Reset Password
Reset Link Sent
| Blogs > saturn1019 > My Blog |
Eccentricities, Mysteries and theTitus-Bode Law:Trying to make sense of Triton
|
Eccentricities, Mysteries and theTitus-Bode Law:Trying to make sense of Triton There are still great mysteries to be solved in our solar system, and in the minds of non-scientists, even matters that aren’t particularly mysterious bring about questions when exposed to them in a graphic way. I encounter this frequently when doing presentations on the Orbits Table at the museum. The uniform, counter-clockwise motion of all the planets around the sun seems to inevitably bring forth the question, why do all the planets orbit the sun in this fashion? The answer is really quite simple: The planets all orbit in that fashion as the result of the properties of the original solar nebula from which the planets and the sun formed. It might have been different. We might have<b> viewed </font></b>it all in a different way as well. In fact, if civilization had principally originated in the southern hemisphere, our globe might well have Antarctica at the top. So the counter-clockwise motion of the planets is a function of both factors that predate the origins of the solar system and human bias. But the uniform motions of the major planets, both in terms of their motions around the sun and their alignment along the plane of the ecliptic is pretty clear evidence of the sole involvement of natural laws of physics, not the intervention of divine creation. Had some great, hairy thunderer played a role in the formation of the solar system, a greater degree of creative, artistic whim in the structure of the solar system might well be expected. I can well imagine planets orbiting the sun in both clockwise and counter-clock directions, and planets with wildly varying degrees of orbital inclination. A much more artistic solar system configuration was clearly possible in the hands of omnipotence. But what we got was a solar system that behaves well understood physical laws. Consequently, among the major planets at least, everything behaves in a predictable and well understood fashion. There was a time when we didn’t understand the workings of the solar system all that well. A few centuries ago, religious biases forced us to accept the conclusion that the Earth was the center of creation and all objects in the heavenly firmament orbited around us. The sun and moon offered no problems to this view of cosmology. Their behaviors appeared pretty consistent to our ancestors, who were far more keen observers of the heavens than most of us. The stars also behaved themselves pretty well. Issues arose, however, when we had to define the motions of the planets. Most of the time they seemed to progress across the sky east to west, but occasionally they would start to move retrograde against the constellations and generally foul up the entire works. This led to extremely complex efforts to explain their apparent motions. This geocentric model of the universe was complex and messy, but held sway for several centuries for two reasons: First, it did match the observations. No one could really explain the complex, loop the loop performance of the planets, but it had the advantage of being observationally useful. Second, it was consistent with the prevailing philosophies of western piety, so it could be offered without objection from officialdom. Then along came Copernicus and Galileo. Copernicus offered a model of the solar system where the sun and not the Earth was the center of the solar system. The telescopic observations of Galileo demonstrated that there were unseen objects in the solar system, specifically the moons of Jupiter, that orbited that body and not the Earth. Both concluded, to the chagrin of the church, that it was the sun and not the Earth that was at the center of creation. However, this model still failed to explain the occasional retrograde movements of the planets against the backdrop of the stars. Johannes Kepler was able to resolve that matter with his laws of planetary motion. Kepler’s first law (there are 3) defines the orbits of the planets as being elliptical, and not circular as was previously assumed. The elliptical nature of planetary orbits once and for all settled the matter of the strange apparent motions of the planets in the sky and removed all possible objections to a solar-centric model. Even the church had to ultimately capitulate to the truth, although the process was still a difficult . In the 70’s Johann Elert Bode and Johann Daniel Titius noted a peculiar Fibonacci order to the placement of the planets. They would define what would become known as the Titius-Bode law, which seemed to define where the planets are aligned around the sun in their orbits. Effectively, the distances of the known planets (there were only 6 at the time including Earth) could be defined the formula, a=4+x where x= 0, 3, 6, , 24, 48 and so on where, except for the first value, every new in the series is twice the value of the previous . So the expected and actual placement of the planets was as follows: Mercury=4 Mercury=3.9 Venus=7 Venus=7.2 Earth=10 Earth=10 Mars= Mars=.2 ?