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banquo's_bumble_puppy
2007-Nov-07, 04:47 PM
Is there a pattern to how our solar system is laid out? You have Mercury, Venus, Earth and Mars closest to the sun, all rocky planets and then you have Jupiter, Saturn and Uranus, Neptune. Does this have something to do with Bodes' Law? Why aren't the rocky planets mixed in with the gas giants?

banquo's_bumble_puppy
2007-Nov-07, 04:49 PM
to add....from what we've seen of extra solar systems this is not typical

Noclevername
2007-Nov-07, 08:54 PM
Does this have something to do with Bodes' Law? Why aren't the rocky planets mixed in with the gas giants?

Bode's "law" was once thought to be an actual law, until we saw that plenty of other distribution patterns exist. We can't say for sure, but present knowledge suggests that the early phases of Solar formation, with a strong flow of matter from the Sun, may have blown large amounts of gasses off the inner planets.

to add....from what we've seen of extra solar systems this is not typical What we're seeing now is somewhat limited by our own detection methods, which are skewed towards large, close planets. Not enough data yet to tell if that's typical, only that it's more easily detectable from interstellar distances.

JustAFriend
2007-Nov-08, 02:51 PM
Until we can fully catalog the entire layouts of enough OTHER solar systems, you cannot judge anything by the layout of OUR solar system.

We've only detected a few hundred Jupiter-sized worlds outside our own system, so we don't even have the vaguest knowledge yet as to was is 'typical'....

Centaur
2007-Nov-10, 03:28 AM
Is there a pattern to how our solar system is laid out? You have Mercury, Venus, Earth and Mars closest to the sun, all rocky planets and then you have Jupiter, Saturn and Uranus, Neptune. Does this have something to do with Bodes' Law? Why aren't the rocky planets mixed in with the gas giants?

The rocky planets vs. gas giants situation is due to differing distances from the Sun and the resultant temperature differences. At cooler temperatures gasses have lower kinetic energy and are less likely to escape a planet's gravitational field. Also, at greater distances from the Sun gasses are less likely to be blown away by the solar wind.

Bode’s Law was flawed right at its basis. It proposed that the set (0, 3, 6, 12, 24, 48, 96) is part of a doubling sequence. It is not. The initial value would have to be 1.5 to create a proper doubling sequence. The initial zero used to include Mercury in the “law” was a fudge factor that is frequently overlooked. Later, Neptune proved to deviate from the so-called law.

Warren Platts
2007-Nov-10, 09:05 AM
In science, a "law" is any mere statistical relation--it doesn't have to be a "rule" that things "must" follow. So, even if Bode's law does not apply to every solar system out there, it would still apply here.

However, I think there is something to Bode's law other than mere coincidence, but its more like a law of "biology", than a law of physics. Protoplanets "compete" for mass. As larger and larger protoplanets "grow" by "ingesting" matter out of the primordial disk, there is a limit to the "search space" they can cover governed by the average orbital eccentricity. In other words, Bode's Law is the result of "niche partitioning" among the major planets.

Mercury's a little off because it's so close to the Sun that atmospheric drag from the Sun itself may have had an effect, plus there are also general relativity effects that aren't predictable using ordinary Newtonian orbital mechanics.

Kullat Nunu
2007-Nov-10, 09:19 AM
Until we can fully catalog the entire layouts of enough OTHER solar systems, you cannot judge anything by the layout of OUR solar system.

We've only detected a few hundred Jupiter-sized worlds outside our own system, so we don't even have the vaguest knowledge yet as to was is 'typical'....

And what's more, our sample is highly biased to massive closely-orbiting planets. We could already discover true extrasolar Jupiter analogs (and we probably have), but discovering one requires data points along the complete orbit, that is over 10 years. An extrasolar Saturn analog would be much harder to find, and other planets would be currently impossible to detect.

Warren Platts
2007-Nov-10, 02:47 PM
And what's more, our sample is highly biased to massive closely-orbiting planets. We could already discover true extrasolar Jupiter analogs (and we probably have), but discovering one requires data points along the complete orbit, that is over 10 years.Why would you need data points along the complete orbit? For example, 2M1207b (the first extrasolar planet directly imaged by a telescope) is roughly Jupiter massed, and separated by 46 AU from 2M1207 giving it an oribital period of ~2,400 years. Obviously we haven't watched it that long.


An extrasolar Saturn analog would be much harder to find, and other planets would be currently impossible to detect.Plenty of Neptune-sized planets have been found, and here's one that's only 5 Earth masses (http://www.planetary.org/news/2006/0126_Discovery_of_Small_Distant_Planet.html).

grant hutchison
2007-Nov-10, 03:34 PM
Why would you need data points along the complete orbit? For example, 2M1207b (the first extrasolar planet directly imaged by a telescope) is roughly Jupiter massed, and separated by 46 AU from 2M1207 giving it an oribital period of ~2,400 years. Obviously we haven't watched it that long.And therefore we have no idea of its orbit. In fact, we don't even know its current distance from its parent star. The distance you give is the current separation projected on to the plane of the sky, and the period is a guess made by adopting that distance as the semimajor axis of the orbit.

But I agree that in general we don't need to watch an entire orbit to compute its characteristics: just a long enough segment to allow the rest to be calculated with useful confidence. However, I think Kullat Nunu is suggesting that to be sure the observed pattern in the data is an orbit, we probably need to observe at least one cycle.

Grant Hutchison

Warren Platts
2007-Nov-10, 05:18 PM
Well, they say Pluto has an orbital period of 248 years, but it was only discovered 1930. Do we really have to sit around for 248 years "to be sure" that Pluto's observed pattern really is an orbit?

Granted, the 2400 year period for 2M1207b was picked out of a hat--there's no telling at this point how eccentric its orbit is. But 2M1207b and 2M1207 were recently both shown to be a "common proper motion pair". (http://lanl.arxiv.org/PS_cache/astro-ph/pdf/0607/0607490v1.pdf) If they're not in orbit around each other, what else would they be doing hanging around together?

But my main point is just that we are getting useful data about planets that are not ultra-close to their parent star.

grant hutchison
2007-Nov-10, 05:38 PM
Well, they say Pluto has an orbital period of 248 years, but it was only discovered 1930. Do we really have to sit around for 248 years "to be sure" that Pluto's observed pattern really is an orbit?You're mixing data sources, here. You can't compare the direct observation of a body in our own back yard with a velocity signal picked out of the background noise from a distant star. The latter has multiple potential causes, which need to be untangled by observation.


But my main point is just that we are getting useful data about planets that are not ultra-close to their parent star.But not data that allow us to say anything much about how the outer regions of a typical planetary system are "laid out". Which I believe is Kullat Nunu's point, and which is certainly my point.

Grant Hutchison

Disinfo Agent
2007-Nov-10, 10:03 PM
In science, a "law" is any mere statistical relation--it doesn't have to be a "rule" that things "must" follow.Even when it's a "mere" statistical relation, a scientific law must be followed. Anything else would be kind of unlawful, don't you think?

Now, in pop-postmodernism, of course, all bets are off -- the "law" can be as lax as you will it.

Kullat Nunu
2007-Nov-10, 11:46 PM
But I agree that in general we don't need to watch an entire orbit to compute its characteristics: just a long enough segment to allow the rest to be calculated with useful confidence. However, I think Kullat Nunu is suggesting that to be sure the observed pattern in the data is an orbit, we probably need to observe at least one cycle.

I'm no expert, but that's what the exoplanet hunters have told. Considering how much distant orbits change when new data points are acquired, a very incomplete orbit probably gives highly unrealistic values. Take for example 55 Cnc d, the outermost planet in the system. It was originally believed to be in a highly eccentric orbit. Now its eccentricity seems to be mere 0.025. Similarly, some of the distant planets have wildly varying values (compare the values of HD 154345 at the Extrasolar Planets Encyclopaedia (http://exoplanet.eu/planet.php?p1=HD+154345&p2=b) and the Catalog of Extrasolar Planets (http://exoplanets.org/planets.shtml). The former suggests a more distant and much more eccentric orbit (9.21 AU, 0.474) compared to the latter more up-to-date values (4.17 AU, 0.050; a very Jupiter-like planet).

Warren Platts
2007-Nov-11, 06:45 PM
I'm no expert, but that's what the exoplanet hunters have told. Considering how much distant orbits change when new data points are acquired, a very incomplete orbit probably gives highly unrealistic values. Take for example 55 Cnc d, the outermost planet in the system. It was originally believed to be in a highly eccentric orbit. Now its eccentricity seems to be mere 0.025. Similarly, some of the distant planets have wildly varying values (compare the values of HD 154345 at the Extrasolar Planets Encyclopaedia (http://exoplanet.eu/planet.php?p1=HD+154345&p2=b) and the Catalog of Extrasolar Planets (http://exoplanets.org/planets.shtml). The former suggests a more distant and much more eccentric orbit (9.21 AU, 0.474) compared to the latter more up-to-date values (4.17 AU, 0.050; a very Jupiter-like planet).
Well, that's good! It shows that the early estimates are rapidly converging on lower eccentricity orbits, so we may not have to wait more than another few years to maybe see other solar systems with Bode-like arrangements.


