Talk:Numerical model of the Solar System

Accuracy Claim
The article claims that it is possible to achieve accurate results in a Runge-Kutta integration of a Solar System model with a step size of 10 days. This is fine for the planets (if errors of a few kilometers in position are acceptable), but not for their satellites. The orbit of the Moon, for example, with its ~28 day period, would not be accurately modeled with a 10-day step size. I'm going to change this and clarify this section, if nobody has any objections. -Thucydides411 (talk) 16:25, 24 January 2010 (UTC)

(random heading)
(inserted by Said: Rursus (☻) 13:37, 30 December 2008 (UTC))

This article needs a complete rewrite, because it goes into far too much detail. It might be appropriate for an undergrad report, or perhaps for a textbook, but not for an encyclopaedia. Nevertheless, simulation of the Solar system, or more generally, simulation of n-body systems, is certainly a topic fit for Wikipedia. -- Jitse Niesen (talk) 02:54, 12 May 2006 (UTC)


 * Yes. Also, the current content has to be original research, because no respectible source on solar system dynamics would recommend such a bad algorithm. All physical quantities should be normalized, not in SI; the motion of the sun should be absorbed into the interaction; the positions should be advanced along Keplerian orbits, not this Verlet business; the outer planets should have longer time steps; and if we care about conserving energy, the integrator should be symplectic. And if we don't want to go through the trouble, would it be so terrible to splurge on Runge-Kutta? Ayá. Melchoir 06:00, 17 May 2006 (UTC)
 * All right, I give it a try. Rather focusing on the idea behind it than going in deep mathematical details --Tauʻolunga 00:04, 21 May 2006 (UTC)

Name change
I moved this article from Numerical model of Solar system to Numerical model of solar system, keeping in line with the lower-case usage at solar system. Please see Talk:Solar_system/Archive_001 and Talk:Solar_system/Archive_001 (with discussion) for rationale. — Knowledge Seeker দ 22:35, 14 May 2006 (UTC)


 * Is there a particular reason why there is no "the" in the title of this page? --Lasunncty (talk) 07:55, 14 February 2011 (UTC)

"Complications"
That paragraph is a train-wreck. It is confusing, has a couple of typos, and just generally needs re-written. Perhaps the entire article needs a "clean up" flag, or something? 74.133.133.186 05:11, 23 August 2006 (UTC)Derek

"Tayler series", Taylor series
There is a problem with the Tayler series equation, the t over 2! should be t^2 I think, someone should change it


 * Yep, you're probably right, so I changed it. Thanks for your note. Do you know that you could have changed it yourself if you are confident about it? Just click on "edit" at the top of the article. Cheers, Jitse Niesen (talk) 06:21, 14 December 2006 (UTC)

Solar energy
what exactly is solar technology —The preceding unsigned comment was added by 219.91.208.71 (talk) 09:07, 21 January 2007 (UTC).

Ehhmm!
Eehh, why this name? What is the topic range of "Numerical model"? Numerical computations for planet positions have been performed for at the very least 2400 years (Hipparchus) if not much more. Hipparchus was the first to create models, based on cycles and epicycles, which he used to compute the planet positions. Ptolemy improved on this, and so Arabic astronomers. Copernicus switched cycle assembly system, but kept the cycles and epicycles. Kepler was the first to leave cycles and epicycles for ellipses. First semi-modern computation, using Kepler's formulae. Then Newton took the effort to derive three of Kepler's laws from a general formula of gravitation that he developed, partially pilfering an inversed square from Robert Hooke, without giving proper credit. First fully modern modelling, where laws are derived from each other. Einstein created the relativistic system, which is used just in special cases of higher gravity, then mostly to derive size of perturbations. Latest modern computation. Newton's formula seems to me to be the one on which most modern numerical computations rely on, therefrom deriving VSOP:s, DE400, N-body models and such. The article could be such an overview, linking to individual models. Said: Rursus (☻) 13:36, 30 December 2008 (UTC)
 * Sections: Integration and Modern method are just about N-body successive integration with unspecified integration method. I would think that those section would be the basis for an article about N-body computations. Said: Rursus (☻) 13:42, 30 December 2008 (UTC)
 * No I'm partially wrong: Celestial mechanics is about the aforementioned models. "Numerical model of solar system" is a misnomer for "Newtonian gravity based numerical models", which is not a good title either. A name change would be good though. Said: Rursus (☻) 13:46, 30 December 2008 (UTC)

Miscellaneous Comments
Several comments which should be addressed, I think:

1. It is false to claim, as is done here, that computers can not integrate. They can, both numerically and analytically.

2. The lead (lede) should admit that the orbits of the planets are inherently chaotic on time scales of tens of millions of years and that approximate orbits can only be computed for +/- this length of time. (Lyapunov time is 50 million years)

3. The sentence:"The advantage of this method is that for a computer it is a very easy job to do, and it yields highly accurate results for all bodies at the same time, doing away with the complex and difficult procedures for determining perturbations." is ambiguous and unclear: WHAT is easy to do? - determine the initial very accurate positions and velocities? determine the mass of each object? determine the time step? Determine the acceleration? Etc.

4. The next sentence is just wrong:"The disadvantage is that one must start with highly accurate figures in the first place, or the results will drift away from the reality in time..." The difference will be continuous, but the notion that they are "drifting" is in direct contradiction to the fact that the orbits are chaotic - We don't know if planets will collide, be ejected from the Solar System, or be swallowed by the Sun in the long run. (As is made clear in the article Stability of the Solar System - which is eventually cited at the bottom of this article.)

5. I think it should be made clear in the lede that the simplest approximations treat all of the planets as point masses, and ignore MOST known objects (some because we don't know enough about their mass, position, or velocity; and some because there just too many or they're just too small to be considered important enough to include). And when more accurate results are desired, more detailed physics must be used. For instance, spherical masses with known diameters replace point masses, actual shapes of planets (oblate spheriods) replace spheres, treating density as nonhomogenous, etc. (see, for example IPN Progress Report 42-196 • February 15, 2014 The Planetary and Lunar Ephemerides DE430 and DE431, W. Folkner,et al).

6. Finally, I am removing the RIDICULOUS claim that a Δt of 10 days is "satisfactory". As was previously pointed out, it would completely fail to predict the Moon's orbit (would force it into a triangle!). (This was the last line in the Integration section). I welcome anyone to correct the statement and add it back - with suitable references.71.29.173.173 (talk) 19:47, 16 July 2016 (UTC)