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Thread: Titius Bode

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    Titius Bode

    I just read something about Titus-Bode law on this board. Because I did not know what it was, I had a look in wikipedia. The first thing that came to me was: quantum physics at large. Is this a ridiculous idea?

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    The prevailing attitude among astronomers is that it's coincidence, and that the odds of planets being in positions according to some ad-hoc law is pretty good. I'm not aware of any arguments of note that the distances are determined by any sort of underlying physics.

    The similarity to quantum physics is there, but there doesn't seem to be any reason for it.
    Everything I need to know I learned through Googling.

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    Thanks.

    To few objects to make it a law I think. And one object, Neptune, is not even follwing the rule With any physical explanation it is likely a very nice coincidence. Maybe we can say more when we know the exact distances to their star of the exo-planets.

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    I like Titus-Bode!

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    Quote Originally Posted by Candy
    I like Titus-Bode!
    No wonder he is winking
    We know time flies, we just can't see its wings.

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    The correlation with our solar system is not especially impressive; most of the figures get fudged a bit to make it look better. A survey of extrasolar systems so far shows that T-B is followed maybe... maybe 30 percent of the time. And so far, no one has come up with an adequate explanation for how it would work.
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    Orbital stability can be found in resonance. Neptune and Pluto share a 2/3orbital resonance. Many moons of Jupiter and Saturn also show resonance. However, orbital resonance among the other planets does not seem to exist. [Albeit, there is a possiblity that there is a spin to orbit resonance between Venus and Earth.] FWIW, I vaguely recall a 17th century(?) musical composition which used the orbits for notes.
    We know time flies, we just can't see its wings.

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    Quote Originally Posted by Jim
    The correlation with our solar system is not especially impressive; most of the figures get fudged a bit to make it look better.
    IIRC, the Titus-Bode law was "noticed" just before the discovery of Uranus. Uranus' discovery seemed to "fit" and everyone got excited. That excitement died out when Neptune was discovered, and found not to "fit".
    The facts, gentlemen, and nothing but the facts, for careful eyes are narrowly watching. Isaac Asimov

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    Quote Originally Posted by George
    I vaguely recall a 17th century(?) musical composition which used the orbits for notes.
    Can you remember the title of this composition?

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    Quote Originally Posted by Thomas(believer)
    Can you remember the title of this composition?
    It might have been Kepler, you might try looking up stuff on him. He was into trying to fit the orbits into objects with equal sides. It might have been him with the "music of the spheres".

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    Quote Originally Posted by George
    No wonder he is winking
    Me thinks Bode was looking in the telescope for way too long.

    That photo is priceless.

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    Quote Originally Posted by Thomas(believer)
    I just read something about Titus-Bode law on this board. Because I did not know what it was, I had a look in wikipedia. The first thing that came to me was: quantum physics at large. Is this a ridiculous idea?
    Certainly a lot of people wonder about that, because it's kind of natural; at all these different scales you have small things orbiting around spheres, etc. But like a lot of people have said, it seems to be coincidental. Going out on a limb here, I would say that the only thing that could be happening is that our perception of the quantum world is somehow out of whack. In other words, things in the quantum world appear to be identical, but it is only our perception because we are perceiving patterns, or something along those lines. But this is just interesting speculation. I personally believe, though, as can be seen from my sig file, that there is some sense in which things are self-similar at different scales, or that there is a hierarchy of some form.
    As above, so below

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    Quote Originally Posted by Thomas(believer)
    Can you remember the title of this composition?
    I grabbed Dava Sobel's CD set on her Planets, for I had 700 miles to drive. Her style is quite elegant and dang perrttyyy. She lost me though as soon as Jupiter entered Capricorn, I think. I wasn't expecting astrology.

    It was there she mentioned an astronomer from your neck of the woods, or due north of you. She mentioned the musical style created was popular for some time for the country of origin, too. There is a chance I'll listen again; if so, I'll try to remember to pass it on to you.
    Last edited by George; 2006-Jan-24 at 01:59 PM.
    We know time flies, we just can't see its wings.

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    Quote Originally Posted by Candy
    Me thinks Bode was looking in the telescope for way too long.
    I thought he was winking at you, but you are probably right, since he is winking the wrong eye - the one that looks swollen which does not bode well for...well, Bode. [sorry , you knew someone would spit it out.]
    We know time flies, we just can't see its wings.

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    I just realized we keep spelling Titius-Bode wrong.

