Old outer-planet theories, Great ideas that didn't pan out Options

[Rob Pinnegar]

Several years ago, when I was still at U of Western Ontario, I was browsing through some of the old books in the astronomy section of the main campus science library. One of these dated from the late 1800s and contained a couple of hypotheses, current at the time, that are worth passing along. (I don't think I've posted these before... apologies if I'm repeating myself.)

The first of these had to do with the number of moons around each planet. After Asaph Hall discovered Phobos and Deimos in 1877, no planetary satellites were found for another fifteen years. This book must have been published during that time, because the author pointed out that Earth had one moon, Mars two, Jupiter four and Saturn eight. This had apparently led people to speculate that Uranus had sixteen moons, and Neptune thirty-two, most of them waiting to be discovered. (It seems that Bode's law died very, very hard.) My guess is that this probabaly dates the book to just before 1892, when Amalthea was discovered, as it would have taken people a while to start thinking that all the moons out to Saturn had been found. The death blow came six years later, when Pickering picked up Phoebe.

The second hypothesis was the really neat one. In the late 1800s, Jupiter and Saturn's axial tilts were well known because Jupiter's bands were clearly visible, and of course Saturn's rings provided even better evidence of its tilt. However, since Uranus and Neptune are so bland and so far away, estimates of their axial tilts had to be based on satellite orbits. As a result, although Uranus' axial tilt was pretty well determined, the estimate at the time for Neptune was terribly wrong because it was thought to be same as the plane of Triton's orbit. Since Triton's orbit is circular, everyone (quite reasonably) thought Triton was a regular satellite. In fact, there weren't any irregular satellites known then -- Iapetus and Luna would've had the largest known orbital inclinations. And Proteus hadn't been discovered. So there was no way of telling that this assumption was wrong.

This gave estimates of the axial tilts of Jupiter, Saturn, Uranus and Neptune as 3, 27, 98 and 160 degrees. At this point, someone had the bright idea that there was an unknown process operating in the outer Solar System that was causing the outer planets to flip over from the outside in. I thought this was terrific. Naturally, when better telescopes were invented, this was found to be wrong... but it was still a great idea.

Although it's unscientific to say so, in a way it's always a pity to see a brilliant idea blown out of the water by fact. Nonetheless, even if we can't keep wrong ideas around for sentimental reasons, at least we can appreciate them for the merits they had, given the information that was available at the time.

[alan]

This book must have been published during that time, because the author pointed out that Earth had one moon, Mars two, Jupiter four and Saturn eight. This had apparently led people to speculate that Uranus had sixteen moons, and Neptune thirty-two, most of them waiting to be discovered.

I remember reading a story once claiming Asaph Hall worked so hard searching for moons around Mars because it was expected to have two moons to fit into the pattern you mention.

[JRehling]

Although it's unscientific to say so, in a way it's always a pity to see a brilliant idea blown out of the water by fact. Nonetheless, even if we can't keep wrong ideas around for sentimental reasons, at least we can appreciate them for the merits they had, given the information that was available at the time.

These are great anecdotes, Rob!

In fact, some of the core work in science started with simple pattern-matching.

There is a (nascent) branch of artificial intelligence that tries to reproduce human scientific reasoning. It's not too hard to write a program that can take the appropriate data and spit out Kepler's Laws very quickly -- much faster than Kepler came up with them.

My grad advisor Douglas Hofstadter has pointed out that this is a specious result because the really important insight -- what it took Kepler years to come up with -- is being handed to the computer. And that important insight is... natural laws tend to be expressible to a decent approximation with polynomials.

At the beginning of the 17th century, that wasn't known. Kepler spent a lot of time exploring the ratios found in the regular polyhedra looking for mathematics that explained the orbits of the planets. Eventually, polynomials were found to express their motion... and polynomials were found to provide good models of many other scientific phenomena.

As a consequence, we now learn polynomials as a cornerstone of our mathematical education. And those AI researchers can build "polynomial smarts" into their programs. But it was basically trial and error work that led to the original observation that polynomials are so useful... we can derive the reasons why with hindsight, but the usual caveats regarding highsight all apply.

Likewise, we now understand that the basic distribution of stuff in the solar system was the result of some stochastic nature of the initial distribution. Certainly, dynamics constrained certain final hypothetical statuses from occurring, but we all can assume that there could have been one fewer big satellite around Jupiter, and Mercury could have been smaller, Saturn probably could have been a little farther out, etc. But without a really solid model of solar system formation that could be "run" computationally, that wasn't so obvious in 1891 -- maybe the solar system was the way it had to be, just as the sequences in chemical-element families follow unbreakable rules. The periodic table was discovered within a decade of the discovery of Phobos and Deimos. The meta-level regularities in the natural world were just being established.

[helvick]

My grad advisor Douglas Hofstadter ...

I would happily sacrifice a limb or two to be able to make a comment that included that sentence...Oh well I just have to make do with what I got.

[dvandorn]

My grad advisor Douglas Hofstadter...

Yes, that explains a great many things, John. I may occasionally disagree with your assumptions, but I always find your logic impeccable.

-the other Doug

[qraal]

Old models of planet structure are a lot of fun too, especially the late 19th Century versions which had Jupiter and Saturn still in formation with volcanic surfaces and primordial life. Or then there's the cold Jupiter models from the 1930s, in which the planet formed so slowly the whole planet was frozen and it had an actual surface, with the Red Spot being the last volcano. Ammonia seas were a common feature, though early temperature measurements hinted it was probably frozen.

Adam

[Gsnorgathon]

The whole 1, 2, 4, ... moons thing gord back awfully far - Kepler thought Mars must have two moons, though I don't believe I've read anywhere who first had the notion that Saturn must therefore have 8.

