Bode's 'Law' (Titius Bode law)

From Wiki:

QUOTE
Finally, raw statistics from exoplanetary orbits strongly point to a general fulfillment of Titius–Bode-like laws (with exponential increase of semi-major axes as a function of planetary index) in all the exoplanetary systems; when making a blind histogram of orbital semi-major axes for all the known exoplanets for which this magnitude is known, and comparing it with what should be expected if planets distribute according to Titius–Bode-like laws, a significant degree of agreement (i.e., 78%)[20] is obtained.[21]
QUOTE

Interesting? (My emphasis)

Cat :)
 
  • Like
Reactions: Helio and rod

rod

Oct 22, 2019
1,668
571
2,560
FYI. This site shows 4410 confirmed exoplanets now, http://exoplanet.eu/catalog/

My MS SQL query shows these stats for semi-major axis in au. Compared to our solar system, most documented now are a zoo :)

Copy Of exoplanet_current_properties stats3

CountOf# nameCountOfsemi_major_axisAvgOfsemi_major_axisMinOfsemi_major_axisMaxOfsemi_major_axisStDevOfsemi_major_axis
4410​
2862​
25.7904989667603​
0.00263​
9200​
300.1303598951​
 
Jun 1, 2020
840
555
1,260
From Wiki:

QUOTE
Finally, raw statistics from exoplanetary orbits strongly point to a general fulfillment of Titius–Bode-like laws (with exponential increase of semi-major axes as a function of planetary index) in all the exoplanetary systems; when making a blind histogram of orbital semi-major axes for all the known exoplanets for which this magnitude is known, and comparing it with what should be expected if planets distribute according to Titius–Bode-like laws, a significant degree of agreement (i.e., 78%)[20] is obtained.[21]
QUOTE

Interesting? (My emphasis)

Cat :)
That's really surprising. I recall that many attempted to apply TB to the known, perhaps 500 exoplanets, but with nothing close to a TB relationship could be found.

I am still cautious as to if their claim (ref. 20) is true, but it is interesting.
 
  • Like
Reactions: rod

rod

Oct 22, 2019
1,668
571
2,560
Good observation by Helio in post #4. The ref 20 is, https://arxiv.org/abs/2003.05121

"[Submitted on 11 Mar 2020] The reliability of the Titius-Bode relation and its implications for the search for exoplanets Patricia Lara, Guadalupe Cordero-Tercero, Christine Allen The major semiaxes of the planets in our Solar System obey a simple geometric progression known as the Titius-Bode Relation (TBR), whose physical origin remains disputed. It has been shown that the exoplanetary systems follow a similar (but not identical) progression of the form a_n= a_0 e^(bn), where a_0, b are constants to be determined for each system. Since its formulation, the Titius-Bode Relation has proved to be highly predictive in our Solar System. Using data from 27 exoplanetary systems with 5 or more planets and applying a proposed method, we conclude that reliable TB-like fits can be obtained for systems with at least 4 planets and that the precision of the TBR is 78%. By means of a statistical test we show that the periods of planets in real exoplanetary systems are not consistent with a random distribution. Rather, they show signs that their configuration is shaped by their mutual interactions."

Note the study used exoplanets with 4-5 or more exoplanets in orbit around the host star. Presently the site I showed lists 722 multiple planet systems, 88 have 4 or more exoplanets which includes the TRAPPIST-1, 7 exoplanet system.
 
Jun 1, 2020
840
555
1,260
After looking a little closer, FWIW, their modeling seems to be for very close orbits only. This is logical given that the low hanging fruit has given us the closer orbiting exoplanets.

About 95% of those orbits are within the orbital radius for Mercury, about 80% half that radius.

It's still interesting, but how robust will it be once the bigger picture comes along that would include the exoJupiters and exoSaturns of many of those systems?

Titius-Bode, though a mathematical tool and not a physics-based model, was so well respected -- it is still called a law, after all -- that it was used to justify the search for a "missing planet" at 2.8 AU, which is where the asteroids were found.

The variance with actual AU results are only off a few percent, even less for Jupiter.