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    That there are (or were) several different formulations is a clue that its status may not be much more than a nice pattern pleasing to our eye, plus some constraints from basic physics. Wikipedia and Wolfram Research give slightly different forms - they're not really the same, if you want to consider some general case.

    Tests - exosolar systems, the regular moons of the gas giants - don't seem to give it much support. Further, if the main belt asteroids are fudged (why Ceres?) as an entry in the series, why leave out the Edgeworth-Kuiper Belt?

    Finally, if a planetary system has a Jupiter and a Saturn, what are the semi-major axes of stable orbits of (any) planets with (considerably) smaller masses? In other words, the 'law' may be an epiphenomenon (think of the main belt asteroids - where else could they go in a solar system with MVEMJSUN other than between M&J (or beyond N), and between M&J, why pick Ceres' orbit as representative?

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    Quote Originally Posted by Nereid
    That there are (or were) several different formulations is a clue that its status may not be much more than a nice pattern pleasing to our eye, plus some constraints from basic physics. Wikipedia and Wolfram Research give slightly different forms - they're not really the same, if you want to consider some general case.
    They both look the same to me. What do you mean by that?
    Tests - exosolar systems,
    We don't have the data yet, unfortunately.
    the regular moons of the gas giants - don't seem to give it much support.
    There is a neat progression there, details below
    Further, if the main belt asteroids are fudged (why Ceres?) as an entry in the series, why leave out the Edgeworth-Kuiper Belt?
    Why Ceres? It's just representative of the larger population--it's the first and largest. The orbits of the rest of the main belt asteroids are not far off of Ceres's orbit--at the scale that we're looking at the law.

    As to whether the regular moons of the gas giants give it support, using the values from this website, and normalizing their distance from Jupiter to the third (Ganymede) so that it matches our Earth-based convention, I get a progression of 0.39, 0.63, 1.00, 1.76. That's pretty close to Titius-Bode's 0.4, 0.7, 1.0, 1.6, and almost as good as the Mercury/Venus/Earth/Mars 0.39, 0.72, 1.00, 1.52

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    Quote Originally Posted by hhEb09'1
    Quote Originally Posted by Nereid
    That there are (or were) several different formulations is a clue that its status may not be much more than a nice pattern pleasing to our eye, plus some constraints from basic physics. Wikipedia and Wolfram Research give slightly different forms - they're not really the same, if you want to consider some general case.
    They both look the same to me. What do you mean by that?
    The formulae give the same results; the difference is for Mercury - one (arbitrarily) sets k = 0, the other (arbitrarily) sets n = -∞. For a single application (the solar system) this is neither here nor there; for any generalisation, it matters a great deal ("how to generalise? well, we could add a bunch of new, arbitrary k's, or we could see if the 2n could be generalised by finding a function involving n.")
    Tests - exosolar systems,
    We don't have the data yet, unfortunately.
    This source gives one 4-planet (Main Sequence primary) system, and four 3-planet ones.

    Given the arbitrariness of the T-B 'law' (let's not forget the arbitrariness of which objects we choose as 'planets'!), there isn't enough data to test ... yet. However, there may be enough to show just how arbitrary the 'law' will need to be, to accommodate all systems.
    the regular moons of the gas giants - don't seem to give it much support.
    There is a neat progression there, details below
    Further, if the main belt asteroids are fudged (why Ceres?) as an entry in the series, why leave out the Edgeworth-Kuiper Belt?
    Why Ceres? It's just representative of the larger population--it's the first and largest. The orbits of the rest of the main belt asteroids are not far off of Ceres's orbit--at the scale that we're looking at the law.
    And that's the point isn't it ... any serious test (or generalisation) of the 'law' requires unambiguous specification of inputs (as well as some attempt to address 'acceptable' degrees of not-far-offness).
    As to whether the regular moons of the gas giants give it support, using the values from this website, and normalizing their distance from Jupiter to the third (Ganymede) so that it matches our Earth-based convention, I get a progression of 0.39, 0.63, 1.00, 1.76. That's pretty close to Titius-Bode's 0.4, 0.7, 1.0, 1.6, and almost as good as the Mercury/Venus/Earth/Mars 0.39, 0.72, 1.00, 1.52
    Aye.

    But why Ganymede (and not Europa, for example)? And why just Jupiter?

