Talk:Titius–Bode law

message: I'm updating the article to reflect the latest(!) work on the Titius-Bode Law. Please be patient, this is a substantial update. Note: this is thoroughly grounded in science; it is essential to correct long-held misconceptions about about the Law. The comprehensive authority for this is Michael Martin Nieto's book "The Titius-Bode Law of Planetary Distances: Its History and Theory" (1972). --Jekkara (talk) 05:47, 26 March 2021 (UTC)
thread_title: Updates

message: I have had to modify the first para of the text, which originally described a planet's distance from the sun as the "semi major axis" of its elliptical orbit. This is not true; it wrongly assumes the star to be at the center of the ellipse where the major and minor axes intersect. According to Kepler's First Law, a planet orbits a star in an elliptical path with the star at one focus of the ellipse and nothing at the other focus. In other words, the planet's distance from the star is the distance from the focus occupied by the star, to the opposite end of the major axis. User:Alan Marshall floratwokettles@hotmail.com     —Preceding unsigned comment added by 198.163.53.10 (talk) 19:16, 16 January 2009 (UTC)
thread_title:  Kepler's First Law 

message: I have never seen the last section with the table and Mercury units and the 2:1 ratio elsewhere.  Is this original work?  Unless a reference gets tagged on it in the next few days, I recommend removing the section.  The whole page needs references, too...  --zandperl 14:57, 26 August 2005 (UTC)
replies: text: I think almost a year waiting for the ref to appear is more than long enough, and have deleted this section. The whole entry has enough of a cranky feel to it as it is, without more of this stuff. Robma 14:18, 17 June 2006 (UTC)
thread_title: Original work?

message: Because the New Bodes Law competes with the IAU definitions, I will continue to support it.
I have known of 1ceres.com for years.  And, the previous works done on megspace.com/science/ceres first introduced the equation to myself years before this issue.  Please refrain from accusations.
The information has been verified. The article content has been edited by others.  Your just playing god.  Enjoy your toadstool.
Nice detective work there.  I got a username just so we could discuss the matter.  I can't believe that you used the "hello" portion of the web site while ignoring the information.  Yah, and if you do a little archive search you'll see that information has been around for awhile. Thanks for communicating. But, deletion is all you seem to know. OK fine.
The offensive information that is not good enough:
—Preceding unsigned comment added by PlanetCeres (talk • contribs) 
:Please indicate when you're done rewriting your comment so that I can reply. --Ckatzchatspy 08:32, 18 August 2006 (UTC)
replies: text: OK - first off, please don't devolve this difference of opinion into a fight. I'll ignore the insults, and the fact that you've rewritten an older comment to focus it on me. By the way, I did read through the site (your site?), and not just the front page. It's an interesting theory. However, the point of all this hasn't been to debate the correctness of the theory. It is the fact that the citations you've presented - and the web site itself - do not provide sufficient reference to warrant adding your theory to Wikipedia's astronomy articles. That does not in any way mean that it shouldn't be published, or be on a web site, or discussed, or anything like that. It just means that it is not verifiable in a manner that meets the standards set by this project. --Ckatzchatspy 09:11, 18 August 2006 (UTC)

text: Please be aware that PlanetCeres is trolling multiple articles and talk pages with his periodicity theory. Check his contributions and those of anonymous IP 71.215.54.11 for details. Nick Mks 09:03, 18 August 2006 (UTC)
thread_title: IAU Special Interests

message: Shouldn't we just replace Asteroid Belt with Ceres? The data is for Ceres. And indeed Ceres has been used historically for that particular position on the table, so it is not original research (as a synthesis of existing data). 132.205.93.19 02:56, 25 August 2006 (UTC)
replies: text: Go right ahead; I'm not sure why the asteroid belt is there in the first place. Melchoir 06:14, 25 August 2006 (UTC)
thread_title:  Asteroid Belt, Ceres 

