I'm not sure what you guys think of the so-called Titius-Law, and I'm also not sure whether this explanation/theory I'm about to expound has been raised before.

But does anyone here think that the end result of orbital clearing in our Solar System could well, (granted - in a crude way), be explained by the Titius-Bode Law.

Having a look at the wikipedia entry on Titius-Bode, there is this table.

Titius-Bode

In AUs
a = 0.4 + (0.3 x k)

where k = 0,1,2,4,8,16,32,64,128

So,

Mercury: k=0; TB Rule = 0.4; Real Distance(RD) = 0.39;
Venus: k=1; TB Rule = 0.7; RD = 0.72;
Earth: k=2; TB Rule = 1.0; RD = 1.00;
Mars: k=4; TB Rule = 1.6; RD = 1.52;
Asteroid Belt (Ceres): k=8; TB Rule = 2.8; RD = 2.77;
Jupiter: k=16; TB Rule = 5.2; RD = 5.20;
Saturn: k=32; TB Rule = 10.0; RD = 9.54;
Uranus: k=64; TB Rule = 19.6; RD = 19.2;
Neptune: k=128; TB Rule = 38.8; RD = 30.06

But, interestingly,
Plutinos (Pluto): RD = 39.44
(I'm presuming this measurement for Pluto is its mean distance from the Sun given it's elliptical orbit.

Whatever one says about TB, the above table is amazingly well correlated. The correlation almost begs for a more rigorous explanation than simply a mathematical proof.

What also struck me about this is that it seems that the mean distance for Pluto, and its band of Plutinos - is pretty much exactly where the orbit of Neptune should be under the Titius-Bode Law. So why are the Plutinos there, but not Neptune? (If this Law really has any basis in orbital dynamics)

Well, the first thing that I thought of when I saw this was - haven't we got a lot of evidence of gas giant/ice giant like planets migrating out from the star in their system in extra-solar planetary systems? Have we also concluded that something similar may have gone on in our own System? (I'm not sure what the current thought is on that - so I post the question - is there any understanding or current thought that planetary migration (In this case outward) may have occurred in our own System?

It would also seem to make sense to me that the closer into the Sun one got the more likely that the major bodies would have eventually orbited into stable orbits unlikely to be internally (that is - within the given System) disrupted, but that by the same token - the further one gets away from the Sun, the slower this process is going to be - which is why looking out in the Kuiper Belt could well hold clues to how the Solar System was in its early years - and which is also, IMO, why the accretionary process out beyond Uranus is still progressing.

(I've decided to split this because it was getting too long)

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.

For exhibit 1A in that sense - we have Triton. Clearly recognised as a regular Kuiper Belt object - but what is its seemingly inevitable fate? In the blink of an eye in the time frames of the Solar System - it is destined to be swallowed up by Neptune - a clear example that the process of accretion in relation to Neptune is ongoing.

But how did Neptune capture Triton? Well, if one looks at the TB Law, it appears that Neptune has not yet reached its stable point in orbit around the Sun and is quite possibly still migrating out to reach this point - so its inevitable that Neptune is going to capture some of these KBOs, gain resonant orbits with others - and perhaps scatter others out of the Solar System or turn some into comets that dive into the Inner Solar System.

So, given all the above - and I will look for this now that I've thought of it, is anyone aware of any literature, any papers that talk about the possibility that Neptune is still in the process of outward migration - to the place that TB suggests it may end up? Has the possibilty that Neptune is still to complete its accretionary process been investigated and rigorously debated in the Astronomical world? Can anyone point me in the direction of anything relating to this?

The next interesting point is looking at what the subsequent values of TB suggest.

For k = 256; TB = 77.2
For k = 512; TB = 154.

Obviously, our explorations of the Solar System at this distance are very patchy - so its impossible to draw any conclusions, but (and I do need to do more research on this), isn't it well accepted that there is something of a `Kuiper Cliff' at about 50AU?

