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parallaxicality
2010-Sep-10, 09:55 AM
The recent announcement of the planetary system around HD 10180

(www.en.wikipedia.org/wiki/HD_10180)

has given us a sample of planets in one system about as large as ours was when the law was first formulated (5 confirmed planets, as opposed to 6). It does seem, from a cursory examination, that their ratios do seem to fall vaguely into a Bode-like pattern, but I can't work out the math.

AndreasJ
2010-Sep-10, 10:41 AM
Ignoring the unconfirmeds, the estimates semimajor axes are:

c 0.0641 AU
d 0.1286 AU
e 0.2699 AU
f 0.4929 AU
g 1.422 AU

d-f are each about twice the distance than its inner neighbour, suggesting a Bode-like pattern, but then g is almost trice the distance of f. Assuming a missing "Ceres" between f and g doesn't help as g would now be too close in (if exo-Ceres was at ~1 AU, g "should" have been at ~2 AU).

Also, the apparent doubling this close in would imply a much smaller constant in the Law, with no obvious physical difference to explain it.

So I don't think this system supports Bode's Law as anything but a coincidence.

Paul Beardsley
2010-Sep-10, 11:28 AM
The fact that we can even have this conversation is... awesome.

I remember learning about Bode's Law over 30 years ago. I thought we'd have to wait for interstellar travel before being able to check it out.

Centaur
2010-Sep-11, 05:15 AM
Bode’s law begins with fallacious reasoning that sneaks by most people. It starts with a supposed doubling sequence (0, 3, 6, 12, 24, 48, 96, 192, 384) to which 4 is added, then the values are divided by 10 resulting in theoretical radial distances from the Sun in astronomical units. Can you see the immediate flaw? The first value should be 1.5, not zero, in order for that to be a true doubling sequence.

AndreasJ
2010-Sep-11, 06:53 AM
Given that no reason has been given that there should be a doubling sequence in the first place, it's not clear to me why a "true" doubling sequence would be more legitimate than the (0, 3, 6, 12, ...) one.

A far larger problem for the Law is Neptune ...

tusenfem
2010-Sep-11, 09:28 AM
Bode's law (or rather Titius-Bode Law) is still an active region in research (http://esoads.eso.org/cgi-bin/nph-abs_connect?db_key=AST&db_key=PRE&qform=AST&arxiv_sel=astro-ph&arxiv_sel=cond-mat&arxiv_sel=cs&arxiv_sel=gr-qc&arxiv_sel=hep-ex&arxiv_sel=hep-lat&arxiv_sel=hep-ph&arxiv_sel=hep-th&arxiv_sel=math&arxiv_sel=math-ph&arxiv_sel=nlin&arxiv_sel=nucl-ex&arxiv_sel=nucl-th&arxiv_sel=physics&arxiv_sel=quant-ph&arxiv_sel=q-bio&sim_query=YES&ned_query=YES&adsobj_query=YES&aut_logic=OR&obj_logic=OR&author=&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=AND&title=bode+law&txt_logic=OR&text=&nr_to_return=200&start_nr=1&jou_pick=NO&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1) even in peer reviewed journals. The papers by Dubrulle & Graner (1994) are interesting as a starting point as they show that all kinds of "TB laws" can be generated, not just the one we use in our solar system (for the innermost planets). Apparently if there is a region where there is scalar invariance, like in the protoplanterary disk, TB-like distributions seem to be a natural result from linear instabilities in the disk. (the D&G and G&D papers 1994, are freely available from ADS, see above link).

Kullat Nunu
2010-Sep-11, 02:09 PM
The paper describing the discovery (http://www.eso.org/public/archives/releases/sciencepapers/eso1035/eso1035.pdf) of the planets discusses extrasolar Titius-Bode laws.

Jens
2010-Sep-11, 02:28 PM
Bode’s law begins with fallacious reasoning that sneaks by most people. It starts with a supposed doubling sequence (0, 3, 6, 12, 24, 48, 96, 192, 384) to which 4 is added, then the values are divided by 10 resulting in theoretical radial distances from the Sun in astronomical units. Can you see the immediate flaw? The first value should be 1.5, not zero, in order for that to be a true doubling sequence.

Why 1.5? Why not half of 1.5, which is 0.75, or half of that? I think you would have to start with an arbitrary first number.

baric
2010-Sep-11, 07:23 PM
Why does Bode's Law not apply to the moons that formed naturally around Saturn & Jupiter?

R.A.F.
2010-Sep-11, 11:04 PM
Why does Bode's Law not apply to the moons that formed naturally around Saturn & Jupiter?

The question you should be asking is "why should it apply?"

