro is for historic
> or prehistoric dates?  I am specifically interested in how much error to
> expect in the sun's position during the first thirty minutes after sunrise
> on the morning of the Winter Solstice, say during year -3000 at the

> 
> Also, is there a handy way to determine on which day the solstice occurred
> during that year?
> 
> I'm hoping to be able to illustrate, with a nice POV-Ray animation, the
> exceptional service life of Newgrange during a presentation for my civil
> engineering practice course.

sunpos is too "simple" to give good results. but the web give you a lot 
of sites as "institut de mecanique celeste et de calcul des ephemerides" 
<http://www.imcce.fr/imcce.php?lang=en> (the english version)

try the "ephemeris generator" :))




-- 
klp

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"waggy" <hon### [at] handbasketorg> wrote:
> So, does anyone have any idea how accurate the sunpos macro is for historic
> or prehistoric dates?  I am specifically interested in how much error to
> expect in the sun's position during the first thirty minutes after sunrise
> on the morning of the Winter Solstice, say during year -3000 at the

>
> Also, is there a handy way to determine on which day the solstice occurred
> during that year?
>
> I'm hoping to be able to illustrate, with a nice POV-Ray animation, the
> exceptional service life of Newgrange during a presentation for my civil
> engineering practice course.
>
> Thanks in advance for your help,
> -David Wagner

As far as I can tell, sunpos.inc doesn't correct for precession, which means
it's useless for calculations that far in the past. The link contained in
sunpos.inc is dead, but I found http://www.stjarnhimlen.se/comp/ppcomp.html
that seems to have identical formulas. On that site, point 8 explains how to
correct for precession, although that looks a little too easy to me, as
precession is supposed to be vastly complicated.
There are C programs (with source, so that you can include them in POV!)
here:
http://www.moshier.net/
aa-56 should be what you are looking for. It's supposed to go back
accurately to 3000 BC, but of course 'real' accuracy is unknown.
For finding the solstice that year, I'm sure there's an easy way, but I
can't think of any apart from brute force.

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Thank you all for your combined wisdom on this matter.

I managed to find a spreadsheet (link to descriptive page of it below) to
calculate what I hope will be all the corrections needed for sunpos to
estimate the location of the Winter Solstice sunrise a few millennia ago at
the location of interest.  These data, combined with the links y'all have
provided to explain the formulas, should be enough to figure out how to
modify the macro.  It will be interesting to see how much the time of day,
perhaps even the day of the year, has changed as well.

http://jqjacobs.net/astro/epoch_2000.html#download

Luckily for me, civil engineers seem to be satisfied with linear
approximations for darn near everything, so the math shouldn't get to be
too involved.

Regardless of my success or failure, I plan to post back here with what I
find.

-David Wagner

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"waggy"  wrote in message
<web.45c9603e92dd103d442464bf0@news.povray.org>:
> I managed to find a spreadsheet (link to descriptive page of it below) to
> calculate what I hope will be all the corrections needed for sunpos to
> estimate the location of the Winter Solstice sunrise a few millennia ago at
> the location of interest.  These data, combined with the links y'all have
> provided to explain the formulas, should be enough to figure out how to
> modify the macro.  It will be interesting to see how much the time of day,
> perhaps even the day of the year, has changed as well.

As I said earlier, I doubt you will have a correct precision for such a
distant date. But in your case, it is probably not a problem. Let me
explain.

The course of the sun in the sky can pretty accurately be decomposed in two
components: the course of the sun along its daily path through the sky, and
the position of that path, low in winter and high in summer.

The former defines the local time of the place. And that is the point where
you lack accuracy: if you try to calculate it with earth-rotation models in
absolute time, you will have an offset of several minutes.

The latter is much slower, and therefore can bear a few minutes error.

Now, what you ask is the "sunrise". You can not make more localtimeish than
that.

Therefore, what you can do is:

- Compute the instant of the winter solstice in the year you are interested
  in. You can probably achieve better than a few seconds accuracy.

- Find the nearest sunrise at the place you are interested in. You will have
  a few minutes error, but this error would only visible through the
  position of the sun along its path through the sky, which is precisely the
  parameter you have fixed.

Well, all this is theory, and you probably can not do it with sunpos.inc.
The first step can probably be done with ephemerides programs. As for the
second, I have no idea.

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