    More generally, why does a pattern like the T-B 'law' seems appealing to (some) folk? I mean, it's ~8 datapoints fitted to a relationship involving ~5 (arbitrary) numbers. Among the orbital parameters of the main belt asteroids, it is almost certain that one could find a relationship fitting ~800 datapoints with ~500 arbitrary numbers - would that have no appeal because of the number of numbers? Or, among the sky positions of a selection of ~8 bright stars, it is almost certain that one could find a relationship involving ~5 arbitrary numbers, which numbers aren't at all pretty (say, 830982, 0.54899, 31.5, 0, and 743.01) - would that have no appeal because of the awkwardness of the numbers?

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    Quote Originally Posted by Nereid
    The formulae give the same results; the difference is for Mercury - one (arbitrarily) sets k = 0, the other (arbitrarily) sets n = -∞. For a single application (the solar system) this is neither here nor there; for any generalisation, it matters a great deal ("how to generalise? well, we could add a bunch of new, arbitrary k's, or we could see if the 2n could be generalised by finding a function involving n.")
    But k = 2n

    They're the same!
    This source gives one 4-planet (Main Sequence primary) system, and four 3-planet ones.
    Cool page! I think I can do something with that
    Aye.

    But why Ganymede (and not Europa, for example)?
    I normalized to Ganymede because it was the third one out, just as the Titius-Bode law is normalized to Earth. Otherwise, it would be difficult to compare the two.
    And why just Jupiter?
    Hey, it was the first one I tried! And it works!
    More generally, why does a pattern like the T-B 'law' seems appealing to (some) folk? I mean, it's ~8 datapoints fitted to a relationship involving ~5 (arbitrary) numbers.
    The Balmer Formula used what? four datapoints (I had to look it up). It's a similar ad hoc fit, but it resulted in Bohr's quantum theory of the atom. Why did the Balmer series appeal to Bohr?

    Pretty much why Thomas(believer) asked in the OP

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    Quote Originally Posted by hhEb09'1
    But k = 2n

    They're the same!
    Not really (except, as I said, wrt the result).

    For the 'n', why should 'Mercury' be n = -∞ (and not -1, which would be the next in the sequence)? In the case of k=0, it's just arbitrary.
    Cool page! I think I can do something with that

    I normalized to Ganymede because it was the third one out, just as the Titius-Bode law is normalized to Earth. Otherwise, it would be difficult to compare the two.
    Well, Io, Europa, and Ganymede have a well-known relationship ... one that's inevitable (given enough time), from standard celestial mechanics. Anyway, Ganymede isn't #3 (Amalthea is) ... unless you want to say 'only big satellites', but then you've got another arbitrary choice (what's 'big'?).
    Hey, it was the first one I tried! And it works!
    Oh? I thought you'd just read to the bottom of the Wiki page
    The Balmer Formula used what? four datapoints (I had to look it up). It's a similar ad hoc fit, but it resulted in Bohr's quantum theory of the atom. Why did the Balmer series appeal to Bohr?

    Pretty much why Thomas(believer) asked in the OP
    Well, for starters, the Balmer series lead to an immediate prediction (or series of predictions), which when tested panned out (same is not true of T-B). Second, it has only two inputs (or one, or three ... depends on how you're counting). Third, it's a very much tighter relationship.

    And last, the OP's question was triggered by a (rather long) thread in the ATM section (check out Sylwester Kornowski).

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    Quote Originally Posted by Nereid
    Not really (except, as I said, wrt the result).
    No, really, they're identical. The wiki page even mentions that k is powers of two.
    Anyway, Ganymede isn't #3 (Amalthea is) ... unless you want to say 'only big satellites', but then you've got another arbitrary choice (what's 'big'?)
    What did you mean by "regular moons"? I just tried the obvious ones--but I'd actually started to do that last week, and didn't have their orbits handy at the time.
    Oh? I thought you'd just read to the bottom of the Wiki page
    The comment on the wiki page says they "adhere to a regular, but non-Bode, spacing" whereas I showed pretty much that they do adhere to a Bode spacing. My conclusion was different from theirs.
    Well, for starters, the Balmer series lead to an immediate prediction (or series of predictions), which when tested panned out (same is not true of T-B).
    The wiki page says Bode advocated for a search for a planet between Mars and Jupiter, which was found.
    And last, the OP's question was triggered by a (rather long) thread in the ATM section (check out Sylwester Kornowski).
    The OP mentions quantum physics.