Even when it's a "mere" statistical relation, a scientific law must be followed. Anything else would be kind of unlawful, don't you think?

Now, in pop-postmodernism, of course, all bets are off -- the "law" can be as lax as you will it.If it's a statistical law, there are always going to be the exceptions that prove the rule--that's what makes it statistical.

But I take back what I said about Bode's Law being a statistical law. I didn't mean that our solar system is somehow the average of all solar systems.

Instead, I'll stick with the physical (or rather quasi-biological) basis I proposed to explain the striking, obviously nonrandom pattern we observe here. The initial conditions required to produce that pattern may be rare (single, bright star and well-organized disk), but given those initial conditions, one should expect a Bode's-like (logarithmic) spacing of planets.

Disinfo Agent
2007-Nov-11, 07:13 PM
If it's a statistical law, there are always going to be the exceptions that prove the rule--that's what makes it statistical.Exceptions do not prove rules, they disprove them, even in statistics. If the law is statistical, then "exceptions" will turn up with a low frequency, which can quantified and checked against observation. If the observed proportion is inconsistent with the theoretical predictions, then something is wrong.

grant hutchison
2007-Nov-11, 07:34 PM
Exceptions do not prove rules, they disprove them, even in statistics. If the law is statistical, then "exceptions" will turn up with a low frequency, which can quantified and checked against observation. If the observed proportion is inconsistent with the theoretical predictions, then something is wrong.I think this is exactly Warren Platt's meaning. In the phrase "the exception that proves the rule", the verb "to prove" is used in the same way as it is used in the phrase "proving ground" -- meaning "to test".
The exceptions test the statistical rule: if they turn up in the wrong proportions, then the rule fails the test; if they turn up in the expected proportions, the rule passes the test.

Grant Hutchison

Warren Platts
2007-Nov-11, 08:13 PM
And also the fact that an outlier just is so rare and odd carries with it the implication that the normal state of affairs is normal.

Noclevername
2007-Nov-11, 09:12 PM
And also the fact that an outlier just is so rare and odd carries with it the implication that the normal state of affairs is normal.

We don't know that it's rare. Only that it's more difficult to detect using current methods.

Disinfo Agent
2007-Nov-11, 09:59 PM
I think this is exactly Warren Platt's meaning. In the phrase "the exception that proves the rule", the verb "to prove" is used in the same way as it is used in the phrase "proving ground" -- meaning "to test".
The exceptions test the statistical rule: if they turn up in the wrong proportions, then the rule fails the test; if they turn up in the expected proportions, the rule passes the test.

Grant HutchisonWell argued, and we must remember that definition of "proving" the next time someone comes crying that "evolution is just a theory, it hasn't been proven". The proof is in the pudding. ;)

So I guess the question here is what qualifies as an exception to Bode's Law, and what margin of error should be accepted in the preditions.

grant hutchison
2007-Nov-11, 10:05 PM
And also the fact that an outlier just is so rare and odd carries with it the implication that the normal state of affairs is normal.That seems to be so basic as to be pretty much circular, though. Stuff that happens often is "normal"; stuff that happens rarely isn't "normal". Finding a rare aberrant event doesn't confirm normality, any more than finding a black swan reinforces the whiteness of the others.

Looking to see how often nature throws a result outside your predicted 95% confidence interval: that's "proving the rule".

Grant Hutchison

Warren Platts
2007-Nov-12, 01:26 AM
Well argued, and we must remember that definition of "proving" the next time someone comes crying that "evolution is just a theory, it hasn't been proven". The proof is in the pudding. ;)

So I guess the question here is what qualifies as an exception to Bode's Law, and what margin of error should be accepted in the preditions.

To my way of thinking, Bode's law is merely that the orbital radii of planets should vary logarithmically. There's going to be variation. No two solar systems will be alike.

Warren Platts
2007-Nov-12, 01:29 AM
That seems to be so basic as to be pretty much circular, though. ".

Grant Hutchison
:D But that's the beauty part: that's what we spend our whole lives looking for! :razz:

Warren Platts
2007-Nov-12, 01:38 AM
We don't know that it's rare. Only that it's more difficult to detect using current methods.Yeah, Baby! :surprised

Lord Jubjub
2007-Nov-12, 01:57 AM
The exception proves the rule EXISTS.

This is a legal concept NOT a scientific term. If you feel the need to argue that this particular case must be considered outside the normal rules of law, you assume that this case has elements that fall within the normal rule of law.

This phrase has NOTHING to do with science.

Disinfo Agent
2007-Nov-12, 10:32 AM
To my way of thinking, Bode's law is merely that the orbital radii of planets should vary logarithmically. There's going to be variation.How much variation, and under which conditions? If you don't quantify that, how can you be doing science?

Maksutov
2007-Nov-12, 11:01 AM
What's a "planet"?

The IAU definition (http://www.iau.org/iau0601.424.0.html) leaves a lot of leeway, to the point of being useless (http://www.ipetitions.com/petition/planetprotest/).

grant hutchison
2007-Nov-12, 11:33 AM
What's a "planet"?

The IAU definition (http://www.iau.org/iau0601.424.0.html) leaves a lot of leeway, to the point of being useless (http://www.ipetitions.com/petition/planetprotest/).Your link seems to be to an earlier draft which wasn't passed. The final resolution is recorded here (http://www.iau.org/iau0603.414.0.html). That applies only to our solar system, so at present we get to do what we like elsewhere. :)

Grant Hutchison

grant hutchison
2007-Nov-12, 12:03 PM
This phrase has NOTHING to do with science.Not in 17th century legal Latin, anyway: Exceptio probat regulam [in casibus non exceptis]: "The exception proves (or confirms) the rule ". (The verb [i]probo seems to have the same, or worse, ambiguity in Latin as to prove does in English, BTW; it's variously defined as "to test, recommend, approve of, prove".)
Since the sense of the Latin and its translation aren't at all clear, I've previously tried to track down the original usage of the phrase, and found two versions:
1) If the rule makes an exception, this (somehow) intensifies the rule in those case that are not excepted. So if the parking regulations stipulate "No parking, 0800-1800", then they are very serious about the no-parking injunction during that time period.
2) The rule applies, in negation, to the exception. So the parking regulation above implies that parking is permitted during other hours.

Number 2) seems like a reasonable and necessary clarification, and I can imagine the settlement of many disputes might hinge on it. Number 1) seems rather an odd bit of illogic, perhaps derived from the rhetorical device of litotes.

Grant Hutchison

Doodler
2007-Nov-12, 01:30 PM
I wouldn't go testing any laws of planetary development or distribution until we're to the point of reliably locating light terrestrial planets (1 Me and lighter).

Right now, we're seeing short to medium term gas giants all over the distribution, with a few heavy terrestrials at the absolute low end of the mass detection spectrum. Trying to posit a guess with barely half a picture's a little foolish.

Doodler
2007-Nov-12, 01:32 PM
Your link seems to be to an earlier draft which wasn't passed. The final resolution is recorded here (http://www.iau.org/iau0603.414.0.html). That applies only to our solar system, so at present we get to do what we like elsewhere. :)

Grant Hutchison

This alone makes their definition utterly useless...as if the Solar system were something special (beyond being where we happen to reside).

grant hutchison
2007-Nov-12, 01:36 PM
This alone makes their definition utterly useless...as if the Solar system were something special (beyond being where we happen to reside).It makes it utterly useless outside the Solar System, certainly. :)

Grant Hutchison

Warren Platts
2007-Nov-12, 01:40 PM
How much variation, and under which conditions? If you don't quantify that, how can you be doing science?
I guess you'd have to do some kind of least squares analysis to see how far the observed pattern differed from random expectations. It shouldn't be to hard to come up with a probability that the observed pattern was in fact randomly generated. The lower that probability is, the more likely that there is some kind of physical story to be told about how the pattern came about.


I wouldn't go testing any laws of planetary development or distribution until we're to the point of reliably locating light terrestrial planets (1 Me and lighter).

Right now, we're seeing short to medium term gas giants all over the distribution, with a few heavy terrestrials at the absolute low end of the mass detection spectrum. Trying to posit a guess with barely half a picture's a little foolish.

Here's the data on the five known planets in the 55 Cancri (http://en.wikipedia.org/wiki/55_Cancri) system:

Semimajor axes in AU's


0.038
0.115
0.240
0.781
5.77


(eburacum45's artistic renderings of these planets may be found here (http://www.bautforum.com/1110080-post170.html)--no red spots though!:boohoo:)

If you stretch your mind enough, you can barely pick out a Bode's like pattern here. Bode's law would predict that there should be another planet (or at least an asteroid belt) around ~2-3 AU's out. I'm not exactly sure how one should attack the problem statistically.

Warren Platts
2007-Nov-12, 01:45 PM
Originally Posted by Doodler
This alone makes their definition utterly useless...as if the Solar system were something special (beyond being where we happen to reside).


It makes it utterly useless outside the Solar System, certainly. :)

Grant Hutchison

Isn't the working definition between a gas giant (a planet) and a brown dwarf (a star) is that planets shouldn't be burning deuterium much, which limits planets to a mass of about 13 MJUP?

