earth orbit accuracy

[dab]

I have discovered a passage in the Anglo-Saxon chronicle
(Project Gutenberg text #657) that describes a solar eclipse:

A.D. 1135. In this year went the King Henry over sea at the
Lammas; and the next day, as he lay asleep on ship, the day
darkened over all lands, and the sun was all as it were a three
night old moon, and the stars about him at midday. Men were very
much astonished and terrified, and said that a great event should
come hereafter.

Now, this is a pretty precise description. Lammas should be Feb 2nd,
and the ecplise seems to have been near-total. Where exactly the king
was is unclear, but probably somewhere near the Channel.

I have tried to identify this ecplipse. Here be screenshots:
http://flaez.ch/scratch/1135.1.png
http://flaez.ch/scratch/1135.2.png
http://flaez.ch/scratch/1135.3.png

both celestia and xephem predict an eclipse on January 16th
for around 4 o'clock in the morning! Now unless good king Henry
went all the way to the Pacific, there is no way he could have seen
this eclipse at "midday" (or indeed, at all).

The reason I am posting this is, we could conceivably use this
eclipse to increase the quality of the custom orbits.
Could we not add just a new least significant term to earth
orbit to tweak it for this eclipse?

the problem is, I am not clear, whether the inaccuracy will more
likely be due to earth's orbit or the moon's.

also, please note that this eclipse should not take place
in mid-january but at Lammas, i.e. Feb. 2nd. I suspect
that will be one lunation later, "Feb 15th": We have to account
for the Gregorian 10-day-leap in 1582.

This brings to mind, would it not make sense to display the Julian
calendar for dates earlier than Oct 1582? The Gregorian dates
are simply misleading.

Another point apparent from the screenshot (1135.3): I attribute
the slight difference (compared to xephem)
in background stars for this eclipse
to celestias neglect of earth-axis precession. this should
be easy to fix.

In any case, this gives a good idea of celestia's accuracy.
Over the time of some 900 years, it is already deteriorating,
but still not completely off.

Please note I have been using celestia 1.2.2 -- I still have
trouble to get 1.2.4 to compile


best regards,

Dieter Bachmann

[granthutchison]

Celestia seems to be doing a pretty good job!
If you check the list of eclipses for the 12th century at this site
http://sunearth.gsfc.nasa.gov/eclipse/SEcat/SE1101-1200.html
you'll find no eclipse listed for 2 Feb 1135, but one exactly as you describe, reaching maximum at 03:27 on 16 Jan 1135, 30.8N 114.1E.

Whatever happened to King Henry, it doesn't seem to have been a solar eclipse ...

Grant

[chris]

The reason I am posting this is, we could conceivably use this
eclipse to increase the quality of the custom orbits.
Could we not add just a new least significant term to earth
orbit to tweak it for this eclipse?

the problem is, I am not clear, whether the inaccuracy will more
likely be due to earth's orbit or the moon's.

also, please note that this eclipse should not take place
in mid-january but at Lammas, i.e. Feb. 2nd. I suspect
that will be one lunation later, "Feb 15th": We have to account
for the Gregorian 10-day-leap in 1582.

This brings to mind, would it not make sense to display the Julian
calendar for dates earlier than Oct 1582? The Gregorian dates
are simply misleading.

Yes they are . . . But I think that there are also reasons for keeping the calendar consistent over time. Switching to the Julian calendar may show up as an option at some point though.

Another point apparent from the screenshot (1135.3): I attribute
the slight difference (compared to xephem)
in background stars for this eclipse
to celestias neglect of earth-axis precession. this should
be easy to fix.

In any case, this gives a good idea of celestia's accuracy.
Over the time of some 900 years, it is already deteriorating,
but still not completely off.