=28 *Ceres=27.7 Jupiter=52 Jupiter=52 Saturn=100 Saturn=95.5 When the Titius-Bode series was first defined, the largest object in the asteroid belt, Ceres, or even the belt itself had not yet been discovered. The empty spot in the series set off a flurry of efforts to discover the missing planet and Ceres was discovered in 1801. A of other bodies in what is now known as the asteroid belt were to follow, but the infallibility of the Titius-Bode law was already accepted. Around the time the Titius-Bode law was published, astronomers began searching for a possible 7th planet that, if the law were accurate, should orbit the sun at 6. Uranus was discovered in 81, about 9 years after Johann Bode published the law. It was discovered at a distances of 2.2, less than 2% closer than the law predicted. This seemed an almost complete vindication of the law. That it took so long to discover Uranus is almost astonishing, given how keenly talented our ancestors were at sky observation. Uranus is a naked eye object, just barely, but it had been seen and entered on star maps dating back to Assyrian times. The problem may have been that is is so faint and moves so slowly against the backdrop of the stars that the time sky maps were updated, it wasn’t unusual to note the new location of Uranus and simply assume it hadn’t previously been entered on sky maps. But almost as soon as Uranus was discovered, anomalies in its orbit suggested that another world should exist beyond it. The existence of Neptune was established mathematically before it was ever actually observed, and even its position in the sky was accurately calculated. The problem was, it was in the predicted part of the sky, but not the right distance from the sun according to Titius-Bode. Neptune should have been located at a distance of 388 units, or 38.8 A.U. One A.U. is an astronomical unit, the distance of Earth from the sun. Neptune was only . A.U. from the sun, a variation of 22.4% off the predicted value. Either something was fundamentally wrong with the Titius-Bode law, perhaps it was entirely coincidence, or something anomalous had to be explained in the far reaches of the known solar system. So it can be established that the Titius-Bode Law works for most of the solar system. Why it falls apart beyond Uranus is unknown, but it is a point to which we will return later. With the existence of other solar systems now firmly established, it becomes possible to test the idea out elsewhere. Our solar system is something of an anomaly in the galaxy. The typical model seems to be the “hot Jupiter” system, where a large Jovian type world develops early and migrates in towards the primary star. This discourages the formation of smaller, rocky worlds, like the terrestrial worlds in our solar system. But we have found a lot of systems out there with at least 3 planets, giving us other opportunities to test the Bode sequence. Out of 1 exo-systems evaluated to date, 4 of them fit the model pretty well. In fact, 5 exoplanets have been discovered in other systems applying Titius-Bode derived predictions. So to some degree and up to some point, Titius-Bode actually works. Why it only works up to a certain point is worthy of conjecture. In our solar system, like many others we are discovering, Jupiter evidently was the first to form and had it not been for some extreme good luck, our system might have followed the hot Jupiter model that seems so common. The stroke of good luck that befell us goes the name of Saturn. Once Jupiter formed, it did start migrating inward and probably made it as close to the sun as the present asteroid belt. Most of the available material in that area was probably either swallowed up Jupiter or ejected from the solar system, explaining why no reasonably large planet formed there. But Saturn arrested Jupiter’s inward motion, enabling small, rocky worlds to form and survive closer to the sun. Jupiter settled into its present orbit and Uranus and Neptune also formed further out. However, the gravitational interplay of Jupiter and Saturn had a significant effect on these two worlds as well. Neptune was probably the closer of the pair to the sun originally, but the gravitational effects of Jupiter and Saturn likely caused Uranus and Neptune to exchange orbits, possibly a few times. This might have ultimately caused Neptune to settle into an orbit closer to the sun than would