| The Success of Newtonian Gravity:
The Discovery of Uranus.
Through all of recorded history, human civilisation has been aware of the existence of the five naked-eye planets: Mercury, Venus, Mars, Jupiter and Saturn. As we noted earlier, the existence of these five, plus the moon and sun, led to
speculations which are reflected today in various ways including the naming and number of the days of the week. Indeed, Kepler devised a
half numerological and half geometrical, to explain why there were precisely six planets (including the Earth). By his reasoning, there could be no more!
The passage of time brings technical and intellectual progress, however, and it came as an interesting surprise but not a world-shattering one when William Herschel, a German expatriate who became a great English astronomer, discovered the planet Uranus entirely accidentally in 1781. Uranus is big enough and near enough to be resolved as a real disk when seen through a telescope, and indeed Herschel's attention was first caught by an object of non-stellar appearance. Only thereafter did he notice that it moved around with respect to the stars, proof of its actual nature. Uranus can just be seen with the naked eye, if you enjoy a really dark sky and know exactly where to look. (Of course, to the unaided eye it would appear just as a faint point of light, indistinguishable from a star.)
The Prediction and Discovery of Neptune: A Real Success?As I remarked in the an early lecture, and one of the attributes it should have is the power to predict consequences in quantifiable ways. The accidental discovery of Uranus was a perfect opportunity to demonstrate this, because Newton's theory of gravity allowed astronomers to predict precisely how the newly-discovered planet ought to orbit the sun, given its distance and so forth. Of course, they would have to wait quite a while for the prediction to be borne out, since it takes Uranus about 84 years to go around the sun, but they were confident that Newton's law would provide the correct answers. Unfortunately, by about half a century later it had become increasingly clear that Uranus was not moving along precisely the orbital path it should follow. Why not? There were two obvious possibilities: 1 Perhaps Newton's law of gravity is wrong, or breaks down in some way for objects that are very far from the sun; or 2 Perhaps Uranus is being affected ('perturbed') by the gravity of things we don't know about, so that its orbit is not as expected. Actually, the second point had already been taken into account in one sense. Uranus does not follow a simple elliptical orbit, because it is being tugged on by the massive planets Jupiter and Saturn. This had been fully considered in determining how Uranus would be expected to orbit the Sun, but even so there were problems. But which of the proposed solutions is correct? Do we have to abandon or modify Newton's law of gravity, or can it be retained? The simple elegance of the law of gravity, and in particular the fact that it had so neatly explained Kepler's three laws, encouraged astronomers to prefer the second explanation. Surely there must be some perturbing influence -- a new planet, perhaps? -- in the outer parts of the Solar System! But how could one hope to discover it? Your textbook tells the story, too briefly, on page 217. A British astronomer named John Couch Adams, who had demonstrated enormous mathematical powers while studying at the University of Cambridge, did the necessary complex calculations to work out the probable location of the hypothetical eighth planet. Unfortunately, he was unable to persuade the Astronomer Royal, a man named George Airy, to make any real effort to find it. Largely this was because of Airy's rather peculiar personality. Misinterpreting the most inconsequential oversights, he persuaded himself that Adams had terribly insulted him with transgressions of etiquette and 'ungentlemanly behaviour.' In the end, Airy became so hostile that he scarcely made even a token effort to have his staff of astronomers carry out the hunt. Meanwhile, in France, another astronomer named Leverrier had made similar calculations and drawn pretty much the same conclusions as Adams. He was more warmly received, however, and efforts were made right away to carry out the search -- and it was successful! In 1846, a new planet, later to be called Neptune, was discovered exactly where Leverrier and Adams had independently predicted it. Immediately this was announced, Airy had his staff astronomers reconsider Adams's prediction and do the belated observing. Moreover, he then announced that Adams had made the prediction before Leverrier, and that it really represented a British success. You can imagine the fallout, with nasty international squabbles continuing for years thereafter. Consistent with his personality, Airy never took any part of the responsibility for the debacle, but the nice part of the story is that Adams and Leverrier became good friends and held no grudges about the episode. Of course, history correctly records that both men were successful in predicting the existence of Neptune and stimulating the observations which led to its discovery. By the way, Neptune had already been observed telescopically, by no less a personage than Galileo himself, at a time when Neptune lay close to Jupiter on the sky. Because Galileo's telescopes were not of very high quality, he did not record (and presumably did not even notice) that one of the bright 'stars' in the vicinity of Jupiter showed up as a real disk of light, not just a pinpoint. As noted, it was not recognized as a planet until 1846. The long-lasting importance of the prediction and discovery of Neptune was that it seemed to confirm the universal applicability of Newton's law of gravity. The episode served to reassure astronomers that if, at some future time, they were to discover an orbiting object which moved in apparent disagreement with the predictions of Newton's law, then there must have been some overlooked gravitational influence. The law itself seemed beyond reproach and unnecessary of any modification. As we will see in the next section of notes, this comfortable view was incorrect. For the moment, though, let us continue our exploration of the successes, both real and apparent.