message: I have added a point-of-view tag to this article, as it seems insufficiently critical.  In particular, the discussions of 'updating the law" worry me.  Among astronomers and planetary scientists, the relationship is generally held to be a combination of equal parts resonance, coincidence, and shortage of degrees of freedom (at least three parameters and only eight or ten points).  For example, Murray and Dermott, in the standard reference work 'Solar System Dynamics', show that the arrangment of the moons of Uranus can be fit very well by a Titius-Bode relationship, but that so could any arbitrary stable system.  As an example of how lowly regarded Titius-Bode is, the planetary science journal Icarus specifically states in their instructions to authors that they will not accept submissions discussing it or similar relationships.Michaelbusch 05:24, 28 August 2006 (UTC)
replies: text: That sounds about right. I didn't know about Icarus, but I'm not surprised! Melchoir 06:22, 30 August 2006 (UTC)
replies: text:  Having just put together a review of the Titius-Bode law controversy for a science magazine over here in the UK, I took another look at this entry, and I feel it needs a complete re-boot. Trouble is, who has the time to do this - esp. given the virtual guarantee of having the new version trashed by monomaniacal trolls in 24 hrs flat ? Robma 07:51, 30 August 2006 (UTC)

text: Actually, Icarus will not entertain a paper about "improved" versions of the erstwhile "law", unless it is "accompanied by some detailed physical/chemical arguments to explain why the new relation is to be preferred."  One gets the impression this is the perpetual motion machine of dynamics:  too many pseudo-numerological fruitcakes in the world, I guess.  This needs to be mentioned in the article, as well as Murray and Dermott's statistical counter-argument given in Solar System Dynamics.  mdf 13:26, 31 August 2006 (UTC)
thread_title:  point-of-view tag 

message: What about the Saturnian satellites? How closely do they follow the rule? CFLeon 05:46, 27 April 2007 (UTC)
replies: text: In some cases, planetary satellites fit similar rules—but not the very same rule! SharkD (talk) 04:26, 27 February 2008 (UTC)
thread_title: Saturn's Moons?

message: I added a table comparing the Bode's Law prediction of orbital periods between adjacent planet pairs to the suggested (perhaps coincidental) orbital resonances listed for planets in that article.  The main reasons for this table are (1) to demonstrate that Bode's Law does not translate to the orbital resonance ratios commonly proposed, (2) to demonstrate that the proposed orbital resonances are not consistent but are picked out to match whatever the actual numbers are, (3) to remind people that Mercury's relationship in Bode's Law has been "fudged" - 0 is not a power of two!, (4) to hint that perhaps "around 2.3" is as good a power law as any (unless you can pull something informative out of The Well-Tempered Clavier).  I do not believe I am committing any "original research" by dividing ratios or taking orbital distances to the 1.5th power, so don't even start with that - I'm just putting the models next to one another in the same language because until I thought about it I hadn't realized Bode's law predicts all irrational orbital resonances. 70.15.116.59 (talk) 21:08, 9 December 2007 (UTC)
replies: text: While your statements are correct, they do start to tread into original research and I'm afraid I don't see what they add to the article.  We already state that the apparent fit of the law is due to 'a combination of orbital resonance and a shortage of degrees of freedom'.  I don't think a table is really needed - especially since, as you say, there is cherry-picking to fit the data points. Michaelbusch (talk) 00:29, 10 December 2007 (UTC)
replies: text: The problem is, the table did not appear to support the idea that Bode's Law was due to orbital resonance, since it gives one value and orbital resonance gives the other.  I never figured out what "shortage of degrees of freedom" meant, I'm afraid...  Also, the orbital resonances provided were not my idea; they're from the orbital resonance article. 70.15.116.59 (talk) 05:03, 10 December 2007 (UTC)
thread_title:  Table of Bode's vs. orbital resonances 

message: I am having trouble plotting the function as it appears in the article. I can only get the curve to "line up" with the first several planets if I change it to the following:
:a  = 0.4 + 0.3 · 2 (m - 1)
See this image of where I've plotted both functions in some math software. The purple function f(x) is the original, as it appears in the article. The orange function g(x) is the modified function. Only the latter fits any of the plotted points. SharkD (talk) 07:39, 8 February 2008 (UTC)
thread_title: Plotting the function

message: The formulation paragraph needs to be written in such a way that someone who doesn't already know the law can understand it: the current paragraph has two equations (the description of how they are related is either glib or simply wrong) and no clear algorithmic process for calculating the distance of a given planet.
It's a simple algorithm, and the formulation paragraph ought to be able to explain it so any idiot (like me) can understand and apply it at once.
82.153.72.124 (talk) 16:38, 13 April 2008 (UTC)
replies: text: But that's just it; it's not a simple algorithm. It's somewhat cobbled together, and really doesn't have an easy, universally applicable formulation. The best is that which is described at the top. Any algebraic formulation, such as that at the bottom, requires a power that yields zero, which, apparently (I wasn't aware of this) is minus infinity. Serendipodous 19:13, 16 June 2009 (UTC)
thread_title:  Incomprehensible formulation 