Thus so-called "rogue" planets are still planets even though they don't orbit stars.

grant hutchison
2007-Nov-12, 02:19 PM
Isn't the working definition between a gas giant (a planet) and a brown dwarf (a star) is that planets shouldn't be burning deuterium much, which limits planets to a mass of about 13 MJUP? Sure, but that's not part of the recent IAU definition, which is the one Doodler finds useless.

Grant Hutchison

Warren Platts
2007-Nov-12, 04:05 PM
:dance: *** PRESS RELEASE *** :clap:

Independent astronomer Warren Platts recently announced his discovery of a Bode's Law like relation in the planetary system associated with the yellow dwarf star 55 Cancri A, located in constellation of Cancer at a distance of 41 light-years.

Warren invented a simple formula (he calls it Warren's Law) that accurately predicts the distance of the 5 planets known to be circling 55 Cancri A.




a = 0.39en-1

where a is the semimajor axis of the orbital distance from the 55 Cancri A, n is the number of each planet in increasing order starting from the parent star, and e is the natural logarithm constant (2.71828 ...). The following table gives the observed distances (in astronomical units or AU's--1 AU is the distance from the Earth to the Sun or about 93,000,000 miles) in the left column, and the distances predicted by Warren's Law are on the right.



0.038 --- 0.039
0.115 --- 0.106
0.240 --- 0.288
0.781 --- 0.783
????? --- 2.129
5.770 --- 5.788


As can be seen by inspection, the observed and predicted values are in quite close agreement. Interestingly, Warren's Law predicts that a "Planet V" should be found at a distance ~2.1 AU's from 55 Cancri. Astronomers are anxiously studying the yellow dwarf in hopes of filling in the missing piece of the puzzle. When questioned as to why Warren's Law predicts a wider spacing than Bode's Law, he replied "It's because of the greater eccentricity of the orbits surrounding 55 Cancri."

:D

laurele
2007-Nov-12, 06:07 PM
This alone makes their definition utterly useless...as if the Solar system were something special (beyond being where we happen to reside).

I wholeheartedly second that motion.

Doodler
2007-Nov-12, 06:20 PM
I guess you'd have to do some kind of least squares analysis to see how far the observed pattern differed from random expectations. It shouldn't be to hard to come up with a probability that the observed pattern was in fact randomly generated. The lower that probability is, the more likely that there is some kind of physical story to be told about how the pattern came about.



Here's the data on the five known planets in the 55 Cancri (http://en.wikipedia.org/wiki/55_Cancri) system:

Semimajor axes in AU's

0.038
0.115
0.240
0.781
5.77
(eburacum45's artistic renderings of these planets may be found here (http://www.bautforum.com/1110080-post170.html)--no red spots though!:boohoo:)

If you stretch your mind enough, you can barely pick out a Bode's like pattern here. Bode's law would predict that there should be another planet (or at least an asteroid belt) around ~2-3 AU's out. I'm not exactly sure how one should attack the problem statistically.

I wouldn't dismiss the possibility of a planet with an orbit like that in some kind of resonance that keeps it from detection. However, there are weirder configurations out there that can throw a major monkeywrench in the works.

The one example that's coming to mind is a pair of gas giants that are in overlapping orbits. Forgive me that I can't rattle off the star name/designator off the top of my head. Only so much space available between the ears. ;)

Noclevername
2007-Nov-12, 06:58 PM
There is a pattern to how our Solar System is layed out. The Sun goes in the middle. ;)

Warren Platts
2007-Nov-12, 07:11 PM
I should add that 55 Cancri obeys Warren's Law better than our own solar system obeys Bode's Law. The tables show the data for 55 Cancri and the Sol system (1st column = observed value; 2nd column = predicted value; 3rd column = the square of the difference between the first two columns; Sol system data from the Wikipedia):



55 Cancri



0.038 --- 0.039 --- 0.0000010
0.115 --- 0.106 --- 0.0000808
0.240 --- 0.288 --- 0.0023207
0.781 --- 0.783 --- 0.0000055
????? --- 2.129 --- ??????????
5.770 --- 5.788 --- 0.0003281
????? --- 15.73 --- ??????????



Solar system (planet #5 is Ceres)



00.400 --- 0.390 --- 0.0001
00.700 --- 0.720 --- 0.0004
01.000 --- 1.000 --- 0.0000
01.600 --- 1.520 --- 0.0064
02.800 --- 2.770 --- 0.0009
05.200 --- 5.200 --- 0.0000
10.000 --- 9.540 --- 0.2116
19.600 --- 19.20 --- 0.1600


Thus the average for the squared differences for 55 Cancri is 0.0005472, whereas that for the Sol system is 0.0474250. Even if we just take the average of the squared differences from Mercury through Jupiter, the average is 0.00130--still higher than that predicted from Warren's Law for 55 Cancri.

Strange that the missing planet in our solar system is also the 5th slot. . . . :rolleyes:


I wouldn't dismiss the possibility of a planet with an orbit like that in some kind of resonance that keeps it from detection.
Or maybe there's some kind of resonance that keeps planets from forming in that zone like apparently happened with Jupiter and the asteroid belt.

Disinfo Agent
2007-Nov-12, 07:23 PM
:dance: *** PRESS RELEASE *** :clap:

Independent astronomer Warren Platts recently announced his discovery of a Bode's Law like relation in the planetary system associated with the yellow dwarf star 55 Cancri A, located in constellation of Cancer at a distance of 41 light-years.

Warren invented a simple formula (he calls it Warren's Law) that accurately predicts the distance of the 5 planets known to be circling 55 Cancri A.




a = 0.39en-1

where a is the semimajor axis of the orbital distance from the 55 Cancri A, n is the number of each planet in increasing order starting from the parent star, and e is the natural logarithm constant (2.71828 ...). The following table gives the observed distances (in astronomical units or AU's--1 AU is the distance from the Earth to the Sun or about 93,000,000 miles) in the left column, and the distances predicted by Warren's Law are on the right.



0.038 --- 0.039
0.115 --- 0.106
0.240 --- 0.288
0.781 --- 0.783
????? --- 2.129
5.770 --- 5.788


As can be seen by inspection, the observed and predicted values are in quite close agreement. Interestingly, Warren's Law predicts that a "Planet V" should be found at a distance ~2.1 AU's from 55 Cancri. Astronomers are anxiously studying the yellow dwarf in hopes of filling in the missing piece of the puzzle. When questioned as to why Warren's Law predicts a wider spacing than Bode's Law, he replied "It's because of the greater eccentricity of the orbits surrounding 55 Cancri."

:DIt's easy to fit curves to a set of points ad hoc. Your law would be more impressive if it made a priori predictions. In other words, if it applied to other solar systems as well. How well does it fit our own solar system?

Warren Platts
2007-Nov-12, 07:51 PM
It's easy to fit curves to a set of points ad hoc. Your law would be more impressive if it made a priori predictions. In other words, if it applied to other solar systems as well. How well does it fit our own solar system?What's so ad hoc about my law? It's about as simple as such a law can be made. The only curve fitting I did was to adjust the starting orbit value from 0.039 to 0.038.

Each solar system is a different animal that obeys its own laws. We should expect logarithmic spacing whenever the conditions are right, however.

And my system does make a priori predictions: it predicts that the next planet around 55 Cancri will be found close to either at 2.1 AU or 15.7 AU. If a planet were found at one of those locations, would that satisfy you? Or would you chalk it up to dumb luck?

Disinfo Agent
2007-Nov-12, 08:21 PM
Fitting a different curve to every solar system is a bit like fitting a different number of epicycles to each planet... not wholly satisfying. As to whether other solar systems have their planets spaced according to a logarithmic scale, that remains to be seen, doesn't it? And you still need to deal with the matter of measurement error. We know very little about these extrasolar planets. Notice how the discovery of new planets orbiting 55 Cancri has led to dramatic changes in our estimates for their orbits. Can we be sure that the accuracy currently available to us is sufficient to establish a logarithmic model, or would any proposed model likely be overwhelmed by the error bars?

grant hutchison
2007-Nov-12, 09:11 PM
What's so ad hoc about my law? It's about as simple as such a law can be made. The only curve fitting I did was to adjust the starting orbit value from 0.039 to 0.038.Latin ad hoc, meaning "to this": as in "to this end".
Your law is as ad hoc as a thing can get, since you concocted for it a single purpose.

Grant Hutchison

Warren Platts
2007-Nov-12, 09:57 PM
Fitting a different curve to every solar system is a bit like fitting a different number of epicycles to each planet... not wholly satisfying. Not at all. There are important theoretical reasons why we should expect different solar systems to be different.


As to whether other solar systems have their planets spaced according to a logarithmic scale, that remains to be seen, doesn't it?
Well, the data so far is that planets are spaced according to a logarithmic scale, as I have shown.

And you still need to deal with the matter of measurement error. We know very little about these extrasolar planets. Notice how the discovery of new planets orbiting 55 Cancri has led to dramatic changes in our estimates for their orbits. Can we be sure that the accuracy currently available to us is sufficient to establish a logarithmic model, or would any proposed model likely be overwhelmed by the error bars?

Error bars?!? Look, I'm just going by what the Wikipedia says, and the error bars they list are very small (http://en.wikipedia.org/wiki/55_Cancri#Planetary_system). The biggest error bar is less than 2% for 55 Cancri d. So the value could range from 5.66 to 5.88 AU's. Hardly overwhelming.