Please note I have been using celestia 1.2.2 -- I still have
trouble to get 1.2.4 to compile

. . . and that's the source of your problem. Celestia 1.2.4 and before had some problems with the orbit of the Earth, and calculations for eclipses were unreliable far in the past. The latest prerelease has a fix, and I can now reproduce, for example, the path of the eclipse of Xerxes in 479 B.C.E.:

http://sunearth.gsfc.nasa.gov/eclipse/SEhistory/SEplot/SE-0479Oct02A.gif

Note that this NASA eclipse site uses the Gregorian calendar even for ancient dates, though I'm not sure that it's indicative of any sort of convention.

On which platform are you running Celestia, and what sort of compilation problems are you having?

--Chris

[dab]

well, I must say, this is a sobering experience as far the
reliability of the anglo-saxon chronicle is concerned...

the eclipse seems to be some sort of literary topos inserted
to make the king's death a bit more dramatic. still, it
strikes me that the eclipse should be inserted at a 'correct'
date, i.e. around the time where there had indeed been one,
although not visible from england. it seems that there must
have been some rough idea at least about the predictability
of eclipses...


anyway, chris, my being unable to compile 1.2.4 (on linux) was just
because I was too lazy to upgrade all sorts of libraries. I have
done so now, and 1.2.4 is compiling cleanly (and it was worth the
effort).

cheers

dab

[dab]

hmmm - since you mention Xerxes' eclipse, I had a look at it,
and celestia seems to be about 5 hours 'late': instead of
11:30, the maximum is around 16:30, and thus over the atlantic
instead of over africa as on the map you linked; this is 1.2.4
now, and I wonder if you see this eclipse over africa and if
so, why I do not....

also, I am wondering how nasa can be so confident about plotting
eclipse paths as far back as 2000 BC.... since there is no
exact solution for the evolution of the solar system, and
eclipses are very delicate to calculate.

[selden]

dab,

Just because ther is "no exact [analytic] solution" does not mean that we do not have an extremely accurate model of planetary orbits. The gravitational effects of the major bodies of the solar system are quite well known these days. The formulas used to calcualte the positions of the earth and the moon have something like 1,000 terms in them.

There are detailed Chinese records of eclipses dating back to about 3BC and fragmentary ones going back to about 1000BC.

[dab]

Just because ther is "no exact [analytic] solution" does not mean that we do not have an extremely accurate model of planetary orbits.

so it seems. i'm impressed. although i would be even more
impressed if they would give error margins for their eclipse
data. i am well aware of the extreme accuracy available to
model the 'contemporary' solar system. but clearly, this is
due to extremely accurate observation. and you know how it goes
with interpolation, the more precisely you model something inside
a given range, the more erratic the system's behaviour will be
outside that range. viz. the much-loved funny orbits of celestia
for very remote dates. so there. all i'm saying is, if these
1000s-of-terms orbit remain valid over several millennia, i am
nothing short of amazed.

re early recorded eclipses, you know, if you find some cuneiform
fragments mentioning an eclipse, you will hardly have enough data
to improve your model. of course, if you _already_ have a model
for the period in question, you can go and try to identify the
eclipse. but otherwise -- just look what happened to me and my
1135 eclipse :) -- and this was from medieval england, not ancient
china or mesopotamia...

[Guest]

In principle, the error bars in professional eclipse preditions are available, just not published in places conveniently found using standard Web browsing. You have to have access to the professional journals. Some are available online through various library services.

Of course, the accuracy of the various methods of predicting planetary orbits gets worse for dates farther away from when accurate measurements have been made. The author of Guide has made comparisons among several different "theories" which can be found at http://www.projectpluto.com/accuracy.htm

Determining the sizes of the systematic errors are in Celestia's eclipse predictions ia rather more difficult, since they depend on the accuracy and precision of the CustomOrbits, which usually improve from one relase to the next as Chris includes more terms in the formulas.

My impression is that the older Chinese astronomical (astrological, actually) observations were rather more accurate than the early European ones. They had a much longer tradtion of precise record keeping. I found one discussion of this on the Web at http://eclipse99.nasa.gov/pages/traditions_morechina.htm#china and another at http://www.astro.uni-bonn.de/~pbrosche/iaucomm41/meetings/ga2000/as_li.html

[selden]

that was me. sigh.