message: The article seems to have something of a negative bias intended to disprove the law before explaining it. The line where it states that the formula has been discredited and made moot in the eyes of the astronomers seems to display the contributors negative POV, It has been marked for citation for a while now and no relevant source has been sighted. The law was posited in the 18th century, for its time the law seems like a great achievement- predicting orbits of planets and bodies not even discovered then, I think someone should remove the questionable line already where the citation needed tag has been placed.  —Preceding unsigned comment added by Theo10011 (talk • contribs) 12:39, 15 December 2009 (UTC)
replies: text: But that's a fact. Astronomers do not accept Bode's Law as real. Many astronomical journals refuse to accept any papers on Bode's Law in principle. Given the number of cranks who've tried to add their own solutions to Bode's Law onto this page, I think such forthright language is appropriate. Serendipodous 12:50, 15 December 2009 (UTC)
replies: text:  Again thats your opinion, or even if it was a generally held consensus among the astronomical community stating in the article without a reputable source makes it inappropriate. That line was marked for citation for that very reason I suppose, since there hasnt been any credible source sighted I think it should be removed. Again, Astronomers might or might not accept Bode's law, doesn't mean it doesn't exist, Newtonian Mechanics didn't lose their place in history with the advent of quantum mechanics, our understanding and the need to explain new phenomenon grew. I would like to point out the line about Icarus refusing to accpet reworked or improved versions of the law was half true pointed out by mdf above, they just require detailed physical/chemical arguments to accompany it. As for the "cranks" submitting there own solutions, well the law itself seems so simple and elegant even to a layman that people feel they can submit their own solutions, perhaps thats one of the attractions about the law. they just need to know that this isn't the place for original research.Theo10011 (talk) 21:17, 16 December 2009 (UTC)
replies: text:  I'm not sure it does exist; it only exists if you accept that the numerical value doesn't hold for Mercury (unless you accept a sequence of powers that goes from -infinity to 1) or Neptune (which it just skips over). As for the page as is, I wouldn't mind changing it but I don't want this article to give the impression that astronomers consider the law scientifically valid. Serendipodous 21:57, 16 December 2009 (UTC)
replies: text: Hi Serendipodous, I dont know what you mean by "it doesnt exist", if you're referring to the semantical argument between a rule or law or whether you believe that such a theory was never presented. Historically far more propostoruos scientfic theories have been proposed, the world believed at a point that the sun revolved around the earth or even that the world was flat in some point in history, do we purge the mention of these older laughable theories from history and encyclopedias today, do we ridicule them. I think you keep overlooking the time it was posited, In the 18th century for its time it was a remarkable achievement no matter what you think of it today. The law or rule isn't entirely useless either, It correctly picked orbits of the first 4 planet with a possible location for a fifth in 1801, you can not overlook the time it predicted those without any observational or empirical scientific evidence, even if it doesnt hold true for trans-jovian bodies it WAS relevant at one point and deserve to be mentioned without any reporter bias. The questionable tone of the article is present through out, the first para of the Theoretical Explanation seems consumed with questioning the validity of the law rather than providing what it should, a theoretical explanation just states alternative arguments for its apparent validity.Theo10011 (talk) 22:36, 16 December 2009 (UTC)
thread_title:  Negative Bias 

message: Bode's law is discussed as an example of fallacious reasoning in Lecture Five (pages 194--196) of his 1898 lectures: 
 
Reasoning and the Logic of Things (RLT) (The 1898 Lectures in Cambridge, MA)
* Peirce, C. S., Reasoning and the Logic of Things, The Cambridge Conference Lectures of 1898, Kenneth Laine Ketner, ed., intro., and Hilary Putnam, intro., commentary, Harvard, 1992, 312 pages, hardcover (, ), softcover (, ) HUP catalog page. Text of the lectures that William James invited Peirce to give in Cambridge, MA. (Extracts variously from drafts and from delivered lectures were earlier published in CP 1.616-677, 6.1-5, 185-213, 214-221, 222-237, 7.468-517.)
:
Editorial Procedures, xi-xii
Abbreviations, xiii-xiv
Introduction: The Consequences of Mathematics, 1-54
  (Kenneth Laine Ketner and Hilary Putman)
Comment on the Lectures, 55-102   (Hilary Putman)
Lecture One: Philosophy and the Conduct of Life, 105-122
Lecture Two: Types of Reasoning, 123-142
[Exordium for Lecture Three], 143-145	
Lecture Three: The Logic of Relatives, 146-164
Lecture Four: First Rule of Logic, 165-180
Lecture Five: Training in Reasoning, 181-196
Lecture Six: Causation and Force, 197-217
Lecture Seven: Habit, 218-241
Lecture Eight: The Logic of Continuity, 242-270
Notes, 272-288
Index, 289-297
Thanks. Kiefer.Wolfowitz (talk) 18:44, 12 March 2010 (UTC)
thread_title:  [[Charles Sanders Peirce]] 