Plus, I notice that you've deftly avoided answering my question, which is what would it take to satisfy you?

Warren Platts
2007-Nov-12, 10:01 PM
Latin ad hoc, meaning "to this": as in "to this end".
Your law is as ad hoc as a thing can get, since you concocted for it a single purpose.

Grant Hutchison
"Concocted"?!? What do mean by "concocted"? By your criterion, Newton's laws of motion are ad hoc. So 'ad hoc' loses its meaning completely. Which is fine by me.

EDIT: However, I will admit to an ulterior motive: to vindicate the teleological epistemological method for the physical sciences. So that's two feathers in my cap in less than a month, for me, a mere amateur philosopher with no special expertise in astronomy. How many more feathers will it take for you to be satisfied, my dear Dr. Hutchison?

Disinfo Agent
2007-Nov-12, 10:09 PM
There are important theoretical reasons why we should expect different solar systems to be different.Are there any important theoretical reasons why we should expect a logarithmic scale? That would also be a plus.


Plus, I notice that you've deftly avoided answering my question, which is what would it take to satisfy you?Where is it? Where did you ask me that question?

Warren Platts
2007-Nov-12, 10:20 PM
Are there any important theoretical reasons why we should expect a logarithmic scale? That would also be a plus. Because planitesimals compete with each other for mass. So eventually one wins out over its rivals. But one planet can only commandeer the mass out of one "alley", and the width of such an alley depends on the average eccentricity of the objects within that alley. Since gravity varies by the inverse squared law, it stands to reason that each individual "alley" will increase in size logarithmically as one progresses from the parent star.


Where is it? Where did you ask me that question?



And my system does make a priori predictions: it predicts that the next planet around 55 Cancri will be found close to either at 2.1 AU or 15.7 AU. If a planet were found at one of those locations, would that satisfy you? Or would you chalk it up to dumb luck?

Centaur
2007-Nov-12, 10:33 PM
These attempts to find formulae that fit the data remind me of a chapter in Jean Meeus’ Mathematical Astronomy Morsels titled On remarkable relations between the mean motions of the planets. He noted that in 1876 astronomer Daniel Kirkwood (of the Kirkwood gaps among asteroid orbits) published an article with a title similar to that of Meeus’ chapter. Kirkwood found that:

13 n(1) + 93 n(2) - 98 n(3) - 238 n(4) + 227 n(5) + 8 n(6) - 2 n(7) - 7 n(8) = 0

Where n(p) stands for the mean annual motion of each planet (p) in celestial longitude. Based on data available at the time the annual error was only -0.309 arcseconds. With modern values the error becomes -4.43 arcseconds per year.

After Meeus first commented on this in a 1988 magazine article, a mathematician sent him a statistical formula indicating that if 240 were the largest allowed coefficient, it’s possible to choose integers for which the annual error is smaller than 0.0000001 arcseconds, no matter what the values might be for the motions of the planets. Although he did not provide an example that might prove his case.

One of Meeus’ readers then sent him the following formula with no coefficient greater than 16:

7 n(1) - 16 n(2) - 10 n(3) + 11 n(4) + 14 n(5) - 3 n(6) + 6 n(7) - 9 n(8) = 0

Based on modern values, the error in this instance is only +0.000387 arcseconds per year.

The same fellow submitted another formula with larger coefficients, but still smaller than Kirkwood’s largest of 238:

31 n(1) - 78 n(2) - 50 n(3) + 86 n(4) + 16 n(5) + 18 n(6) + 91 n(7) - 114 n(8) = 0

Here the annual error is only -0.000000015 arcseconds, thus providing strong evidence to support the mathematician's conjecture. ;)

Disinfo Agent
2007-Nov-12, 10:34 PM
And my system does make a priori predictions: it predicts that the next planet around 55 Cancri will be found close to either at 2.1 AU or 15.7 AU. If a planet were found at one of those locations, would that satisfy you? Or would you chalk it up to dumb luck?That would be one point in favour of your general hypothesis.
But don't the planets in our own solar system seriously deviate from the predictions of Bode's Law? I seem to recall that Neptune, especially, was completely off the chart...

grant hutchison
2007-Nov-12, 10:35 PM
"Concocted"?!? What do mean by "concocted"? By your criterion, Newton's laws of motion are ad hoc ...Oh, for pity's sake.
Newton's laws of motion, even when Newton first proposed them, had been shown to apply in many different situations. They have been tested in a vast number of different settings since, on a daily basis. They can be, and have been, used for many purposes. Warren's Law has been bolted together for the single purpose (that is, ad hoc) of fitting five data points. You have concocted it; it has been "made up, by artificial combination".


So that's two feathers in my cap in less than a month, for me, a mere amateur philosopher with no special expertise in astronomy. How many more feathers will it take for you to be satisfied, my dear Dr. Hutchison?While not wishing to be rude, I must report that I count zero feathers.
Your vindication in my eyes will (as might be expected) take more than zero feathers.

Grant Hutchison

formulaterp
2007-Nov-12, 10:42 PM
That would be one point in favour of your general hypothesis.
But don't the planets in our own solar system seriously deviate from the predictions of Bode's Law? I seem to recall that Neptune, especially, was completely off the chart...

Solar system (planet #5 is Ceres)

1. 00.400 --- 0.390 --- 0.0001
2. 00.700 --- 0.720 --- 0.0004
3. 01.000 --- 1.000 --- 0.0000
4. 01.600 --- 1.520 --- 0.0064
5. 02.800 --- 2.770 --- 0.0009
6. 05.200 --- 5.200 --- 0.0000
7. 10.000 --- 9.540 --- 0.2116
8. 19.600 --- 19.20 --- 0.1600


Why do you think he stopped at 8?

Warren Platts
2007-Nov-12, 10:50 PM
That would be one point in favour of your general hypothesis.
Thank you. We may not have to wait long. :)

But don't the planets in our own solar system seriously deviate from the predictions of Bode's Law? I seem to recall that Neptune, especially, was completely off the chart...That's right. Neptune is the exception that proves the rule. Probably what happens is that when you get that far out the orbital periods are so great that to clear out a path takes a long time, and so eccentricity no longer dominates.

Centaur
2007-Nov-12, 10:52 PM
Solar system (planet #5 is Ceres)

1. 00.400 --- 0.390 --- 0.0001
2. 00.700 --- 0.720 --- 0.0004
3. 01.000 --- 1.000 --- 0.0000
4. 01.600 --- 1.520 --- 0.0064
5. 02.800 --- 2.770 --- 0.0009
6. 05.200 --- 5.200 --- 0.0000
7. 10.000 --- 9.540 --- 0.2116
8. 19.600 --- 19.20 --- 0.1600


Why do you think he stopped at 8?

As I noted in my first post in this thread, the theoretical Bode/Titius value for Mercury is bogus. The first value in the doubling series should be 1.5, not zero. After 4 is added and the sum is divided by 10, the result is 0.55 AU, not 0.40 AU. The deviation from the actual 0.387 AU is a quite significant 42%. I'm amazed how this fudging has been overlooked for so many years.

Warren Platts
2007-Nov-12, 11:03 PM
Oh, for pity's sake.
GARGH!!!

Newton's laws of motion, even when Newton first proposed them, had been shown to apply in many different situations. They have been tested in a vast number of different settings since, on a daily basis. They can be, and have been, used for many purposes. Warren's Law has been bolted together for the single purpose (that is, ad hoc) of fitting five data points. You have concocted it; it has been "made up, by artificial combination".It's true that I typed the numbers into the keypad, but the relation itself is natural and works better than Bode's Law does for our solar system. You have to admit that. It's just the truth. What's the physical basis for that, though, is the question.


While not wishing to be rude, I must report that I count zero feathers.
Your vindication in my eyes will (as might be expected) take more than zero feathers.Sir, you have not hurt my feelings, and I highly value your comments. We can forget about the GRS thread for now (which you never commented on, although I'm sure you did read it), but I wouldn't mind a substantive critique on Warren's Law for 55 Cancri. Is it really your position that the apparent layout of the 55 Cancri system is a mere coincidence???

Warren Platts
2007-Nov-12, 11:11 PM
As I noted in my first post in this thread, the theoretical Bode/Titius value for Mercury is bogus. The first value in the doubling series should be 1.5, not zero. After 4 is added and the sum is divided by 10, the result is 0.55 AU, not 0.40 AU. The deviation from the actual 0.387 AU is a quite significant 42%. I'm amazed how this fudging has been overlooked for so many years.
And as I noted in my first post in this thread, Mercury is a special case. For all we know, it might be an escaped moon of Venus.

But you raise a good point in that Bode's Law for our solar system does in fact invoke a lot of ad hoc curve fitting (that doesn't affect the general logarithmic spacing however) that is absent from the model I proposed for 55 Cancri.

Noclevername
2007-Nov-12, 11:12 PM
Is it really your position that the apparent layout of the 55 Cancri system is a mere coincidence???
Since there's not enough data to even determine the actual layout accurately yet, there's not enough to determine coincidence or not either.