[gef]

This brings to mind, would it not make sense to display the Julian
calendar for dates earlier than Oct 1582? The Gregorian dates
are simply misleading.

IMHO, the primary Celestia screen should stick as is currently.
The reasoning behind that, is that much astronomical software is
working like this, which makes good ground for technical comparisons.

Of course, let's not forget that Celestia could be a great tool in education.
Maybe an internal calculator is some short of menu would be useful,
in particular if it did include the ancient Greek and Roman calendars

[gef]

Celestia 1.2.4 and before had some problems with the orbit of the Earth, and calculations for eclipses were unreliable far in the past. The latest prerelease has a fix, and I can now reproduce, for example, the path of the eclipse of Xerxes in 479 B.C.E.:

http://sunearth.gsfc.nasa.gov/eclipse/SEhistory/SEplot/SE-0479Oct02A.gif

THANKS CHRIS!
(it was me who had requested extra accuracy for that one, a month ago)
Note that, this single match could guarantee enough accuracy for nearly
any celestial arrangement of the trio sun-earth-moon, for historic periods.

So, when is v1.2.5 coming out, finally?

[gef]

well, I must say, this is a sobering experience as far the
reliability of the anglo-saxon chronicle is concerned...
[...]
it seems that there must have been some rough idea
at least about the predictabilityof eclipses...

It wasn't very unlikely:
Thales of Melitus (6th century BC), had succesfully predicted the eclipse
of 28 May -584, probably based on Babylonian or Egyptian observations.
He then gained much respect for his "prophetical" abilities.
http://plato.evansville.edu/public/burnet/ch1a.htm

That trick should still be possible two millenia later...

[gef]

also, I am wondering how nasa can be so confident about plotting
eclipse paths as far back as 2000 BC.... since there is no
exact solution for the evolution of the solar system, and
eclipses are very delicate to calculate.

Good question.
I was wondering the same, while providing that URL on Xerxes' eclipse.

In the meantime, I went to the nearby observatory in Athens/Greece,
found the astronomers there and had a short chat with them on this:
In brief I was told that, modern astronomy is pretty accurate on ecliptic
phenomena, while talking within historical contexts, or +-5000 years.

The de facto standard appears to be the Horizons project from NASA's JPL.
I downloaded a 55-pages document from there and skimmed through it.

Quoting its first sentence:

"The Horizons On-Line Ephemeris System provides access to key solar system data and dynamic production of highly accurate ephemerides for solar system objects."

A little further:

"The underlying planet/satellite ephemerides and small-body osculating elements are the same ones used at JPL for radar astronomy, mission planning and spacecraft navigation."

Well, I could live happy with these Horizons ephemerides!

I believe that Celestia should be aligned with most Horizons' specifications,
such as time conventions and, in particular, SPK-based calculations (p.42).
http://ssd.jpl.nasa.gov/horizons.html

[gef]

all i'm saying is, if these
1000s-of-terms orbit remain valid over several millennia, i am
nothing short of amazed.

FYI,
I've been involved in geological projects a few times, and everything is
unbelievably "linear": continent X goes to that direction with this speed,
mountain Y goes there (every year the same, just with higher accuracy).
What is happening, is that the tools that we have to measure such
phenomena have vastly improved within a brief timerange of a few years
or decades, therefore everything is "constant". Food for thought, hm???

If someone has any comment on the uncertainty of our current solar
system models, it would be great to present it here...

It appears to me that selden had recently "accessed" such info...

[chris]

hmmm - since you mention Xerxes' eclipse, I had a look at it,
and celestia seems to be about 5 hours 'late': instead of
11:30, the maximum is around 16:30, and thus over the atlantic
instead of over africa as on the map you linked; this is 1.2.4
now, and I wonder if you see this eclipse over africa and if
so, why I do not....