Halley and the Comet.The prediction and discovery of Neptune in 1846 does not in fact represent the first new piece of scientific evidence in support of Newton's theory of gravity. More than a century earlier, Edmund Halley had predicted the return of the comet which now bears his name, a prediction which implicitly assumed the trustworthiness of Newton's Law. In what sense did it do so? You will recall that Newton's generalization of Kepler's laws revealed that things orbiting the sun would move in ellipses, but that other orbits were allowed. For example, an object falling in from some remote part of the universe would coast ballistically past the sun on a parabolic or hyperbolic orbit, depending on its energy and speed (assuming that its orbit was not strongly perturbed by the extra gravitational tugs exerted by Jupiter and the other planets). But at the time of Newton, no known solar system object moved on an orbit which was dramatically non-circular. (Even the orbits of Mercury and Mars are fairly circular in appearance.) So there was no astronomical assurance that Newton's laws were indeed correct for orbits of extreme eccentricity. Enter Edmund Halley, a contemporary and supporter of Newton. This man was amazingly accomplished, with a hand in almost every imaginable branch of scientific and social research. Among other things, it was he who persuaded the cantankerous Newton to publish his famous 'Principia,' and he also studied tides, the Earth's magnetic fields, and many other natural phenomena. At some early stage, his attention focussed on the interpretation of comets, and by digging into historical records he realised that there was a striking periodicity for at least one of them. What Halley recognized was that a conspicuous comet had been observed every 76 years, and that on each appearance it was first noticed in the same part of the sky, as though returning along a regular orbit. In fact we now know that the record of reappearances can be traced back into times B.C., more than two thousand years ago! Halley did not have as complete a record as that, but he had enough appearances to persuade him, by the year 1705, that it was the same comet on return visits, and that it was moving along one of the extremely eccentric orbits permitted by Newton's generalised versions of Kepler's laws. Halley was bold enough to make the confident prediction of the next return of the comet in question, in the year 1758. Unfortunately, he did not live to see the prediction borne out. Still, he was quite correct, and his speculations and prediction constituted very strong confirmation of the influence and role of Newtonian gravity in the Solar System.
The Prediction and Discovery of Pluto: An Apparent Success?As decades passed, the orbits of Uranus and Neptune were followed with interest, and attention was drawn to what seemed to be continuing problems: neither planet seemed to be behaving precisely as it should, even accounting for the perturbing effects of Jupiter and the other known planets. Emboldened by the success of Adams and Leverrier, various astronomers ventured to suggest that this implied the existence of yet another planet, a ninth one, beyond the orbit of Neptune. Prominent among these astronomers was Percival Lowell, about whom we shall learn much more when we consider the planet Mars. Lowell was a very wealthy man, from a famous Boston family. His sister was the renowned poet Amy Lowell, and a brother was the President of Harvard University. Percival himself had been the American Ambassador to Korea, and was an erudite man of many interests. Lowell's calculations led him to the firm conviction that there was indeed a ninth planet out there for the discovery. Unfortunately, the numbers suggested that this planet would be rather small, and this circumstance, coupled with its remoteness from the sun, implied that it would be quite faint and thus extremely difficult to detect when seen as a mere dot of light against a myriad of background stars. Still, Lowell was determined to find it. For this reason, and also because of his interest in Mars, he established an observatory in Flagstaff, Arizona. His doing so was a sign of considerable imagination, because he was really the first astronomer to understand the importance of putting a telescope in a location where the observing conditions are first-rate: clear skies, high altitude, little atmospheric turbulence, freedom from city lights, etc. (Before Lowell's time, telescopes were usually put in some 'convenient' location, which meant within easy reach of one's university, for example.) Lowell did not live long enough to celebrate the discovery of the ninth planet, which was found by his assistant Clyde Tombaugh in 1930, after decades of hunting. (The technique, by the way, is to take many photographs of the part of the sky where the target is thought to be found. Intercomparing photographs taken at different times, each with thousands of images of stars, reveals any faint object which is moving.) After some debate, the planet was named Pluto -- an appropriate choice, since it is in the outer inhospitable parts of the Solar System (Pluto was the god of the underworld) and also because the first two letters commemorate P ercival L owell himself. Once again, Newtonian gravity seemed to have been vindicated! The slight irregularities in the orbits of Uranus and Neptune were apparently to be understood in terms of simple applications of the theory of gravity, and had been clear pointers to the existence of the as-yet undiscovered ninth planet. All seemed well.