This strengthened its respect, but theories (even if just mathematical) can still be falsified, which came with the discovery of Neptune, where the formula is about 22% off the mark.

Neptune is about 100x the distance than about 80% those in the modeling in the paper. That limits how robust it seems to be, IMO.

If a physical reason, however, could generate an actual hypothesis for planetary orbits, then this would really be something if it also matched their power law.
 
  • Like
Reactions: Catastrophe and rod

rod

Oct 22, 2019
1,668
571
2,560
Helio's post #6 is interesting but does not show which if any of the exoplanets found as multiples orbiting their host star are like our solar system or have habitable worlds, something I feel is the main goal in these studies to promote abiogenesis and astrobiology :) Going back to the exoplanet site I used in post #3, 722 stars have multiple exoplanets (solar systems), 88 systems show 4 or more as the study used I mentioned in post #5. The min host star mass is 0.08 solar for the TRAPPIST-1 system (7 exoplanets), the max is 1.56 solar mass host star for HR 8799, 4 exoplanet system. HR 8799 min semi-major axis is 16.4 AU, max is 68 AU. We encounter some *real differences* between the multiple exoplanet systems known today when comparing with Earth and our solar system. Such differences should be well documented for the public to understand I feel.
 
Jun 1, 2020
840
555
1,260
Helio's post #6 is interesting but does not show which if any of the exoplanets found as multiples orbiting their host star are like our solar system or have habitable worlds, something I feel is the main goal in these studies to promote abiogenesis and astrobiology :)
At least for me, my posts don't have any such goal. Abiogenesis is just and idea that may take a long time to understand, and the advanced chemistry and microbiology needed to get serious about it is not even an interest of most here, especially one who skipped biology in HS (ie me :)).

Going back to the exoplanet site I used in post #3, 722 stars have multiple exoplanets (solar systems), 88 systems show 4 or more as the study used I mentioned in post #5. The min host star mass is 0.08 solar for the TRAPPIST-1 system (7 exoplanets), the max is 1.56 solar mass host star for HR 8799, 4 exoplanet system. HR 8799 min semi-major axis is 16.4 AU, max is 68 AU. We encounter some *real differences* between the multiple exoplanet systems known today when comparing with Earth and our solar system. Such differences should be well documented for the public to understand I feel.
Yep. No doubt the variety of sizes and orbits has been surprising to discover, but even more surprising would have been to have no surprises. Better observations are scheduled, which might, I hope, take us beyond just the easy (e.g. large) exoplanets to get a better picture of what is out there.

Perhaps super large space-based interferometer scopes will be designed to allow incredible views of the nearby systems. I don't know of any law that would prevent them but I also don't know the engineering challenges that would be ahead for those who try.
 

rod

Oct 22, 2019
1,668
571
2,560
Helio, concerning your post #8 about abiogenesis and exoplanet studies, you said "At least for me, my posts don't have any such goal." However, look at the sources cited in post #1, source or reference 21. https://www.liebertpub.com/doi/10.1089/ast.2017.1720,
"Abstract One of the basic tenets of exobiology is the need for a liquid substratum in which life can arise, evolve, and develop..."

It is clear the need to show abiogenesis and life on some of the exoplanets is a major goal of astrobiology otherwise there would be no astrobiology science today. This should be clearly pointed out to the public I feel and my comments do call attention to this *tenet*. This tenet is clearly anchored in Charles Darwin letter(s) and warm little pond. That may not be where abiogenesis research is today (using Darwin's warm little pond) but his letters are the anchor and foundation of the tenet. This should be clearly acknowledged to the public. The warm little pond tenet or variation on this theme is extrapolated from Earth, the solar system and beyond to the exoplanets.
 