Warren Platts
2007-Nov-12, 11:20 PM
Since there's not enough data to even determine the actual layout accurately yet, there's not enough to determine coincidence or not either.
Dude, like I said before, the error bars posted in Wikipedia are all under 2%--in fact most are on the order of 10-5. No doubt Wikipedia can't be trusted, so maybe you should edit the Wikipedia article to include more realistic error bars.

grant hutchison
2007-Nov-12, 11:28 PM
It's true that I typed the numbers into the keypad, but the relation itself is natural and works better than Bode's Law does for our solar system. You have to admit that. It's just the truth.It works because it's ad hoc: you fitted it to five data points. If it hadn't fitted, you would have hacked it around until it did fit, and then that curve would have also seemed "natural".


Sir, you have not hurt my feelings, and I highly value your comments. We can forget about the GRS thread for now (which you never commented on, although I'm sure you did read it), but I wouldn't mind a substantive critique on Warren's Law for 55 Cancri. Is it really your position that the apparent layout of the 55 Cancri system is a mere coincidence???I have no idea why the 55 Cnc system is laid out the way it is. Nor do you. You have five data points, and you have fitted a curve to them which you describe as "natural". This tells us something about you and curvefitting, but nothing about the 55 Cnc system.

Grant Hutchison

grant hutchison
2007-Nov-12, 11:33 PM
Dude, like I said before, the error bars posted in Wikipedia are all under 2%--in fact most are on the order of 10-5. No doubt Wikipedia can't be trusted, so maybe you should edit the Wikipedia article to include more realistic error bars.You'll find the error bars were much the same magnitude before all the orbital parameters changed, recently; and the time before that. People are fitting curves to data and getting good correlations which later turn out to be wrong when more data are available. That's how it goes.

Grant Hutchison

formulaterp
2007-Nov-12, 11:40 PM
He may be on to something. Take for example HIP 14810, which has 2 known planets at distances of 0.0692 and 0.407 AU's.

The formula a = 0.0692 + ((n -1) * 0.3378)) {where a = distance in AU and n = the order of the planet} accurately describes the orbital relationship of that solar system.

Oh and there's a good chance there's a third planet somewhere in there. I'm guessing at right around 0.7448 AU

Kaptain K
2007-Nov-12, 11:45 PM
My late brother had a penchant for being argumentative just for the sake of arguing. His name was Max and we termed such behavior as "Maxnoxious" - Max+obnoxious. I hereby propose the term "Plattsnoxious".

Disinfo Agent
2007-Nov-12, 11:48 PM
Solar system (planet #5 is Ceres)

1. 00.400 --- 0.390 --- 0.0001
2. 00.700 --- 0.720 --- 0.0004
3. 01.000 --- 1.000 --- 0.0000
4. 01.600 --- 1.520 --- 0.0064
5. 02.800 --- 2.770 --- 0.0009
6. 05.200 --- 5.200 --- 0.0000
7. 10.000 --- 9.540 --- 0.2116
8. 19.600 --- 19.20 --- 0.1600


Why do you think he stopped at 8?If you mean Titius and Bode, that's because Neptune hadn't been discovered yet when they proposed the relation (http://en.wikipedia.org/wiki/Titius-Bode_law).

Noclevername
2007-Nov-12, 11:49 PM
My late brother had a penchant for being argumentative just for the sake of arguing. His name was Max and we termed such behavior as "Maxnoxious" - Max+obnoxious. I hereby propose the term "Plattsnoxious".

Careful Kaptain, no ad homs.

grant hutchison
2007-Nov-12, 11:50 PM
My late brother had a penchant for being argumentative just for the sake of arguing. His name was Max and we termed such behavior as "Maxnoxious" - Max+obnoxious. I hereby propose the term "Plattsnoxious".That seems a little harsh.
I honestly had to get to the last word before I knew whether it was going to be Plattsnoxious or Grantnoxious. I was tense about it.

Grant Hutchison

Warren Platts
2007-Nov-12, 11:50 PM
It works because it's ad hoc: you fitted it to five data points. If it hadn't fitted, you would have hacked it around until it did fit, and then that curve would have also seemed "natural".
Dr. Hutchison, that is so unfair! My formula is a = 0.39en-1. If you can simplify that formula more, I'm dieing to see how. I haven't incorporated 5 different variables with quadratic equations up the yin-yang. Which is what you are accusing me of what I would do if the simple equation didn't work out. But it did work out. Coincidence?


I have no idea why the 55 Cnc system is laid out the way it is. Nor do you.Actually, I do have an idea about why such layouts are apparently common, as I laid out above. Why is it that you think that the average eccentricity of objects that make up a protosolar disk have nothing to do with planetary spacing?

You have five data points, and you have fitted a curve to them which you describe as "natural". This tells us something about you and curvefitting, but nothing about the 55 Cnc system.Really. . . .

What does it tell about me: that I'll go to any length to add variables and fudge factors to fit a curve to any random set of data points? If so, thanks for the complement. :mad: Or is this a general point about statistical reduction? In which case it would count as a substantive critique, but then raises the larger question as to whether science can say something about anything.

Disinfo Agent
2007-Nov-12, 11:54 PM
Dr. Hutchison, that is so unfair! My formula is a = 0.39en-1. If you can simplify that formula more, I'm dieing to see how. I haven't incorporated 5 different variables with quadratic equations up the yin-yang.Where did you get the 0.39 factor from?

Warren Platts
2007-Nov-12, 11:56 PM
He may be on to something. Take for example HIP 14810, which has 2 known planets at distances of 0.0692 and 0.407 AU's.

The formula a = 0.0692 + ((n -1) * 0.3378)) {where a = distance in AU and n = the order of the planet} accurately describes the orbital relationship of that solar system.

Oh and there's a good chance there's a third planet somewhere in there. I'm guessing at right around 0.7448 AU
:lol:

Good one!

:clap:

Warren Platts
2007-Nov-12, 11:58 PM
Where did you get the 0.39 factor from?That's the distance from 55 Cancri A to 55 Cancri e. :)

Kaptain K
2007-Nov-12, 11:59 PM
Careful Kaptain, no ad homs.
Point taken! :doh:

Warren Platts
2007-Nov-13, 12:02 AM
That seems a little harsh.
I honestly had to get to the last word before I knew whether it was going to be Plattsnoxious or Grantnoxious. I was tense about it.

Grant Hutchison

It's all good! There's no such thing as bad publicity! :lol:

But you know, I would appreciate a little credit when it's due though! I get the feeling that the rule of thumb around here is that if Warren says that p, then p is probably false. . . . :shifty: Oh well. I'll deal.


My late brother had a penchant for being argumentative just for the sake of arguing. His name was Max and we termed such behavior as "Maxnoxious" - Max+obnoxious. I hereby propose the term "Plattsnoxious".He sounds like a nice guy! Wish I could have known him! :)

grant hutchison
2007-Nov-13, 12:03 AM
Dr. Hutchison, that is so unfair! My formula is a = 0.39en-1. If you can simplify that formula more, I'm dieing to see how. I haven't incorporated 5 different variables with quadratic equations up the yin-yang. Which is what you are accusing me of what I would do if the simple equation didn't work out. But it did work out. Coincidence?Until proven otherwise with more data, yes indeed.


Actually, I do have an idea about why such layouts are apparently common, as I laid out above. Why is it that you think that the average eccentricity of objects that make up a protosolar disk have nothing to do with planetary spacing?First, I'll need a reference for how you know the average eccentricity of objects in a protostellar disc. Then we might want to discuss the mass function you're using for the theoretical protostellar disc under discussion.


What does it tell about me: that I'll go to any length to add variables and fudge factors to fit a curve to any random set of data points? If so, thanks for the complement. :mad:Not any lengths, since you didn't pitch up with some mad polynomial and an air of triumph. But I think that many would agree it's a little uncritical to be happy with five data points and a good correlation. Especially when your other dataset so far, the Solar System, requires you to throw out a quarter of the sample to get a decent fit to a scaling law.

Grant Hutchison

Disinfo Agent
2007-Nov-13, 12:06 AM
That's the distance from 55 Cancri A to 55 Cancri e. :)...Which you couldn't have known until you actually observed that solar system. Doesn't that strike you as a little ad hoc, too?

I'm not saying this shuts down the hypothesis of a logarithmic distribution completely, mind you. What has shut it down are the major discrepancies between the model and what we find in our own solar system.

Warren Platts
2007-Nov-13, 12:09 AM
That seems a little harsh.
I honestly had to get to the last word before I knew whether it was going to be Plattsnoxious or Grantnoxious. I was tense about it.
Doc, my advice for your high blood pressure is to try and be a little less Grantankerous. .. . :razz:

Warren Platts
2007-Nov-13, 12:15 AM
...Which you couldn't have known until you actually observed that solar system. Doesn't that strike you as a little ad hoc, too?
Whew. So empiricism is to be discounted because it's ad hoc? That strikes me as a little ad hack.

Warren Platts
2007-Nov-13, 12:27 AM
Until proven otherwise with more data, yes indeed.Like I asked Disinfo Agent, what possible future data would cause you to revise your opinion? 55 Cancri g at 16 AU's? Probably not, I'm guessing. . . .