message: Excuse me people but I think that the formula a= 0.4 +0.3*2^m  is WRONG.  You cannot obtain the values in the table here with that law.
Planet 	k	T-B rule distance	Real distance
Mercury	0	0.4              	0.39
Venus  	1	0.7              	0.72
Earth  	2	1.0              	1.00
The correct law is a= 0.4 +0.3*m, this one correctly give the "T-B rule distance (AU)" for the right "m" (try to believe).
For example for the Earth we have ("m" of Earth is "2")--> 0.4 +0.3*2=1.
For Mercury ("m" of Mercury is ZERO) --> 0.4+ 0.3*0=0.4  (with the exponential formula you can never obtain 0.4)
I did not change anything because I was already accused of vandalism (I did a mistake correcting a formula...). -- 22:00, 14 March 2010 85.218.11.204
:Did you notice the line where it says
:\scriptstyle m = -\infty, 0, 1, 2 \ldots
:?  The first value in the series is negative infinity... AnonMoos (talk) 23:59, 14 March 2010 (UTC)
thread_title:  About the formula 

message: The table states the errors way too exact.  For example, the error for Jupiter is said to be 0,00%.  Yes, if Jupiter's real distance was exactly 5,20 AU it would be correct, but now it's not.  Is it necessary to use 2 decimals for the error (as it's decimals of percents, it's actually 4 decimals)? Fomalhaut76 (talk) 12:07, 19 May 2010 (UTC)
thread_title:  Error percentage 

message: The five (possibly seven) planets in the solar system HD 10180 are positioned in a similar pattern as that predicted by Bode's law, according to the following article:
http://www.eso.org/public/news/eso1035/
Might be worth writing up as tentative
-Tristan (anonymous)  —Preceding unsigned comment added by 173.248.194.155 (talk) 01:25, 25 August 2010 (UTC)
thread_title:  Solar system HD 10180 offers new evidence 

message: If Bode's Law is not coincidental, then it ought to be possible to begin with a mathematical model of the early solar system, with a flat protoplanetary disk surrounding a star, and then, by dividing the disk into hundreds of representative points (particles), which of course will all influence each other under the prevailing forces, use Newtonian gravity equations to mathematically derive a relation which encapsulates Bode, in terms of the distance apart of the accreted particle masses (planets), and also predicts alternative spacing patterns. This has never been done. However it would be immensely useful in the search for earth-type planets; for example if we find say 3 large planets around a star, then we could use this math to tell us, at once, if there will also be a planet in that star's habitable zone, without having to spend years or decades of telescope time searching for it. Any mathematicians up for it?  —Preceding unsigned comment added by 142.161.207.211 (talk) 00:30, 22 January 2011 (UTC)
replies: text: Yes that's not very clear. Well if we sequence the planets, like, for Mercury N=1, for Venus N=2, Earth N=3..etc,.....where N means "number".... then k= 2 to the power of (N-2).   Or k=2^(N-2). However this doesn't work for Mercury. Using N=1 for Mercury should give us k= 1/2. However this value works pretty well on the graph, so I don't know why they didn't use it for consistency's sake. (63.163.22.209 (talk) 05:37, 30 November 2011 (UTC)
thread_title:  Newton to Bode 