Bode's "law" is a combination of coincidence and numerology nothing more.

caveman1917
2010-Sep-11, 11:56 PM
The question you should be asking is "why should it apply?"

Bode's "law" is a combination of coincidence and numerology nothing more.

But it is a testable hypothesis.

So the OP makes a valid point that we can finally start testing it, but like you i wouldn't expect it to hold in any way.

tusenfem
2010-Sep-12, 09:05 AM
There is no such thing as THE Titius-Bode law, like clearly described in the papers by Graner (http://esoads.eso.org/abs/1994A%26A...282..262G) & Dubrulle (http://esoads.eso.org/abs/1994A%26A...282..269D) (1994).
Titius-Bode as it is, is "well" applicable for our solar system (well, up until Uranus), would not work for Jupiter. One reason for that is e.g. a migration of the 4 Galilean satellites of Jupiter, leading to the 4:2:1 resonance of the inner three.
In any other planetary system that we find, the "law" may look quite differently e.g. ([0 1 2 4 8 16 32] + 6) / 8, who knows ....

frankuitaalst
2010-Sep-12, 10:38 AM
Agreed , the Bode "law" is nothing more than a tendency that the distances between planets increase with the distance of the planets fromp the center. Not a law .
So we get a power "law" like distribution of the planets.
All we can say is there some tendency that planets which are close to the star are packed more densily then the planets residing far from the central . Thus resulting in a power like distribution

Just for my own interest I've taken the actual known extraterrestial planets from the extraterrestial catalog and did some fitting using the standard excel facilities , which I can share here
The graphs at the bottom seem to support a tendency , not a total fit .
Interesting are the graphs at the right which represent the Mass vs AU of the system .
One can omit the Mass and focus on the distance distrubition of the planets .
In some cases as for 55Cancri there seems to be some "place" to put an extra (fi yet undiscovered ) planet
As one can see the parameters of the fitting curve are very different from system to system . So one can hardly talk about a "law" .
There may be a correlation between the parameters of the fitting curve and the CentralStar Mass , or even the masses of the planets ....

kamaz
2010-Sep-12, 11:56 AM
Why does Bode's Law not apply to the moons that formed naturally around Saturn & Jupiter?

According to Wikipedia, a similar law for planetary satellites is called Dermott's law: http://en.wikipedia.org/wiki/Dermott's_law

See attached spreadsheet for my verification.

EDIT: Seems I am unable to upload .xls files, so I put it here: http://www.mediafire.com/?dnxdy6wyu26ksnb

caveman1917
2010-Sep-12, 02:09 PM
There is no such thing as THE Titius-Bode law, like clearly described in the papers by Graner (http://esoads.eso.org/abs/1994A%26A...282..262G) & Dubrulle (http://esoads.eso.org/abs/1994A%26A...282..269D) (1994).
Titius-Bode as it is, is "well" applicable for our solar system (well, up until Uranus), would not work for Jupiter. One reason for that is e.g. a migration of the 4 Galilean satellites of Jupiter, leading to the 4:2:1 resonance of the inner three.
In any other planetary system that we find, the "law" may look quite differently e.g. ([0 1 2 4 8 16 32] + 6) / 8, who knows ....

But that's essentially the same law after all - it arises through the same mechanism in the same way, though indeed some of the specifics are relative to the parameters of the disk.
Those are models about how a power law arises out of a scale invariant disk, but once you get the planets to form planetary migration could mess up that model.
So wether it is such a good model for explaining the positions in any practical system remains to be seen, and i doubt so, though it is certainly a factor in the formation of the system.

ETA: it seems frankuitaalst gets some fits, but also many outliers.

Jerry
2010-Sep-16, 02:21 AM
There are rational explanations for a 'Bode-like' structure - normal planets sweeping their orbit; more eccentric orbits with increasing debris clearing zones with increasing distance. If there were a 'quantum' explanation for planetary orbital distances, we should expect the orbits to be more circular and predictable. Bodes law actually has three variables: a shifted zero point, a constant and a scaler.

A 'different' Bodes law for a different solar system falls deep into the small number solution problem: you can always draw a fairly simple line through a trivial number of points with a couple or three variables.

Centaur
2010-Sep-16, 02:41 AM
Why 1.5? Why not half of 1.5, which is 0.75, or half of that? I think you would have to start with an arbitrary first number.


Good point, although that would imply an infinite number of planets between Mercury and Venus. As you say, they had to start somewhere, unless they wanted to explain the absence of so many inner planets. Indeed, Titus and Bode might have gone with the more typical doubling sequence of (1, 2, 4, 8, 16, 32, 64, 128, 256) then ask us to add 8/3 before multiplying by 0.15. If the one in that sequence were replaced by zero, then the final result would be precisely equivalent to the Titus-Bode formula.