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parallaxicality
2011-Sep-20, 07:59 PM
I'm currently attempting to merge two Wikipedia articles into one big one:

11th millennium and beyond (http://en.wikipedia.org/wiki/11th_millennium_and_beyond)

and

Timeline of the far future (http://en.wikipedia.org/wiki/Timeline_of_the_far_future)

Problem: I'm angling to get "Timeline of the far future" promoted. To do so it needs to be fully referenced. This has been a poser because much of "11th millennium and beyond" is not referenced at all. So far I have managed to reference about half the material and move it over, but there are two big areas that still need help: Future transits and occultations.

Much of the transit material in "11th millennium and beyond" is taken from the individual transit pages, all of which, as far as I can tell, refer back to a single book: "Transits" by Jean Meeus. Unfortunately, none of the original references use page numbers, and this book is not in any library anywhere in my country of residence.

Humbly asked favour no 1: Is there anyone out there who might have access to the book and could give me the necessary page numbers?

Second problem: occulations. The principal source for the occulation information is this guy (http://www.marco-peuschel.de/), who as far as I can tell is an amateur astronomer with a hobby site, which wouldn't be accepted as a valid source even if his occultation info wasn't only accessible via the Wayback Machine.

Humbly asked favour no 2: Does anyone know of a valid academic source I could use for the occultation information?

Thanking you profusely in advance.

Centaur
2011-Sep-20, 08:58 PM
I have many of Belgian Jean Meeus' books, but not that one from 1989. Much of Meeus’ more recent work on transits and occultations is done through association with Italian Aldo Vitagliano, the author of the Solex numerical integration program for celestial mechanics: http://main.chemistry.unina.it/~alvitagl/solex . His software is free and quite useful. You will find Aldo’s e-mail address at the bottom of that webpage. He knows Meeus' e-mail address, and may provide it to you.

tony873004
2011-Sep-24, 09:11 PM
According to "11th millennium and beyond"
22767 April 18: Ceres occults Aldebaran.
23527 August 1: Pallas occults Castor.
40529 January 11: Ceres occults Aldebaran.
41367 January 7: Ceres occults Aldebaran
and lots of other future predictions.

But can we really know the exact state of the solar system 10s of thousands of years from now?

From the thread http://www.bautforum.com/showthread.php/120869-Computing-an-orbit-3-observations-from-Earth-hmm-that-s-moving-too....

If you think that old well-known asteroids have well established orbits, I invite you to study the orbital elements in MPCORB releases (about once a month) over a year.

{if you have TheSky, you probably haven't updated the asteroid info in years. Bring up Ceres or Vesta and then update the elements and watch how much they shift)

I've never tried this, but I suspect he's right. If so, how can anyone confidentely say that Ceres will occult Aldebaran on January 7, 41367?
There's a reason that JPL Horizons Ephermis system refuses to give you orbital elements of solar system objects beyond a few decades from now. I'd be skeptical to trust ANY of those transit predictions in the 11th millennium article.

Centaur
2011-Sep-24, 09:19 PM
Tony, I seriously doubt those predictions were made using orbital elements. Long term orbital theories have not been developed for asteroids. However, numerical integration seems relatively reliable for the long term, and I imagine that is what was used in this case.

tony873004
2011-Sep-25, 10:02 PM
Hi Curt. I agree with you. I suspect that they used numerical integration for the long-term predictions as well. But output from numerical integration is only as good as your input, and the forces you choose to model. JPL Horizons usually includes Ceres, Pallas, and Vesta as small perturbers in their numerical simulations that generate the ephemeris for solar system bodies. I just performed two simulations using Gravity Simulator to see what effect including/excluding the 5th largest asteroid, Interamnia, has on Ceres’ position after 39000 years. I ran the sim for 100 years, compared the final SMA of Ceres in each sim, used this to compute the period of Ceres after 100 years in each sim, then extrapolated the difference over 39000 years. My two Ceres were about 30 arcseconds apart. That’s enough to cause a predicted transit of a star to miss. I suspect the value would have been much larger if I had allowed Interamnia to perturb Ceres for the full 39k years. Maybe I'll try it again when I can let the computer spend more time on it.

Even if the person who predicted that Ceres would occult Aldebran in the year 41367 included Interamnia in the simulation, what value did he or she use for its mass? Interamnia’s Wikipedia page shows its mass as 3.9 +/- 0.18 E19 kg.

Vesta and Pallas also have error bars associated with their masses. There are hundreds of thousands of asteroids, both discovered and undiscovered. Can we ignore them in our model and still pinpoint Ceres to within an arcsecond 39k years from now?

Even if we could be spot-on about Ceres after 39 thousand years, how about Aldebran? According to its Wikipedia page, its proper motion has a +/- 0.89 mas/yr in RA, and 0.58 in Dec. Just in RA alone, that could translate into 33 arcseconds in 39K years. Ceres is never larger than an arcsecond as viewed from Earth. So how can we confidently state that a transit will take place?

Centaur
2011-Sep-25, 10:35 PM
Good points, Tony.

Jeff Root
2011-Sep-26, 03:26 AM
Could you please explain the differences between making
predictions using orbital elements and making predictions
using numerical integration? I would naively think they
were the same thing.

-- Jeff, in Minneapolis

Centaur
2011-Sep-26, 05:01 AM
Could you please explain the differences between making
predictions using orbital elements and making predictions
using numerical integration? I would naively think they
were the same thing.