message: I will admit I am not in any possible way an expert on this, or deeply knowledgeable on the subject, or at all mathematically correct. I am only a Middle Schooler at the moment, so excuse my errors.
I had a preliminary theory (very simple) that would explain a good many things about Ceres' (or so it seems) involvement in the Titius-Bode law. First of all, as many, I believe, I have assumed that the fifth number, 2.8, does not at all relate to Ceres, but instead to the planet located where the asteroid belt is today that never actually formed. My theory is this:
Some time after planetary formation, most of the planets we know of today are fully formed, excepting the fifth, Theia (ring a bell?), which is disrupted by Jupiter's gravity and prevented from fully forming. I have calculated that Theia existed dangerously close to the 5:2 Kirkwood gap (Țp= 2.53) using the simple equation d³=p². Therefore, Theia's orbit becomes increasingly elliptical towards Jupiter, until, upon entering it's orbit, it is slingshotted towards the inner solar system, increasing it's velocity so that when it approaches earth orbit, Theia overtakes Earth from behind greatly reducing the force of impact and ensuring earth's survival. The rest is history. 
Additionally, I believe that the tenth Titius-Bode measurement, by some believed to be pluto, is in reality the Kuiper Belt, too sparse too form a planet in the first place.  — Preceding unsigned comment added by 69.143.164.189 (talk) 22:09, 4 December 2013 (UTC)
thread_title:  A possibility 

message: Professor Andrew Prentice's work in the 1970s with his modifications to the Laplacian hypothesis of planetary creation by adding a component for turbulence, has provided a great deal of theoretical support for this theory. Amongst other things, he extended this theory to the system of Jupiter and its moons. His resultant predictions for the densities and compositions of the Galilean moons of Jupiter turned out to be far more accurate than anybody else's, as confirmed by the measurements taken by the Voyager and other Jupiter-reaching spacecraft. It resulted in NASA taking his theory very seriously. His theory also explains why the outer planets don't match; or more correctly, why there is a change to the formula that then makes it match. 
Finally, my understanding is that Prentice's work IS indeed accepted by mainstream astronomers. I don't understand enough about it to add this to the article myself, which is why I'm only putting it here.
101.175.94.11 (talk) 11:55, 25 January 2014 (UTC)
replies: text: A paper called  Testing the Titius-Bode law predictions for Kepler multi-planet systems came out. This shows that this law does not apply to most exoplanetary systems as it found about 1 out of 28 predicted planets. However, this number could be significantly larger when taking a chance of the planet non transiting the star or the planet being too small into account.  --Artman40 (talk) 23:09, 19 June 2014 (UTC)
thread_title:  Andrew Prentice and his modified Laplacian hypothesis DOES support  the TB law. 

message: Hello fellow Wikipedians,
I have just added archive links to  on Titius–Bode law. Please take a moment to review my edit. If necessary, add  after the link to keep me from modifying it. Alternatively, you can add  to keep me off the page altogether. I made the following changes:
*Added archive https://web.archive.org/20070928205336/http://www.floridastars.org/9605cohe.html to http://www.floridastars.org/9605cohe.html
When you have finished reviewing my changes, please set the checked parameter below to true to let others know.
Cheers. —cyberbot IITalk to my owner:Online 18:52, 27 August 2015 (UTC)
thread_title:  External links modified 

message: "...supposing the distance of the Earth from the Sun to be divided into ten equal Parts, of these the distance of Mercury will be about four, of Venus seven, of Mars fifteen, of Jupiter fifty two, and that of Saturn ninety five."[1] not 96 as somebody wrote before-
new link for 95 is:
http://dawn.jpl.nasa.gov/mission/background_02.asp
--91.34.222.170 (talk) 19:37, 17 October 2015 (UTC)
thread_title:  correct citation + dead link 

message: Planet X is now officially back on the menu, with different packaging as Planet Nine.  See    The article guesses its semimajor axis is somewhere very roughly around 700 AU.  Titius and Bode tell us it is within a few percent of 614.8 AU, or failing that, 1229.2 AU, or failing that, 307.6 AU.
None of this is sourceable or addable yet - don't even try - but it's bound to get mentioned sometime.  (though one thing to watch for, while trying to drive a stake through this old chestnut until the ichor of mixed metaphors sprays across the stars, is whether it's possible for someone to say no, wait, it's the average distance, it's the perihelion, or the aphelion, or something) Wnt (talk) 16:47, 20 January 2016 (UTC)
replies: text: Alright... I got tempted to add some of the weird distant bodies in the table to see what it looks like.    As a heuristic, this law actually seems pretty nice - I mean, with just a little effort you could use it to immediately understand in your mind which minor planets are in what general league in terms of distance.  That said, I may well have bent the OR rules too far doing this... for example, while some sources refer to semimajor axis I have no idea if this particular near-pseudo-science actually limits itself to that particular measurement.  I'm sort of on the fence about self reverting the whole thing at the moment.  And yet ... my it's nice to just look and see things around Pluto, Eris, CR105, GB174, Sedna as five different classes of planets roughly as spaced out as the more familiar examples. Wnt (talk) 23:08, 12 March 2016 (UTC)
thread_title:  Time for a test: Planet Nine 