From wikipedia again

Kuiper Belt

Really? Is that what is generally accepted?

That may be part of the reason - but wouldn't it be equally possible that there is a Jupiter-like (In the sense that Jupiter 'regulates' the outer edge of the Asteroid Belt - I'm not saying a Jupiter-size object, just performing the same sort of function (actually I would suspect, if there were something there it would be a lot smaller than Jupiter - but its actual size is not central to this argument) that regulates the outer edge of the Kuiper Belt?

This seems, given what we see Jupiter doing, quite a possibility - rather than putting the outer edge of the Kuiper Belt down to resonances with an object on the other side of the Belt.

I'm not sure, but to what extent do we put down the outer edge of the Asteroid Belt to Mars for instance?

Because this idea came to me in looking at the TB Law, I'd hesitantly speculate such an object would be at perhaps 60-80AU out, and given that apparently Neptune is still on an outward migration, it too might still be on an outward migration.

So, from all that - I'd like to ask what you guys think - do you think there could well be another object out there? A LARGE object out there - larger than Earth. Do you think that the evidence - Triton - points to the fact that Neptune is still on an outward migration path?

Do you think TB perhaps points to a region of Space we should be training our telescopes on? An object orbiting in the region of 60-80 AU would, by a rough calculation, have an orbit of approximately 330-450 years.

What do you guys think?

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.

Would that even be possible? There's not much difference in the focus of a scope for 80 AU and 80 ly, is there?

Anyone tried TB on an extrasolar star system to see if it stands up to disproof?

I have no idea with regards to telescopes myself - I don't have one and there's not much point getting one considering where I live - far too much light - but if you know what you're talking about I'll accept what you say about the difficulty in differentiating between the 2 distances.

I guess in relation to TB and this whole possibility,

According to this article of Wikipedia (Actually on the Planet X Talk Page)

Planet X

This seems to be an internally inconsistent statement. I'm not sure exactly where it comes from, but why does it seem to conclude that any object of a reasonable size orbiting beyond 60AU must necessarily not be native to the solar system?

Although, whoever quoted that does provide their own rejoinder.

In any case, if that statement is true it seems certain that there is no reasonable sized object up to 60AU on the plane of the ecliptic - which seems to have been proven by observation.

In regards to what I've said here, I'm assuming that any object that may be located between 60-80AU would be located approximately on the ecliptic plane - otherwise, if found, it would perhaps provide an invalidation of TB.

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.

In relation to this point Doodler - I would say I doubt it would stand up to comparison with a given star system, but there would need to be a number of conditions met to make worthwhile comparisons.

The age of any star system tested would have to be the same age as our own.

The type of star in question would have to be the same as our own.

The speed of rotation of the star would have to be the same as our own star.

Those conditions are straight off the top of my head - no doubt there would be more - perhaps the location of said star within the galaxy, in relation to other stars.

Then, you'd have to get a statistically significant number of these stars to be able to make a valid determination. Not sure how many star systems you'd have to look at - maybe you guys would now what a minimum number of cases would be to make a 95% confidence call on TB.

In any case, I don't expect we'll be able to give this kind of rigourous examination of TB for some-time, but I would expect we'll know within a few decades whether there are any significantly sized objects out to perhaps 100AU. (By significant I mean in excess of Earth sized)

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.

Haha, yeah. It's probably some coincidence... Check this out... The extrasolar system with the largest number of (confirmed) bodies is 55 Cancri, which has 4 planets. Here's a list of distances from the star, inclusing a possible second value for 55 Cancri e (From wikipedia). 55 Cancri is a G8V class star of .95 solar masses.