In 1.2.5 prerelease 7, I increased the accuracy of orbits even further, so you should get better results with 1.2.5. The prerelease can be found here, albeit for Windows only right now:

http://www.shatters.net/celestia/files/celestia-win32-1.2.5pre7.exe

--Chris

[billybob884]

when installing prereleases, it still installs it under the name 1.2.4

[gef]

also, I am wondering how nasa can be so confident about plotting
eclipse paths as far back as 2000 BC.... since there is no
exact solution for the evolution of the solar system, and
eclipses are very delicate to calculate.

Eclipse events follow very regular patterns, called "saros" series and
have a trend to reoccur every approximately 18 years and 10-11 days.
Read this excellent page for more details:
http://www.earthview.com/tutorial/patterns.htm

I believe that Celestia should be aligned with most Horizons' specifications,
such as time conventions and, in particular, SPK-based calculations (p.42).
http://ssd.jpl.nasa.gov/horizons.html

I mean, not necessarily as a its computational engine, but rather provide
some facts on relative accuracy between Celestia and Horizons project,
leaving the big and long discussion for the astronomers among us

BTW. Maybe you are interested...

Astrolabe is a collection of software in Python -what a decent language-
for accurately calculating planet positions.
http://astrolabe.sourceforge.net/

This is a link discussing orbit stability and related laws:
http://www.dausha.net/sciences/orbits.shtml

[gef]

In 1.2.5 prerelease 7, I increased the accuracy of orbits even further, so you should get better results with 1.2.5. The prerelease can be found here, albeit for Windows only right now:

http://www.shatters.net/celestia/files/celestia-win32-1.2.5pre7.exe

--Chris

Hi Chris,

may I ask what kind of adjustments did you do to increase the accuracy?
I mean, was it a kind of bug or rather adding extra corrections?
The reason is that I wonder if this difference could be a systematic error
in other astronomical software as well.

thanks,
Fotis

[chris]

In 1.2.5 prerelease 7, I increased the accuracy of orbits even further, so you should get better results with 1.2.5. The prerelease can be found here, albeit for Windows only right now:

http://www.shatters.net/celestia/files/celestia-win32-1.2.5pre7.exe

--Chris

Hi Chris,

may I ask what kind of adjustments did you do to increase the accuracy?
I mean, was it a kind of bug or rather adding extra corrections?
The reason is that I wonder if this difference could be a systematic error
in other astronomical software as well.

thanks,
Fotis

Celestia was using the VSOP87 series that gave the Earth's position referred to the ecliptic and equinox of date. In 1.2.5pre7, I changed it to the VSOP87 series referred to the J2000.0 ecliptic and equinox (which is very close to the International Celestial Reference Frame). Which series to use is dependent on the application . . . I think xephem uses the equinox of date series. But in Celestia, since the positions of the Sun and other stars are fixed, the right choice is the series that uses a fixed equinox.

--Chris

[gef]

all i'm saying is, if these
1000s-of-terms orbit remain valid over several millennia, i am
nothing short of amazed.

If someone has any comment on the uncertainty of our current solar
system models, it would be great to present it here...

It appears to me that selden had recently "accessed" such info...

In fact, following a link that selden provided and going a little further,
I was able to get a document which is indicative of the accuracy we
may have by reading ancient astronomers' notes.

This is how earth's rotation slow down has been measured by scientists
and day is found to be 47/1000s smaller, back in 5th of June 1302 BC:
http://spacelink.nasa.gov/NASA.News/NAS ... s/89-06-13

Do we really want to add this effect in Celestia? :->

Seriously now,
our (human race) eclipse predictions are fairly accurate,
because the near-earth celestial mechanics model
would be erroneous only if an event happened that gave energy to the
system of planets like earth-sun-moon (and the ones nearby, truly).

So, if another body with high speed came and collapsed on any of these
three, our model could be wrong. But so far, this appears unlikely to
have occured in the past few thousand years or so.

Hey, I didn't read this anywhere, it's just plain physics!