message: A mention of the Nice model in relation to Titius-Bode would be helpful to those who are familiar with it and who wonder about the change in orbits of Neptune and Uranus proposed by it. — al-Shimoni (talk) 10:54, 23 February 2017 (UTC)
thread_title:  No mention of the Nice model 

message: Now, naturally, we can handwave the original figures given, in tenths of AU, as just for the sake of convenience in calculating and writing things down in the 18th century; these days we could modify both the initial measurements and the assumed coefficient between them to be much more precise given that we have magic number slaves to do it all for us (ie computers, or even just pocket calculators).
But, even given that allowance, I, er... can't see how the progression works? There's supposed to be something meaningful there, but as far as I can see at the moment it's just a big old ass-pull. How are each of the numbers for successive planets arrived at, starting with Mercury as the baseline? There's mention of it doubling every time, and something called "k", but everything in the article is so convoluted that I'm having trouble picking it out. Is there any hope of having the concept laid out in a very straightforward manner? If all we're doing is coming up with very limited precision numbers between about 0.4 and 100 (or indeed, integers from 4 to 1000), then it can't be THAT complex.
After all if that's made plain, and there IS any kind of validity to the model which only becomes plain after e.g. integrating the data for dwarf and minor planets in certain bands as notional single items (maybe even combined with a nearby main planet) with an averaged-out orbital radius, correcting the Mercury baseline and adjusting other coefficients to make the datapoints fall more comfortably onto the trendline, we at least need to know what it is we're altering and how it was originally expected to work.
4, 7, 10, 14, 28, 52... etc. It doesn't speak of a particularly obvious relationship to me. Other than the doubling between Mars and Ceres? (I might have misremembered a number or two there?) 146.199.0.251 (talk) 20:01, 27 September 2017 (UTC)
replies: text: It's pretty simple: take Mercury's orbit radius as one constant ("a") and the Venus orbit radius minus the Mercury orbit radius as a second constant ("b"), and then the radiuses of the planet orbits beyond Mercury are predicted as a+(b*2^n), where n=0 for Venus, n=1 for Earth, and so on.  (Actually, "b" is usually chosen so that a+2b equals one astronomical unit, but that's a relatively minor difference.)  The formula has problems, but it did basically predict Uranus and the asteroid belt... AnonMoos (talk) 14:38, 29 September 2017 (UTC)
thread_title:  OK, I'm having trouble getting my head around the maths here. 

message: The introduction to this page says that the law has been superseded. Superseded by what? What was the next theory accepted by scientists, and what is the current theory accepted by scientists? There are links for further reading at the bottom, but I don't see any indication about why the links are relevant to this page, except that they must be about a similar topic (that is without having read the articles).
I feel like this article leaves me at a cliffhanger.  209.133.79.7 (talk) 00:48, 7 January 2018 (UTC)
replies: text: It's been superseded by an understanding that real world orbits don't usually obey simple numerical laws of this type.  -- AnonMoos (talk) 10:45, 17 January 2018 (UTC)

text: According to the article, the law has been discredited... because of Pluto and Eris... which aren't even planets. Go figure! DAVilla (talk) 05:10, 22 December 2021 (UTC)
thread_title:  Superseded by What? 

message: *******************  11Jul2021************************************* 
Under Titius_Bode , Wikipedia page. 
I have programmed the Titius_Bode equation into a Tool Control language TCL  gui program and very interested in modeling  Titius_Bode-like calculations also. I have run the JPL Keplar data with automatic curve fitter.  Maybe there is a contact interested in working or reviewing this  item? The autofitter found a = 5.14E-01 and b = 1.55E+00 for the Modified Power function <y=a*C**x>, which was close to the Armellini formula for planetary distances. In 1921, G. Armellini suggested a planetary distance formula, equivalent to <y = 0.2792 x 1.53**n> . Other authors have suggested 1.73 or, 1.842, for the C term in a planetary distance power function <y=a*b**x>. The Modified Power function error is at 5 percent of the Y axis, which is at the non-significant borderline level generally cited. The Weibull growth curve should fit the Y axis with a 1 percent error. In these growth functions, the Levenberg-Marquardt (L-M) algorithm was used with double precision C's.Thank you. Dewi7 Ps. The TCL WIKI editor is locking, so I have more material than evident. (talk) 15:42, 11 July 2021 (UTC)
thread_title:  programmed the Titius_Bode equation into TCL