have been expected the Titius-Bode law. But it might explain another anomaly in the other system, which we will get to shortly. First, we return to Kepler. As we discussed earlier, Kepler’s first law of planetary motion defines all planetary orbits as ellipses with the sun at one focus. Just how egg shaped these orbits are varies from planet to planet and is known as orbital eccentricity. The orbital eccentricities of the major planets are listed below. The lower the value, the more nearly circular the orbit: Mercury 0.2056 Venus 0.0068 Earth 0.07 Mars 0.0934 Jupiter 0.0484 Saturn 0.0541 Uranus 0.0472 Neptune 0.0086 Pluto 0.2488 Pluto isn’t considered a major planet anymore, but I include it with the 8 major planets for a reason. One of the reasons it is no longer considered a major planet is its orbit. First, it has an extremely eccentricity, significantly higher than any other planet in the solar system except Mercury. Second, it also has a high orbital inclination. Of the major planets, the highest orbital inclination also belongs to Mercury, inclined about 7 degrees to the ecliptic. We used Earth’s orbit to define the plane of the ecliptic, so our orbital inclination is defined at a 0 degrees. Among the rest of the planets, Venus is slightly over 3 degrees and the rest are under 2 degrees. Pluto has an orbital inclination of . degrees. Neptune’s value is 1.77 degrees and I mention that for reasons I will get to soon. As I noted earlier, all the planets orbit the sun, or rather all the planets and the sun orbit their barycenter in a counter-clockwise direction with our geographic north pole arbitrarily defined as “up.” In space, the concepts of up and down are entirely meaningless. All the asteroids also follow this convention, and even the trans-Neptunian Kuiper Belt objects that are being found seem to follow the pattern despite the severe orbital inclinations characteristic to those bodies. Eris, for example, has an inclination of 44.187 degrees. Almost all of the various planetary moons also follow this counter-clockwise convention, although there are a few exceptions. Both Jupiter and Saturn have a few small moons that orbit retrograde or clockwise, but these are invariably very small objects with highly eccentric and severely inclined orbits, suggesting that they are almost certainly captured bodies that wandered too close. In most cases, the gravitational hold these two planets have on the bodies in question is feeble, suggesting that their hold on them is temporary at best. But once again the outer solar system holds a confounding mystery, one that planetary astronomers have yet to answer in a satisfactory manner. Triton is Neptune’s largest moon, the 7th largest moon in the solar system. For a time, some thought that it might be the largest moon in the solar system, but it’s high albedo led to miscalculations of its true size. Voyager 2 settled the issue in 89. The fascinating thing about Triton is that it probably shouldn’t be there. Triton actually orbits Neptune retrograde and it has a rather orbital inclination of 6.885 degrees to Neptune and 9.8 degrees to the sun. This is extreme even trans-Neptunian standards. So the suspicion is that Triton might be a captured object. It is in many ways a twin to Pluto. Its appearance seems to be quite similar to Pluto and the duo are very close in size. Triton’s equatorial diameter is about 2700 km compared to Pluto’s 22 km. There is just one problem with the suggestion that Triton is a captured body: Triton has one of the most perfectly circular orbits in the solar system with an orbital eccentricity of just 0.0000. The odds of a captured body achieving an orbit this close to circular without some other force acting upon it are close enough to zero to be considered untenable. That Triton was, in fact, a captured body seems almost certain. The problem of explaining its close to circular orbit remains confounding. The most reasonable explanation to date is that Triton was once part of a binary system and a close approach to Neptune slowed it sufficiently to not only be captured Neptune, but to settle into a nearly circular orbit. But the question remains of what happened to its binary partner. The same slowing effect on Triton might have accelerated its partner out of the solar system, but there are certain mechanical problems with this hypothesis as well. The mysteries of the outer solar system, Triton, the extreme axial tilt of Uranus, the arc rings of Neptune and other questions beckon us to return to the outer solar system. One or more Cassini class probes might provide a lot of answers. To date, our only close visual inspection of Uranus and Neptune was provided the quick flyby of Voyager 2. We need to return soon. |
Become a member to create a blog