Last edited:
Jun 1, 2020
840
555
1,260
Helio, concerning your post #8 about abiogenesis and exoplanet studies, you said "At least for me, my posts don't have any such goal." However, look at the sources cited in post #1, source or reference 21. https://www.liebertpub.com/doi/10.1089/ast.2017.1720,
"Abstract One of the basic tenets of exobiology is the need for a liquid substratum in which life can arise, evolve, and develop..."
Ah, that explains your viewpoint. But it's certainly not explicit in the title or OP. Titius-Bode discussions rarely address life directly but more as a side note. The bigger issue is whether or not the power law can be tweaked to hold its "law" stature, which fell with Neptune's discovery.

It is clear the need to show abiogenesis and life on some of the exoplanets is a major goal of astrobiology otherwise there would be no astrobiology science today. This should be clearly pointed out to the public I feel and my comments do call attention to this *tenet*. This tenet is clearly anchored in Charles Darwin letter(s) and warm little pond. That may not be where abiogenesis research is today (using Darwin's warm little pond) but his letters are the anchor and foundation of the tenet. This should be clearly acknowledged to the public. The warm little pond tenet or variation on this theme is extrapolated from Earth, the solar system and beyond to the exoplanets.
But this has nothing to do with how planets take their places in orbital configurations. Though abiogenesis is certainly a tenet for nearly all astrobiology, you will find that Darwin never included such a tenet in his famous book. He uses "pond" six times but never as you mention. It might just have been a comment that stems from his grandfather's poem. Darwin also avoided addressing the evolution of mankind, though he did author a book later addressing it. Abiogenesis was way beyond his scientific expertise and he knew it. I suspect he respected the idea that God was the cause. He never became an atheist.

[FWIW, I found a site that allows word searches for Origin of the Species that I think you might like to have, if you don't already.]
 

rod

Oct 22, 2019
1,668
571
2,560
Okay, Helio's post #10 has some misconceptions I feel that must be addressed. Helio says about Darwin's warm little pond, "He uses "pond" six times but never as you mention." My observation. This is a common misconception, it is from his letter, 'Did life evolve in a `warm little pond'?', https://blogs.scientificamerican.com/thoughtomics/did-life-evolve-in-a-warm-little-pond/#:~:text=Charles Darwin was reluctant to publish his views,the first molecules of life could have formed.

Here is the well known quote using the sciam source. "But if (and oh what a big if) we could conceive in some warm little pond with all sorts of ammonia and phosphoric salts, light, heat, electricity etcetera present, that a protein compound was chemically formed, ready to undergo still more complex changes [..] "
~Charles Darwin, in a letter to Joseph Hooker (1871)

FYI creationists use this reference correctly and cite the letter. Helio also said "But this has nothing to do with how planets take their places in orbital configurations."

My point, the study of gas clouds in astronomy today is more than how a gas cloud could collapse and form stars and planets. A central tenet in astrobiology concerns searches for finding the chemical elements for the origin of life in the gas clouds that later, evolve into stars, planets, and by abiogenesis, into life, so this is more than how orbital configurations may develop. 'Ingredients for life appear in stellar nurseries long before stars are born', https://phys.org/news/2020-06-ingredients-life-stellar-nurseries-stars.html, June 2020. ""Complex organic molecules that could serve as building blocks for life are more ubiquitous than previously thought in cold clouds of gas and dust that give birth to stars and planets, according to astronomers at the University of Arizona Steward Observatory...These molecules also appear much earlier than conventional wisdom suggested, hundreds of thousands of years before stars actually begin to form, the researchers found. "

I find it refreshing when science freely acknowledges these tenets, astrobiology is founded upon abiogenesis and gas clouds need to contain the seeds for life to later evolve from non-living matter. Charles Darwin in his 1871 letter may not have thought like this but today the paradigm is there.
 
Jun 1, 2020
840
555
1,260
Okay, Helio's post #10 has some misconceptions I feel that must be addressed. Helio says about Darwin's warm little pond, "He uses "pond" six times but never as you mention." My observation. This is a common misconception, it is from his letter, 'Did life evolve in a `warm little pond'?', https://blogs.scientificamerican.com/thoughtomics/did-life-evolve-in-a-warm-little-pond/#:~:text=Charles Darwin was reluctant to publish his views,the first molecules of life could have formed.