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    Quote Originally Posted by hhEb09'1
    No, really, they're identical. The wiki page even mentions that k is powers of two.
    You mean (my bold) "where k=0,1,2,4,8,16,32,64,128 (0 followed by the powers of two)"?
    What did you mean by "regular moons"? I just tried the obvious ones--but I'd actually started to do that last week, and didn't have their orbits handy at the time.
    Those in (or near) the equatorial plane of the parent planet; those not in retrograde orbits; ...

    This
    is a good site to start with (depending on what you're trying to do, you may need to go to journals, or the MPC, for a history of determinations).
    [snip]

    The OP mentions quantum physics.
    And so does Sylwester

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    Quote Originally Posted by hhEb09'1
    The wiki page says Bode advocated for a search for a planet between Mars and Jupiter, which was found.
    So if you consider Ceres a planet, then you must also consider every object in the Solar System that is larger than 500 miles in diameter a planet.

    So does Bode predict all of the newly discovered objects beyond Pluto?
    The facts, gentlemen, and nothing but the facts, for careful eyes are narrowly watching. Isaac Asimov

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    This morning I was thinking a little bit about this law.
    What if this law or a similar law would exist for other planets?
    I am sure a lot of scientist would try the find the underlaying physics.
    As a non-scientist I can only guess. This morning my guess was that the sun creates ripples in space-time. Like dropping a stone into water.I was thinking that a planet would like the reside best in the low part of the ripple were there is less drag. (Yeap, I heard something about space-time drag ).
    What would be your guess?

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    Quote Originally Posted by Nereid
    You mean (my bold) "where k=0,1,2,4,8,16,32,64,128 (0 followed by the powers of two)"?
    Yes
    Those in (or near) the equatorial plane of the parent planet; those not in retrograde orbits; ...
    not including small particles, rings... ?

    I'm not defending Titius-Bode per se

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    Quote Originally Posted by R.A.F.
    So does Bode predict all of the newly discovered objects beyond Pluto?
    Nope, it blows it on UB313 pretty big (about 10-15 AUs IIRC).

    And, as UB313 is larger than Pluto and Pluto is used in T-B (and "fits"), then you cannot ignore UB313. Unless you also ignore Pluto.

    It also blows it on Neptune (shouldn't be there according to T-B).
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    Quote Originally Posted by hhEb09'1
    not including small particles, rings... ?
    That depends on your purpose ... these are short term denizens, so unless one is looking to the T-B as having some sort of short-term meaning (or have some kind of Velokovski crazy idea), there wouldn't be much point I suppose.

    And this allows me to comment that excluding such is a very great deal less arbitrary than excluding all the main belt asteroids other than Ceres, or excluding some selection of TNOs, or ....
    I'm not defending Titius-Bode per se
    Granted. It's interesting to see how limited and arbitrary it is, in the light of (much) more data, isn't it?

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    Quote Originally Posted by Nereid
    It's interesting to see how limited and arbitrary it is, in the light of (much) more data, isn't it?
    I love reading this thread.

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    Quote Originally Posted by Nereid
    That depends on your purpose ... these are short term denizens, so unless one is looking to the T-B as having some sort of short-term meaning (or have some kind of Velokovski crazy idea), there wouldn't be much point I suppose.
    The wiki link on Almathea makes it appear that it is just agglomerated ring material.
    And this allows me to comment that excluding such is a very great deal less arbitrary than excluding all the main belt asteroids other than Ceres,
    No, I think the point is to include all the main belt asteroids as one entity, with Ceres the representative entity.
    It's interesting to see how limited and arbitrary it is, in the light of (much) more data, isn't it?
    I find it more interesting that people will say that a set of objects doesn't follow Bode spacing, when they pretty much do follow.
    Quote Originally Posted by R.A.F.
    So if you consider Ceres a planet, then you must also consider every object in the Solar System that is larger than 500 miles in diameter a planet.
    It's been a while since Ceres was considered a planet (although there are those today who would consider it one), but basically the idea is that there is one (or maybe two) "failed" planet(s) between Mars and Jupiter.

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    Why should Ceres be the "representative entity?" Relative size? Because it's orbit fits T-B? Or is it's orbit at the mean of the AB orbits?

    Yeah, T-B is cute. But, what would make it work? Why doesn't it work for other solar systems? (Seems to apply to about 30%.) How does it account for Neptune?

    Find plausible resolutions to those issues and T-B may move beyond cute.
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