-- Jeff, in Minneapolis

Jeff, orbital elements are pieces of data fed into an algorithm for determining a body’s position for given dates. For comets and asteroids we only have so-called osculating elements good for very short time frames. They are derived from a two-body solution relative to the Sun based on the smaller body’s position and velocity at a particular moment (the epoch). Temporary perturbations from planets are cooked into the solution permanently. Here’s the NASA/JPL resource for such elements: http://ssd.jpl.nasa.gov/sbdb.cgi . The charts I’ve drawn on my website for comets and asteroids are based on that system: www.CurtRenz.com/astronomical

The major planets have more complex orbital elements that allow for a theoretical base orbit to bend and twist. In addition, cyclical factors are thrown in to allow for perturbations. That system was used for the planets from Kepler’s time until late into the twentieth century. Due to high speed computers it became more practical to ignore Kepler and add up a series of cyclical factors. The ancients might have called them epicycles, but shhh, don’t tell anybody. The planetary and lunar charts on my website are based on that latter so-called analytical method.

The other computer era method is numerical integration. Essentially it also ignores the laws of Kepler and relies on the two more basic force formulae of Newton. One is related to a law of motion and the other to his law of gravitation. The method considers mass, position and velocity of all significant bodies in the solar system and the gravitational forces they exert on each other at a particular instant. Then new positions and velocities are determined for a very short time later based on accelerative effects. This is then repeated numerous times. If you’re familiar with calculus, this is sort of a cheating form of integration that relies on brute manipulation rather than the elegant method of calculus. The multi-body problem is simply too complex to develop reasonable solutions from pure calculus. Numerical integration is what I use for my graphics illustrating occultations and transits since high precision is required. I do that with the aid of Aldo Vitagliano’s Solex program. It’s free for you to use too: http://main.chemistry.unina.it/~alvitagl/solex . Perhaps we should invite Aldo to join this discussion. He is the one who aids Jean Meeus for long term or particularly precise predictions in Jean’s books.

Daggerstab
2011-Sep-26, 12:46 PM
A bit off-topic - if we are discussing integrators, there's also ORSA:
http://orsa.sourceforge.net/

Kangetsu
2011-Sep-27, 09:46 PM
Would it be in bad form to send your request to the astronomy department of a university that holds the book? I noticed there's a copy at the University of Northern Colorado. Perhaps Prof. Richard Dietz (see http://www.unco.edu/people.asp) could route your request to a sympathetic student?

parallaxicality
2011-Sep-28, 04:28 AM
Thanks for the advice guys! :)

I managed to locate the guy who (I think) posted the information onto Wikipedia in the first place and (shock of shocks) he replied. So assuming he gets back to me the first favour should be sorted soon. But I'm holding your ideas in reserve, as you can never put your faith in anything (or anyone) on Wikipedia.

tony873004
2011-Sep-28, 05:01 AM
...as you can never put your faith in anything (or anyone) on Wikipedia.
But thanks to people who fact check, like you, it becomes better each day. This morning, Wikipedia's page on "Density" defined density as
The '''mass density''' or '''density''' of a material is defined as its density per unit squared.
This afternoon, it was fixed.

grapes
2011-Sep-28, 06:31 AM
Density wiki (http://en.wikipedia.org/wiki/Density) now says "The mass density or density of a material is defined as its mass per unit volume." Fixed two errors. :)

O, sharp attack there (http://en.wikipedia.org/w/index.php?title=Density&action=history), was fixed less than an hour and a half later.

tony873004
2011-Sep-28, 07:23 AM
...O, sharp attack there (http://en.wikipedia.org/w/index.php?title=Density&action=history), was fixed less than an hour and a half later.

That's my point! I'm pro-wiki. Unlike a printed encyclopedia, mistakes are short-lived.

grapes
2011-Sep-28, 07:32 AM
You'd think changes to the first sentence would be harder to make. Like slow-pokes (http://www.youtube.com/watch?v=v_vz6Me_TIY&sns=fb) on Facebook.

Solfe
2011-Sep-28, 01:16 PM
Phil did this post a number of years ago, but it is still funny: Canada the smallest planet. (http://blogs.discovermagazine.com/badastronomy/2008/01/17/canada-the-smallest-planet/)

alvitagl
2011-Oct-20, 10:55 AM
... Perhaps we should invite Aldo to join this discussion. He is the one who aids Jean Meeus for long term or particularly precise predictions in Jeanís books.
Hi Curt! It has happened by chance, but here I am! :)

So how can we confidently state that a transit will take place?
Indeed, we cannot, and nobody can. Such a long-term prediction would be quite uncertain for a major planet, it is more or less nonsense for an asteroid.
Asteroids are so much affected by small gravitational perturbations from other companion bodies, especially due to frequent mutual close approaches, that their position along the average orbit becomes affected by chaotic unpredictability rather soon (from a few centuries to a few millennia according to the case).
When this chaotic behavior is at work, the uncertainty of the "along-track" position of the body tends to increase exponentially with time, no matter the accuracy of the starting data and no matter how many additional perturbers are taken in account. Roughly speaking, it might happen that you are successful in extending the accuracy of your prediction 100 more years in the future, at the cost of a 10 times increased accuracy of your model. But then, to extend it 1000 more years in the future, you will need 10^10 = ten billions more accurate starting model.
Perhaps, if somebody is interested and I can find the time to do the job, I can run an example involving Ceres or Pallas, demonstrating the concept...

Best regards.
Aldo Vitagliano

P.S. I'm new here, but since Curt already introduced me, I don't feel the need to go to the "Introduce yourself" thread

tony873004
2011-Oct-25, 12:50 AM
...Perhaps, if somebody is interested and I can find the time to do the job, I can run an example involving Ceres or Pallas, demonstrating the concept...
Welcome to the Baut forum, Aldo. Thanks for your reply. I'd be interested in your demonstration involving Ceres or Pallas if you can find the time.