55 Cancri e: 0.038 AU k= -6/5
55 Cancri b: 0.115 k= -1
55 Cancri c: 0.240 k= -1/2
55 Cancri e: ~0.77 (unconfirmed analysis) k= 1
55 Cancri d: 5.257 k= 16

Interestingly, planet d is at nearly exactly the same distance from 55 Cancri as jupiter is from the sun, but the rest of the planets are inside of the orbit of mercury, and the values of k needed to approximate the orbits don't really make any sense

HD 69830 is another multiplanet extrasolar system, with 3 confirmed planets and an asteroid belt. Again, some of these bodies require significant fudging with k to make any sense. HD 69830 is a K0V class star, weighing in at .86 solar masses.

HD 69830 b: 0.08 k= -1
HD 69830 c: 0.18 k= -2/3
HD 69830 Asteroid Belt: 0.42 k= 0
HD 69830 d: 0.63 k= 1

Let's also look at PSR B1257+12, a pulsar with a multi-planet system. Again, k needs some signifigant fudging, specifically for planet d.

PSR B1257+12 b: 0.19 AU k= -2/3
PSR B1257+12 c: 0.36 k= 0
PSR B1257+12 d: 0.46 k= 3/2
PSR B1257+12 e (unconfirmed): 2.6 k= 8

Some patterns emerge, and it's tempting to say that there is some way to expand titus-bode to make it apply to all these systems, but the range of values is too wide. We would need to find a corrolation to this extension of Titus-Bode inside our own solar system for it to be meaningless.

It is interesting to see how the formula applies to other systems, though, especially since 55 Cancri and HD 69830 are so close in size to the sun.

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I think that the current set of known objects provide an invalidation of TB, don't they?

Definitely interesting information you provide there - but are these systems the same age as our own?

Comparing a teenager to an adult and concluding they're different is hardly a surprise and can't be used as a disqualifier.

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.

The first two are, in general. The ages of other stars aren't known to as much precision as the sun's age. 55 Cancri is estimated at 5.5 Billion years old, whereas the best estimate I can find for HD 69830 is between 4 and 10 billion years. The pulsar, being the remnants of a much higher mass star, is only 800 million or so years old.

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No, not as far as looking at our own Solar System.

Given Neptune is still in the process of accreting objects - Triton - and one explanation for this may be that it is still on an outward migratory path, and therefore still prone to disturbing the orbits of various objects out there - how can we know for sure if there are not some gravitational rules at work here that create this kind of outcome?

Given that, according to what I quoted earlier - the plane of the ecliptic has apparently only been observed to a distance of 60AU - when TB suggests that were there another reasonably sized object/planet out there it would perhaps be at a distance approaching 80AU - I would hardly say that observational data currently proves TB is invalid.

Just to be clear to anyone who wishes to talk about Titius-Bode and what I've said here - I don't regard it as a worthwhile theory to use and apply to extra-solar star systems. I don't think what we observe in this system can in any way be drawn upon and used to predict how other systems will behave - we simply don't know enough about them! As well, and I did mention a few in an earlier post - there are a long list of parameters that define any star system that are inherently going to effect how any star system evolves - and unless those conditions exactly match our own - how can we make a worthwhile comparison?

In saying that, it doesn't necessarily mean that the conditions and evolution of our own system - do not in some way lend themselves to the distribution that TB suggests.

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.

I assume you don't mean other than Newton/Einstein.

The dynamics of N/E have been modeled extensively. I'm pretty sure that TB has been consigned to the dustbin.

TB specifically doesn't work, but models of planetary system formation do suggest that a planetary system will tend to have a regular distribution of planets, due to the physics of accretion from a disk of gas.

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I think that, ultimately, the Titus-Bode Law is an example of finding a formula that fits the data. Like any scientific theory, it must make testable predictions and be falsifiable.

It predicts that the next orbital region after Uranus should be at approx. 39 AU. There is no dominant body at that spot. Pluto ranges from 30-49 AU, so its mean is in the right area. But Pluto is just one of many, many large bodies in the Kuiper Belt and none of the others center around 39 AU.