[Rob Pinnegar]

These are great anecdotes, Rob!

Yeah, they are. If only I could remember the reference!

I have to admit to being very fond of story telling. In fact, I'm so fond of it that listening to me tell stories for the hundredth time often inspires my friends to want to smash my head in.

Kepler spent a lot of time exploring the ratios found in the regular polyhedra looking for mathematics that explained the orbits of the planets.

Well, exponentials deserve a bit of credit, too... although, really, once you've got Taylor and Laurent series in your arsenal, everything's a polynomial.

The really amazing thing about Kepler's polyhedral approximation is how close it comes to nailing the positions of the planets *when you include their orbital eccentricity*. This is discussed in the first chapter of Murray and Dermott's book "Solar System Dynamics" which I quote a lot around here because I happen to own a copy. (This of course doesn't imply that I understand the book's content, but, to quote "On The Riverbank", that's another story.)

Anyways, if you can get your hands on Murray and Dermott at the local university library, there's a fairly simple exercise question at the end of Chapter 1 that demonstrates how including eccentricity really improves Kepler's model. I'm too lazy to work through this problem right now, but have done it before, and the result really *does* give a good idea of why Kepler thought he was on to something.

[Rob Pinnegar]

Although this doesn't strictly deal with Uranus and Neptune, it _is_ an old outer-planet "theory", so I'm dropping it here instead of creating a new thread:

This past week I was in a conference hall where one of the ornamental decorations was a grand piano with an old book sitting on top of it. Of course I had to look at the book and it turned out to be Volume IX of the 1892 edition of Chambers's Encyclopedia. This was the volume that roughly covered the R-S section of the alphabet.

I tried to look up Saturn, but only the mythological god Saturn was listed there. Presumably the planet Saturn was described under "Planets" in volume VIII. However I did run across "Satellites" and found the 1892 estimates for the diameters of Saturn's moons (in MILES):

Mimas: 1000
Enceladus: ?
Tethys: 500
Dione: 500
Rhea: 1200
Titan: 3300
Hyperion: ?
Iapetus: 1800

The really striking thing about this list is of course the vast overestimation of the size of Mimas, listed as being four times larger than its true diameter. I guess this is probably due to Mimas' proximity to the rings; this may have made it difficult for observers to determine its apparent brightness.

Iapetus' estimated diameter here is almost twice the true value as well. This is perhaps understandable; the huge variations in Iapetus' albedo, as observed from Earth, would have made estimating its diameter very difficult.

The other moons listed were Phobos and Deimos, the Galileans, the four biggest moons of Uranus, and the "satellite of Neptune", still without the name Triton attached to it. Amalthea was not included in the chart, but was mentioned in the text -- it was discovered in 1892, so it must have been found just as the book was being typeset. Too late to change the chart! Only the moons of Jupiter and Mars had any diameter estimates given, and they seemed pretty close to the true values, so I didn't copy them down.

[Decepticon]

Kinda off topic, but in the movie War of the Worlds (1953) They say that Jupiter has a surface with Volcano's!

[algorimancer]

I recall reading a popular science book by Isaac Asimov back when I was in high school that argued that Jupiter had huge water oceans filled with fish, and advocated commercial fishing there. His science was better when he stuck to chemistry, but generally he was entertaining. One of the more interesting anecdotes he described was of an occasion when he need to know the orbital velocity of particles in Saturn's rings. Basically he played around with the math a bit and suddenly found himself having re-derived Kepler's laws of planetary motion. He rationalized something to the effect that this was a problem which a common person had no hope of solving, a bright person would have remembered Kepler's laws and applied them, but a true genius could safely forget Kepler's laws with the assurance that he could simply re-derive them as needed. Asimov wasn't shy about stroking his own ego. I've always found this little story inspirational, and when taking courses in physics and mathematics tried to make a point of deriving the equations rather than simply memorizing them - and of course learned a lot in the process, and still practice. I tried conveying this notion when I was teaching high school math, but few high school kids have any interest in anything beyond learning the ONE procedure which solved the problem at hand (and these were honors classes, including calculus). Naturally I enjoyed confusing the heck out of them by demonstrating multiple paths to solving a particular problem.

Okay, rambling mode off

[edstrick]

"...Asimov wasn't shy about stroking his own ego...."

He referred to that as his "cheerful self appreciation". He did it ostentatiously, with a wink, as a "just between us two" joke and everybody went along with it. People who didn't realise it was half put-on got vastly annoyed by it.

[ngunn]

"...Asimov wasn't shy about stroking his own ego...."

He referred to that as his "cheerful self appreciation". He did it ostentatiously, with a wink, as a "just between us two" joke and everybody went along with it. People who didn't realise it was half put-on got vastly annoyed by it.

Some people, realising that it was only half put on, found it a bit tiresome too.

[JRehling]

His science was better when he stuck to chemistry, but generally he was entertaining.

That's where I learned all of my grade-school science. I think the remarkable thing about Asimov's science-fact essays was how much love he showed for the subject matter. He was seriously grateful to the universe for providing us with such fascinating things as the various families of the periodic table and the simple arithmetic that could get you started thinking about them.

Back when every asteroid and every outer planet satellite was, as far as we knew, a smooth gray sphere lacking any physical properties besides radius, mass, and orbital elements, I'll be damned if Asimov couldn't find something interesting about them to write about.

[nprev]

Kinda off topic, but in the movie War of the Worlds (1953) They say that Jupiter has a surface with Volcano's!

Although I can't find a Web reference, I seem to recall that there were a couple of relatively fixed areas on Jupiter that were sources of radio emissions. This probably led to the 'volcano' hypothesis.

Unless these have since been identified as Io/ionosphere/Jovian "surface" current path points, nobody has any idea what they really are...