First, I'll need a reference for how you know the average eccentricity of objects in a protostellar disc. Then we might want to discuss the mass function you're using for the theoretical protostellar disc under discussion.There is no reference because it's a new idea. This thread is the reference. I have this crazy idea that the eccentricity of a solar system's planets is a fossil relict of the primitive eccentricity. But then that's probably just a relic of my biological view of the universe. . . .


Not any lengths, since you didn't pitch up with some mad polynomial and an air of triumph.Sorry about the air of triumph. It's that eureka feeling that keeps us coming back to science. Can't help it.


But I think that many would agree it's a little uncritical to be happy with five data points and a good correlation.Five data points is pretty good. It's better than the two that Formulaterp's Law is based on.


Especially when your other dataset so far, the Solar System, requires you to throw out a quarter of the sample to get a decent fit to a scaling law.I threw out Neptune; but if I was a true curve fitter, I would have come up with a polynomial that could easily include Neptune.

Pluto doesn't count because it's not a real planet.

As for Mercury, I haven't looked into the details of Centaur's charge that Mercury was fudged in the Titius-Bode's equation.

grant hutchison
2007-Nov-13, 10:49 AM
Like I asked Disinfo Agent, what possible future data would cause you to revise your opinion? 55 Cancri g at 16 AU's? Probably not, I'm guessing. . . .Move it to other solar systems. Demonstrate how the exponential fit applies. You never test your theory on the same dataset with which you built your theory.


There is no reference because it's a new idea. This thread is the reference. I have this crazy idea that the eccentricity of a solar system's planets is a fossil relict of the primitive eccentricity.So your crazy idea supports your curve-fit and your curve-fit supports your crazy idea? That's handy, if a little self-referential.
You might care to factor into your idea some measure of how long eccentric orbits would last in a nebula, how little information about the eccentricity of the components can be retained by an accreted object, and how eccentricity can be exchanged gravitationally between planets after they have formed.


Sorry about the air of triumph. It's that eureka feeling that keeps us coming back to science. Can't help it.Some people are just cursed with a low eureka threshold, I guess. :)


Five data points is pretty good. It's better than the two that Formulaterp's Law is based on.Five data points is quite appallingly bad. Which is, I believe, the point formulaterp is making with the joke formula.


I threw out Neptune; but if I was a true curve fitter, I would have come up with a polynomial that could easily include Neptune.But then you'd have had to compromise your fit at 55 Cnc.


Pluto doesn't count because it's not a real planet.But Ceres does? Ceres and the asteroids are precisely as much non-planets as Pluto and the KBOs.


As for Mercury, I haven't looked into the details of Centaur's charge that Mercury was fudged in the Titius-Bode's equation.Well, you certainly had the chance, because they were given in full detail in this thread.
But despite not having looked into them you were quite happy to throw Mercury out as a non-problem because: "Mercury is a special case. For all we know, it might be an escaped moon of Venus."

You are building ad hoc on ad hoc all the way through this process.
When I studied philosophy we had to learn about reasoned argumentation and standards of proof. Has this been abandoned these days, in favour of more rarified pursuits?

Grant Hutchison

Warren Platts
2007-Nov-13, 02:23 PM
You might care to factor into your idea some measure of how long eccentric orbits would last in a nebula, how little information about the eccentricity of the components can be retained by an accreted object, and how eccentricity can be exchanged gravitationally between planets after they have formed.I miswrote here when I said that "the eccentricity of a solar system's planets is a fossil relict of the primitive eccentricity." I meant to write the spacing of a solar system's planets is a fossil relict of the primitive average eccentricity.


Some people are just cursed with a low eureka threshold, I guess. :)And some are cursed with the inability to think outside the box. ;)


But Ceres does? Ceres and the asteroids are precisely as much non-planets as Pluto and the KBOs.Removing Ceres doesn't affect the analysis--I tried it.


Well, you certainly had the chance, because they were given in full detail in this thread. I checked it out some more, and now I think Centaur's point about starting the doubling series at zero instead of 1.5 is a red herring.


When I studied philosophy we had to learn about reasoned argumentation and standards of proof. Has this been abandoned these days, in favour of more rarified pursuits?Internet fora aren't particularly conducive to organized presentations because of the cat-herding effect of trying to answer a bunch of random questions at once. And in any case, since the OP question had more to do with rocky versus gas giant planets rather than Bode's Law per se, what I think I'll do is start a new thread in the ATM section. I don't want to be accused of threadjacking or discussing ATM ideas outside of the ATM section--and apparently Bode's Law is an ATM concept judging from the vehemence of the objections to my version of it for 55 Cancri. There I can better address all of your concerns and more--I do have answers for everything. ;)

Disinfo Agent
2007-Nov-13, 03:06 PM
Removing Ceres doesn't affect the analysis--I tried it.If the prediction is that a planet will be found at each value of n, then either you count Ceres as a planet, or the prediction fails.

grant hutchison
2007-Nov-13, 03:59 PM
... apparently Bode's Law is an ATM concept judging from the vehemence of the objections to my version of it for 55 Cancri.I think you're right about ATM. Titius-Bode is the astronomical journal's equivalent of eternal motion devices: many journals refuse to consider papers on the topic.
This is not because they wish to visciously suppress those who think outside the box. It's because:
1) The dataset is tiny
2) We know the dataset is not representative
3) We don't know in what way the dataset is not representative

So producing a paper about Titius-Bode is tantamount to saying: "I wish to indulge in some uninformed speculation." Not in my astronomical journal, you won't. :)

Grant Hutchison

Kullat Nunu
2007-Nov-13, 06:04 PM
It works because it's ad hoc: you fitted it to five data points. If it hadn't fitted, you would have hacked it around until it did fit, and then that curve would have also seemed "natural".

How this differs from Bode's law? That too looks awfully lot like curve-fitting.

grant hutchison
2007-Nov-13, 07:13 PM
How this differs from Bode's law? That too looks awfully lot like curve-fitting.Indeed. My impression is that Warren Platts wants to emulate the Titius-Bode Law, so I presume he's happy with that similarity.

Grant Hutchison

tusenfem
2007-Nov-14, 12:30 PM
Just a little reminder that Titus-Bode like "laws" have already been discussed on this forum. There have been published papers by Graner & Dubrulle that explain a lot of stuff. Here you can find them on ADS. (http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&qform=AST&sim_query=YES&ned_query=YES&aut_logic=AND&obj_logic=OR&author=Dubrulle+%0D%0AGraner&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=OR&title=&txt_logic=OR&text=&nr_to_return=100&start_nr=1&jou_pick=ALL&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)

Just to quote the abstract of the first paper published in Astronomy & Astrophysics (so if done correctly, the discussion of Titus Bode is not necessarily ATM):


According to the Titius-Bode law, the planetary distances to the sun follow a geometric progression. We review the major interpretations and explanations of the law. We show that most derivations of Titius-Bode law are implicitely based on the assumption of both rotational and scale invariance. In absence of any radial length scale, linear instabilities cause periodic perturbations in the variable x = ln(r/r0). Since maxima equidistant in x obey a geometric progression in the variable r, Titius-Bode type of laws are natural outcome of the linear regime of systems in which both symmetries are present; we discuss possible nonlinear corrections to the law. Thus, if Titius-Bode law is real, it is probably only a consequence of the scale invariance of the disk which gave rise to the planets.


So, I think you guys have some reading to do, have fun.

grant hutchison
2007-Nov-14, 06:11 PM
So, I think you guys have some reading to do, have fun.Yes, Graner & Dubrulle are in my file already, and it appears Warren Platts has read it, too.
But "Warren's Law" as it appears on this thread isn't remotely in the same category.
I, and others, are objecting (and I think quite reasonably) to what strikes me as an egregious overinterpretation of five data points, especially since it is also being used (rather mysteriously) as a defence, or even a vindication, of teleology.

Grant Hutchison

Warren Platts
2007-Nov-14, 07:59 PM
Yes, Graner & Dubrulle are in my file already, and it appears Warren Platts has read it, too.
But "Warren's Law" as it appears on this thread isn't remotely in the same category.
I, and others, are objecting (and I think quite reasonably) to what strikes me as an egregious overinterpretation of five data points, especially since it is also being used (rather mysteriously) as a defence, or even a vindication, of teleology.

The original law proposed by Titius was based on six data points. If we can find one more planet on 55 Cancri, then will you be satisfied? As it was, with a mere six data points, the Titius-Bode law successfully predicted the discovery of both Ceres and Uranus. Not bad, considering that the original Titius-Bode law was teleologically motivated!


Take notice of the distances of the planets from one another, and recognize that almost all are separated from one another in a proportion which matches their bodily magnitudes. Divide the distance from the Sun to Saturn into 100 parts; then Mercury is separated by four such parts from the Sun, Venus by 4+3=7 such parts, the Earth by 4+6=10, Mars by 4+12=16. But notice that from Mars to Jupiter there comes a deviation from this so exact progression. From Mars there follows a space of 4+24=28 such parts, but so far no planet was sighted there. But should the Lord Architect have left that space empty? Not at all. Let us therefore assume that this space without doubt belongs to the still undiscovered satellites of Mars, let us also add that perhaps Jupiter still has around itself some smaller ones which have not been sighted yet by any telescope.