2003 UB313: 38-98 AU
2005 FY9: 39-53 AU
2003 EL61: 35-52 AU
2002 TC302: 39-72 AU
Quaoar: 42-45 AU
1996 TL66: 35-136 AU

In my opinion, Pluto is an interesting case for the T-B law only if you ignore all of the other similarly-sized bodies in the KB. Before 1992, you had no choice about that!

So the existence of a dominant body at a non-TB distance (Neptune @ 30AU) and the lack of a dominant body at a TB distance (39 AU) effectively falsifies the theory.

It is an interesting mathematical curiosity, much like the fact that the ratio between the diameters of the Sun and Moon is the same as the ratio between the distance from the Earth to the Moon or Sun (thus the perfect fit on the solar eclipse).

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It doesn't falsify the theory (Your call - as TB is not a theory in my eyes) - because you are making an assumption there that the Solar System is a static place and that all the bodies have reached a state of orbital equilibrium. Can you, or anyone - provide proof that none of the recognised planets in the Solar System have altered their orbits in any way over the past 1 billion? 2 billion years?

I suggest you read the entirety of what I've posted again.

Yes, Neptune is at a non-TB distance currently - but how long has it been there? 10 million years? 100 million years? 1 billion years? I don't know - but over the course of the past 1 billion years is it possible that Neptune has migrated outwards away from the Sun?

If it has migrated outwards over the past 1 billion years, then surely its possible that it is still in the process of outward migration - and therefore still in the process of accreting smaller bodies in the region in which it now resides.

As evidence that it is in the process of accreting bodies in the Kuiper Belt - look at Exhibit 1A - Triton. Doesn't Triton suggest to you, or anyone - that Neptune has encroached more upon the Kuiper Belt than it was doing in the past - how else can you explain the relatively recent capture of Triton? If Neptune has been in a static orbiting position for billions of years, why did it suddenly capture Triton relatively recently - can anyone provide an explanation for that backed up by hard facts please?

Triton was a regular member of the Kuiper Belt, now it is in the process of being accreted into Neptune - who is to say that this process will not continue and that over the course of the next billion years Neptune will not continue to gobble up, eject, or put into resonance other objects in the Kuiper Belt - as it migrates further out and perhaps settles at the place suggested by TB.


This thought came to me because thinking of Neptune and trying to work out why it captured Triton, it made me wonder - why was Triton captured so recently? Surely the most logical reason it was captured so recently was that Neptune had begun to encroach upon its territory - ie the Kuiper Belt. And if this encroachment was so recent, that must mean that Neptune has at some point recently been in a process of outward migration - which if it was that recent, its probably still going through.

So, the question is - how far will this possible outward migration take Neptune? Surely the amazing correlation between the orbits of the other planets and TB suggests one must wonder - and disprove (something that is unfortunately at this time beyond me) that it will eventually stop this outward migration and gain some sort of orbital stability at the distance suggested by TB.

I don't deny that TB is an example of finding a formula that fits the data - no doubt about that! In that sense, I don't accept it as a theory - merely (perhaps?) a simple explanation of forces - complex gravitational interactions and forces that to nail down completely accurately would require a much more rigourous examination.

I would ask - can anyone here prove that Neptune has not experienced any outward migration over the past 1 billion years? And, if you accept that some outward migration of Neptune may have occured over the past 1 billion years - can you tell me at what distance this outward migration will stop.

Actually, just found a PDF about Neptune's Outward Migration - which should be interesting to read.

Various Astronomy Papers

Neptune's Planetary Migration - Why did it stop at 30AU?

Ok, this sounds like something that may help answer some of the thoughts I have here - I would like to know when this migration stopped and how they know it has stopped.

Anyway, I suggest you guys check these papers out - quite a lot of interesting ones to peruse.

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"All truth passes through three stages. First, it is ridiculed, second it is violently opposed, and third, it is accepted as self-evident." Arthur Schopenhauer - renowned 19th Century German philosopher.