Serendipity in Astronomy: The Story of Pluto's Moon.Like any science, astronomy has enjoyed moments of real serendipity, by which we mean lucky discoveries or a lucky set of circumstances which lead to an important insight. (You may know of examples of serendipity in other sciences, such as Fleming's accidental discovery of penicillin.) The planet Pluto provides an interesting case in point. Pluto is so far from the Sun and the Earth that even through the best telescopes it appears as little more than a dot of light. Consequently, it is very difficult even to figure out how big it is. As I noted earlier, requires determining what gravitational influence it has on other bodies, preferably a 'test particle' orbiting it or coasting past it. For remote Pluto, this was long thought not to be possible, and estimates of its mass were terribly uncertain. But then came a breakthrough. Astronomers at the U.S. Naval Observatory were examining a set of photographic plates of Pluto when the machine they were using broke down. A repairman was called, but his repairs took much longer than they had expected, so one of the astronomers spent the enforced idle time in looking again in detail at one of the images, using a small magnifying glass. He noted that the image of Pluto looked a bit elongated, and remembered having seen that before. Rather than dismiss this as a small blemish on the photograph, and having nothing better to do, he began to examine other images and soon persuaded himself that he had discovered a barely-resolved moon of Pluto. I think that you will agree that this is mildly serendipitous, but you might want to dismiss the episode as a happy but inconsequential accident. After all, the Hubble Space Telescope would have revealed the moon's existence quite clearly only a few years later (see the figure on page 216). But this is where the really serendipitous nature of the discovery becomes apparent. Charon, the moon of Pluto, orbits in such a way that it occasionally passes between us and Pluto in a series of eclipses. As it does so, it blocks off some of the sunlight which is reflected from the planet, and the way in which the brightness varies tells us a great deal about the size of Pluto and even the patterns of light and dark areas on its surface. (See the figure on page 382.) The remarkable thing is that the moon was discovered in 1978, just a few years before a series of eclipses (1985-1991) which will not be repeated for over a century! The Hubble Space Telescope was not launched until 1990, so would have missed almost the entire series. There is yet more serendipity here. This series of eclipses happened at a time when Pluto was as close to the sun as it ever gets -- indeed, at present Pluto is closer to the sun than Neptune is, although this circumstance will not last long. (See the figure on page 381 of the text.) At such times, Pluto is sufficiently warmed by the sun that some of the frozen material on its surface evaporates to give the planet a temporary atmosphere. As Pluto moves farther away, that atmosphere will re-condense and disappear, so we were lucky to be able to use the eclipses in studying this process, which occurs only once every 248 years! Serendipitous indeed!
Using Gravity in Studying Pluto: A Reconsideration of Its Discovery.As noted, the existence of Pluto's moon allowed a precise determination of its mass. The interesting conclusion is that Pluto is much less massive than had long been thought - only a few percent as massive as Mercury, for instance, and much less massive than all the other planets. It is more like one of the small frozen moons of the outer planets than like a planet itself. Indeed, if Pluto had remained unknown until today, only then to be discovered, it is unlikely that we would classify it as a planet at all. In the last decade or so, we have discovered many objects in the outer Solar System which are like Pluto, and its orbital properties, size, mass, and composition all seem to suggest that it did not originate in the same way as the rest of the planets. Our revised determinations of the mass of Pluto have one further implication. Percival Lowell's calculations, we now realise, were irrelevant. There are no 'problems' with the orbits of Uranus and Neptune, the motions of which are in fact quite in accord with Newton's Law and the known perturbations caused by Jupiter and Saturn. Lowell used a set of imperfect data, spanning a limited range of time, and deduced the existence of a planet which was unnecessary; but he was posthumously rewarded with the discovery of a planet named [in part] after him. This is yet another example of serendipity! - Pluto just happened to be in the right place at the right time. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Wednesday, 21 April, 2021.)