:lol:

grant hutchison
2007-Nov-14, 08:20 PM
The original law proposed by Titius was based on six data points. If we can find one more planet on 55 Cancri, then will you be satisfied?Well, given that Titius-Bode is thoroughly unsatisfactory for reasons already discussed, it's difficult to see why I should apportion any more belief to a different "law" cooked up elsewhere.


As it was, with a mere six data points, the Titius-Bode law successfully predicted the discovery of both Ceres and Uranus. Not bad, considering that the original Titius-Bode law was teleologically motivated!It was certainly fashionable in the eighteenth century to offer the Universe helpful hints on how best to go about its business. After repeatedly discovering that the Universe had its own plans, people moved on to more useful pursuits.

Grant Hutchison

Warren Platts
2007-Nov-14, 10:00 PM
Well, given that Titius-Bode is thoroughly unsatisfactory for reasons already discussed, it's difficult to see why I should apportion any more belief to a different "law" cooked up elsewhere.OK, so Titius-Bode didn't predict Neptune (Pluto, as a Kuiper Belt object in orbital resonance with Neptune doesn't count, since it's not an independent sample.) So, Titius-Bode's batting average is only .667. How horrible! If I had a designated hitter on my team that couldn't hit better than that, I'd fire him for sure, as well!

Beside's "my" law isn't mine at all, and so it isn't different, it's the same Titius-Bode model described by Graner and Bruelle, as I describe in excruciating algebraic detail in my ATM thread.


After repeatedly discovering that the Universe had its own plans, . . .
Gee, that's a rather odd (as in teleological) way of expressing the common 19th century belief that only humans have real plans! :D

grant hutchison
2007-Nov-14, 10:15 PM
Beside's "my" law isn't mine at all, and so it isn't different, it's the same Titius-Bode model described by Graner and Bruelle, as I describe in excruciating algebraic detail in my ATM thread.In which case you presumably now accept that you have, wittingly or not, selected particular values from a large parameter space, simply to suit your five chosen data points. Ad hoc.



After repeatedly discovering that the Universe had its own plans, . . . Gee, that's a rather odd (as in teleological) way of expressing the common 19th century belief that only humans have real plans! :D<Sigh.>
It's called a metaphor, Warren. Being unable to distinguish metaphor from teleological thinking is a significant handicap, even for someone who isn't writing a thesis about teleological thinking.

Grant Hutchison

Jerry
2007-Nov-14, 10:39 PM
There is a possible scientific underpinning to Bode's law without (pray tell) exceptional physics.

We know the moon's distance from the Earth is increasing at a rate that would have 'unwound the moon' many millennia ago if the distance were always increasing. We can find rough resonance formula's that over a great time scale will cycle the moon between greater and closer distances.

If there are 'tidal' effects within the sun, the current planetary orbits may also reflect weak tidal relationships.

This concept also has some merit when we discuss the moons of Mars - They have the appearance of captured asteriods, but much too circular of orbits to be asteriods jettisoned from the asteroid belt; unless there is an unknown tidal/resonance relationship.

grant hutchison
2007-Nov-14, 11:03 PM
We know the moon's distance from the Earth is increasing at a rate that would have 'unwound the moon' many millennia ago if the distance were always increasing. We can find rough resonance formula's that over a great time scale will cycle the moon between greater and closer distances.The usual story is that it is a simple two-way trip. The Moon forms close to the Earth and evolves outwards tidally until the two become tidally locked, billions of years from now. Round about that point, in the real world, all bets are cancelled by the Sun's evolution to the red giant phase. But if that did not happen, the Sun's tides would force further evolution, and the Moon would drift back inwards again until it hit the Earth or disintegrated in the Roche zone.
Maximum separation is only about 1.4 times the present distance between Earth and Moon, at which point the Earth would be tidally locked with a "day" of about seven weeks.

Grant Hutchison

Warren Platts
2007-Nov-14, 11:16 PM
<Sigh.>
It's called a metaphor, Warren. Being unable to distinguish metaphor from teleological thinking is a significant handicap, even for someone who isn't writing a thesis about teleological thinking.

Grant Hutchison
I know how you feel. That's why I recommend taking a close look at what the the content of 'metaphor' really is, because, as Dennett writes in his new Oxford Handbook of the Philosophy of Mind entry (http://ase.tufts.edu/cogstud/papers/intentionalsystems.pdf), there is no principled theoretical or empirical reason to draw a distinction between the metaphorical and the literal:



there is no principled (theoretically motivated) way to distinguish ‘original’ intentionality from ‘derived’ intentionality, and

there is a continuum of cases of legitimate attributions, with no theoretically motivated threshold distinguishing the ‘literal’ from the ‘metaphorical’ or merely ‘as if’ cases.

Warren Platts
2007-Nov-15, 08:06 AM
One minor point I overlooked earlier:


Move it to other solar systems. Demonstrate how the exponential fit applies. You never test your theory on the same dataset with which you built your theory.

The Titius-Bode Law was originally built for our solar system. It was later tested using the solar system's gas giant satellite systems; but testing the theory on gas giants was easily criticized as not representing an independent data set because it's in the same solar system for which the TBL was originally developed (hence it's not surprising that the K TB scale factors for the gas giants are on the order of the K for the solar system as a whole).

So, bringing in 55 Cancri into the picture: (1) does in fact represent a "move" to another solar system; (2) I did in fact demonstrate how the exponential fit applies (although the scale factor K is radically different for 55 Cancri than for our solar system); and (3) 55 Cancri therefore constitutes a test of the theory on a dataset separate from the dataset that the theory was built on. :)

tusenfem
2007-Nov-15, 09:01 AM
It can only be a "law" these days if you also put some explanation behind it. You have found an exponential scaling (different from TB). G&D have shown that a TB type scaling can be explained by some effects, so now it is up to you to show that an exponential scaling can also occur through similar effects. Otherwise it just remains numerology, you can fit an awful lot of stuff with exponentials and/or polynomials to a rather good agree, but not having a solid base on which to argue your assumed fitting model makes it more like a chance occurrance.

Warren Platts
2007-Nov-15, 09:42 AM
You have found an exponential scaling (different from TB). G&D have shown that a TB type scaling can be explained by some effects, so now it is up to you to show that an exponential scaling can also occur through similar effects.
:confused: TB type scaling is a type of exponential scaling.

grant hutchison
2007-Nov-15, 10:26 AM
I know how you feel. That's why I recommend taking a close look at what the the content of 'metaphor' really is ...Metaphor has been an interest of mine since reading Julian Jayne's book in the 70s, and more recently in studying theories of language. The majority of vocabulary derives from metaphor, to the extent it's difficult to string together a useful sentence without employing some sort of metaphor.
So while pretending that people have teleological intentions when they use metaphor may help your score in teleology bingo, it's not a remotely convincing position.

Grant Hutchison

Warren Platts
2007-Nov-15, 01:09 PM
pretending that people have teleological intentions when they use metaphor
But that's my whole point, that I can only pretend that you, a human being, have real intentions, because there is no scientific evidence that such quaint, outmoded, folk psychological notions are in fact real.

Your position, on the other hand, if I understand you correctly, is that to speak of a human as having real, non-derived, intrinsic plans and intentions is to speak literally; but to use the words 'plan' or 'intention' in any other context (with possible allowable exceptions to be made for honorary humans like dogs, cats, and aliens) is "purely as if", and "merely metaphorical". Yes, no?

tusenfem
2007-Nov-15, 01:48 PM
TB type scaling is a type of exponential scaling.

yes it is 2n, you find en, so then you have to come up with why it should be e and not 2.

grant hutchison
2007-Nov-15, 02:31 PM
Your position, on the other hand, if I understand you correctly, is that to speak of a human as having real, non-derived, intrinsic plans and intentions is to speak literally; but to use the words 'plan' or 'intention' in any other context (with possible allowable exceptions to be made for honorary humans like dogs, cats, and aliens) is "purely as if", and "merely metaphorical". Yes, no?No.
As Dennett says, there is no way we can tell if the Universe has an intention or simply behaves as if it has an intention.
As a conscious communicating entity, however, I can tell you if I believe I am treating something as if it has a purpose or intention, or if I believe I am using a metaphor to illustrate some aspect of its behaviour while considering it to be purposeless and intention-free. The first is a use of teleology; the second is a use of metaphor. That is a distinction precisely as real as my consciousness, however real consciousness is.
By assuming that every time someone uses a biological metaphor they are thinking teleologically, you risk making an error in diagnosing their conscious stance, and therefore an error in estimating the usefulness of teleological thinking.
Now, whether you believe that my decision-making is a real or illusory product of my consciousness doesn't matter.
It may be that I am incapable of choosing how I think about things (and merely suffer the illusion that I can): in which case, I can no more choose to adopt a teleological stance than refuse to adopt one. Or it may be that I make a "real" report of my rejection of teleology. If you claim the first, then I contend that you are incapable of adopting the stance you claim to find so useful, incapable of knowing whether you adopted it or not, incapable of altering whether anyone else adopts it or not, and incapable of detecting whether they have adopted it or not; the argument ends in confusion for your side. If you claim the second, then your argument founders on my steadfast report that I am using metaphor.