Here is the well known quote using the sciam source. "But if (and oh what a big if) we could conceive in some warm little pond with all sorts of ammonia and phosphoric salts, light, heat, electricity etcetera present, that a protein compound was chemically formed, ready to undergo still more complex changes [..] "
~Charles Darwin, in a letter to Joseph Hooker (1871)
Okay, this explains your view. But, IMO, Darwin wasn't making any significant statement.

According to your own source, they note,
"Charles Darwin was reluctant to publish his views on life's origin. His only speculations on the subject are known from a private letter to his friend and colleague Joseph Hooker, in which he speaks of a 'warm little pond' in which the first molecules of life could have formed. " [my underline]

Science is always about "how", and he was guessing, privately, about "how" abiogenesis may have taken place. It's clear to me that he is simply guessing and, given his background, isn't addressing anything to be taken seriously, at least in terms of the likely conditions and ingredients. Hence, speculation is the right word.

My point, the study of gas clouds in astronomy today is more than how a gas cloud could collapse and form stars and planets. A central tenet in astrobiology concerns searches for finding the chemical elements for the origin of life in the gas clouds that later, evolve into stars, planets, and by abiogenesis, into life, so this is more than how orbital configurations may develop.
My point is that astronomy and astrobiology are actually separate. Certainly they both have significant overlap, but Titius-Bode itself is not in the overlap. Titius-Bode is a mathematical contrivance and doesn't attempt to address the origins of life.

I find it refreshing when science freely acknowledges these tenets, astrobiology is founded upon abiogenesis and gas clouds need to contain the seeds for life to later evolve from non-living matter. Charles Darwin in his 1871 letter may not have thought like this but today the paradigm is there.
Have you experienced astrobiology (mainstream) discussions where abiogenesis isn't considered a priori, thus a tenet?
 
Last edited:

rod

Oct 22, 2019
1,668
571
2,560
Helio in post #12 said "Have you experienced astrobiology (mainstream) discussions where abiogenesis isn't considered a priori, thus a tenet?"

My answer is never. Mainstream astrobiology is not based upon special creation as a tenet for the origin of life on earth or exoplanets, only abiogenesis is the tenet. Obfuscating this tenet and its historical origins (Charles Darwin letter) is a problem, that appears to me what you do. Clearly admitted this is refreshing.
 
Last edited:
Jun 1, 2020
840
555
1,260
My answer is never. Mainstream astrobiology is not based upon special creation as a tenet for the origin of life on earth or exoplanets, only abiogenesis is the tenet.
Agreed.

Given that abiogenesis isn't a working hypothesis in the strictest sense but taken as a sound idea that is upon a scientific foundation, it is, nevertheless, unfair to completely dismiss the idea for a divine intervention. This, however, is a philosophical argument and not a scientific argument. As a result, those that favor a divine action are seriously limited in what scientific arguments they can make against it, IMO.

Obfuscating this tenet and its historical origins (Charles Darwin letter) is a problem, that appears to me what you do. Clearly admitted this is refreshing.
How am I, and I assume others elsewhere, causing confusion about this tenet?

I'm not convinced that Darwin, in a private letter and never publicly stating it (apparently), constitutes anything close to a historical origin of it. Long before Darwin, Aristotle explicitly argued for "spontaneous generation" from non-life substances.

In the 17th century, Aristotle hypotheses were tested and falsified. They found that only life came from life, at least in their tests.

Erasmus Darwin (decades before Charles) was also explicit, but more philosophical when he wrote in his 1803 work (The Temple of Nautre) a poem which includes...

Organic life beneath the shoreless waves
Was born and nurs’d in Ocean’s pearly caves;
First forms minute, unseen by spheric glass,
Move on the mud, or pierce the watery mass;
These, as successive generations bloom,
New powers acquire, and larger limbs assume;
Whence countless groups of vegetation spring,
And breathing realms of fin and feet and wing.


But I see no way to segue this back to Titius-Bode. Perhaps a moderator will move these abiogenesis posts to a new thread. :)
 

ASK THE COMMUNITY

Latest posts