Grant Hutchison

Warren Platts
2007-Nov-15, 02:36 PM
yes it is 2n, you find en, so then you have to come up with why it should be e and not 2.

Already did it yesterday:


Originally posted by Warren Platts

I suggest that the K factor says something about the rate of formation of planets and solar systems: the higher the K factor, the faster the rate of formation (you heard it here first folks! :D).

On both the classic and natural formulations [of Titius-Bode laws] for 55 Cancri and the Sol system, 55 Cancri has a larger K factor. So why would I say that the 55 Cancri system formed faster than our own system?


55 Cancri A is more enriched than our sun in elements heavier than helium, with 186% the solar abundance of iron; it is therefore classified as a rare "super metal-rich" (SMR) star. (Wikipedia)

So what happened is that at 55 Cancri--because of the superabundance of iron and other heavy elements--heavy, iron-rich, powerful, hungry cores capable of holding mass-sucking atmospheres were able to rapidly form at the center of large vortices; and so planetary and orbital evolution at 55 Cancri was accelerated, compared to the Earth's solar system. Hence, the wider spacing of planets at 55 Cancri--which, paradoxically, allowed planets to form much closer to the sun than at our solar system.

Meanwhile, back here, there was less iron, core's formed less readily, evolution was slower, and so the primordial disk had time to become more organized (less eccentric), and that furthermore, since K, the Bode scale factor, for the outer planets is 1.86, but only 1.57 for the inner planets, then the evolution must have progressed inward starting with the outer planets first, with the inner planets forming somewhat later.

:cool:

Warren Platts
2007-Nov-15, 03:10 PM
I can tell you if I believe I am treating something as if it has a purpose or intention, or if I believe I am using a metaphor to illustrate some aspect of its behaviour while considering it to be purposeless and intention-free.

I think you intended to write:


I can tell you if I believe that something literally has a purpose or intention, or if I believe that I am using a metaphor to illustrate some aspect of its behaviour while considering that it is literally purposeless and intention-free.

The first is a use of a literal teleological description; the second is a use of a metaphorical teleological description. That is a distinction precisely as real as my consciousness, however real consciousness is.

I'll accept your distinction between literal and metaphorical descriptions.

But the question is whether literal descriptions that purport to describe real human plans and intentions are:


accurate; or
such descriptions are more akin to descriptions of phlogiston that were intended at the time to be taken literally, but were later shown to be false.
You believe (1), and I believe (2). We're just going to have to agree to disagree for now (because we could go back and forth on this forever, and we wouldn't want to get in trouble for off-topic babbling in the astronomy section :)).

grant hutchison
2007-Nov-15, 03:28 PM
I think you intended to write:No, I didn't intend to write that. I intended to write what I wrote.
Any argument that allows you to reject my claim to be using metaphor (as a concept different from teleology) allows me to reject your claim to be using teleology. Only by preserving the distinction can you argue in a coherent way for teleology as an alternative tool for thinking; in which case I necessarily get to keep my metaphor.

Grant Hutchison

Warren Platts
2007-Nov-15, 04:05 PM
No, I didn't intend to write that. I intended to write what I wrote.
Any argument that allows you to reject my claim to be using metaphor (as a concept different from teleology) allows me to reject your claim to be using teleology. Only by preserving the distinction can you argue in a coherent way for teleology as an alternative tool for thinking; in which case I necessarily get to keep my metaphor.

Grant Hutchison
It scares me when people use the word 'teleology' in its noun form, because I literally don't know what they're talking about or where they're coming from because the very idea is so alien to my way of thinking.

There are telelogical descriptions and there are mechanical descriptions.

Teleological descriptions are members of that class of descriptions that make use of words like 'end', 'goal', 'purpose', 'value', 'mind', 'desire', 'belief', 'good design', and so forth. Mechanical descriptions are members of the class of descriptions that are not members of the class telelogical descriptions.

Teleological descriptions are of two kinds: the literal, and the metaphorical. Both kinds of descriptions describe the external, observable behavior of various objects.

However, literal teleological descriptions go further in that they also describe unobservable entities that really exist inside of someone's head, and it is the interaction of these inner entities that cause the outer behavior. Metaphorical teleological descriptions, on the other hand, do not take that extra step, and are not committed to the existence of unobservable entities.

You, sir, apparently believe that literal telological descriptions have their proper place (human psychology); I, on the other hand, believe that all literal teleological descriptions are metaphysical nonsense, and therefore literally false.

Thus, my only constraint when it comes to using metaphorical teleological descriptions is epistemological usefulness.

Because of your metaphysical commitment to literal telological descriptions, however, you believe that the only proper teleological descriptions are literal teleological descriptions within their proper domain (i.e., human psychology). Hence your fear that metaphorical teleological descriptions are epistemologically suspect.

grant hutchison
2007-Nov-15, 05:40 PM
You still seem to be arguing with what you think I believe. (Or perhaps "accuse me of believing" would fit the bill better.) I actually don't care that much about the truth or falsity of "literal" teleological descriptions, except as a diverting thing to think about when there's nothing on the television.

It is the nature of language that what you call "mechanical descriptions" can, and very often do, use metaphor when being transferred from one brain to another. To borrow Jayne's terminology, we speak or write a metaphier which imparts a metaphrand to our audience. So the language used may employ any of the teleological words you mention, without transmitting any teleological content. The grossest example of this sort of thing is when people place scare quotes around an overtly teleological word or phrase, to flag that the word or phrase is being used as a metaphier, simply to allow economical transmission of a perhaps purely mechanical metaphrand, and not to be taken seriously as part of the description itself.
I'd suggest that, because of the particular philosophical terminology you've signed up to, you have been led into a recurring category error when confronted by such purely linguistic conceits: a spoken or written biological metaphor immediately suggest to you that the underlying description is teleological. Not so; not even remotely so.

In essence, I suggest that you are missing or ignoring the very important distinction between metaphor as a means of communicating ideas and metaphor as an idea.

The epistemological usefulness of "metaphorical teleological descriptions" is of course a separate issue, but it is dogged and damaged by the metaphorical richness of language: we can tell many metaphorical stories about the same mechanical system, and so find many more ways to make wrong predictions than to make right ones.

Grant Hutchison

jkmccrann
2007-Dec-01, 10:02 AM
There is a possible scientific underpinning to Bode's law without (pray tell) exceptional physics.

We know the moon's distance from the Earth is increasing at a rate that would have 'unwound the moon' many millennia ago if the distance were always increasing. We can find rough resonance formula's that over a great time scale will cycle the moon between greater and closer distances.

If there are 'tidal' effects within the sun, the current planetary orbits may also reflect weak tidal relationships.

This concept also has some merit when we discuss the moons of Mars - They have the appearance of captured asteriods, but much too circular of orbits to be asteriods jettisoned from the asteroid belt; unless there is an unknown tidal/resonance relationship.

Interesting you say this - would you suggest that the effect you describe here with relation to the Moon may still be playing out with the orbits of the planets in our Solar System?

In other words, are the current orbits of the planets "static" or are they still evolving?

If they are not static, then I don't believe one can comprehensively prove or disprove the so-called TB's Law.

neilzero
2007-Dec-01, 03:27 PM
The hypothesis, I heard, long ago, millions of small objects (planetismials) mostly smaller than our moon. They collided frequently, until some had enough mass to eject near misses out of our solar system. After a few million years the remaining orbits were such that collissions were very rare, and we were down to about 2 dozen Pluto size or bigger. Changes have been rare the past 4 billion years. Likely other arrangements could have been equally stable, but what we got was by dumb chance,plus some early differization which occured about 4.7 billion years ago. Neil

Jerry
2007-Dec-03, 04:51 AM
Interesting you say this - would you suggest that the effect you describe here with relation to the Moon may still be playing out with the orbits of the planets in our Solar System?

In other words, are the current orbits of the planets "static" or are they still evolving?

If they are not static, then I don't believe one can comprehensively prove or disprove the so-called TB's Law.
The increase in the Moons orbit is very small, but when you look at the amount of energy that must be transfered to increase the orbit of a mass the size of the moon, it is staggering.

Standard theory tells us the orbits of all of the planets should be constantly getting smaller, but I don't know of any evidence that this is true - the time scales are too great. So as others have said, the best evidence for a 'Bode-type' relationship, if there is one, will have to come from other planetary systems.

(As an ATM theorist, I think there are resonant orbits, and that the resonant orbit is a function of the mass & composition of the planet and also of the star.) In any case, it will take careful observations of a number of extra solar systems to put together conclusive evidence. This is something to look forward to in the next century of astonomical observations.

I was thinking as I was typing this, that it is too bad that only a few observatories will have the power to do this type of analysis, but then I realize distributive lensing systems AND distributive analytical systems will spread like wildfire in the next few decades - there may be thousands of astonomers and tens of thousands of amatures out there who will be processing the images. Cool.

Warren Platts
2007-Dec-05, 02:16 AM
I was thinking as I was typing this, that it is too bad that only a few observatories will have the power to do this type of analysis, but then I realize distributive lensing systems AND distributive analytical systems will spread like wildfire in the next few decades - there may be thousands of astronomers and tens of thousands of amateurs out there who will be processing the images. Cool.

Indeed! :D