B00B7H7M2E EBOK, page 13
Here at last in this simple description were the dynamics that cause the planets to move as they do rather than in some other way, the physical reasons behind Kepler’s laws. The answer that eluded Ptolemy, Copernicus, Galileo and Kepler – but to which Kepler’s laws point – was summed up in one sentence: the gravitational force between any two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. It took Newton’s genius to see that it is this same force – gravity – that keeps us from flying off the ground, dictates the path of a ball thrown on the Earth, underlies the motions of the planets, and governed the way Galileo’s two objects landed at the foot of the Tower of Pisa (if they did).
Newton’s ‘laws of motion’ could be tested by experiments as well as by astronomical observations, and this was an era that rejoiced in such testing. The scientific rigour that had made Galileo exceptional was beginning to be considered essential for any scientific activity. It became clear that Newton’s formulae did indeed describe the way things happen. Nature was law-abiding and she was following these laws! It’s difficult for us, who take for granted that science is able to predict reality and that simple, dependable mathematical and scientific rules underlie the apparent complications of nature, to appreciate how awe-inspiring it must have been for the many men and women who were realizing this in the 17th century for the first time. Not only did such laws exist, but human minds could discover them and understand them. The concept was not a complete novelty to scientists, although to see it demonstrated as beautifully as it was in Newton’s Principia was a novelty. To the non-scientific public Newton’s revelation was sensational, miraculous. The fame of his book spread quickly throughout Europe, and his ideas were popularized in many forms. There was a publication called Newton for Ladies in France. Principia did encounter some hostility on philosophical grounds, uneasiness with the notion that gravitation could act through empty space. ‘Action at a distance’ suggested the occult.
Newton’s attempt to estimate the distances to the nearest stars by assuming that all stars, including the Sun, have approximately the same brightness, is one of his less celebrated efforts. In the analogy with the elephants, you and I assumed that all elephants are about the same size, but suppose we had seen only one elephant close up. It would be risky to jump to the conclusion that all elephants are the same size – that our local elephant is a typical elephant – based on such limited experience. The difference in apparent size between the local elephant and other elephants whose distance we don’t know might actually be due to differences in size, not an indication of their distance at all. Newton’s situation was even more ambiguous than that. Elephants look pretty much alike, but the Sun, as seen from Earth, doesn’t resemble the other stars. Most experts in Newton’s time did think that the Sun was a star. But was it a typical star? It wasn’t unreasonable to decide to assume that it was, and see where that would lead.
Newton did that in an ingenious but rather convoluted way, using a technique suggested by Scottish mathematician and astronomer, James Gregory. Judging by the size of Saturn, Newton estimated that about one part in a billion of the Sun’s light hits the planet Saturn. He reasoned that Saturn doesn’t reflect all of the sunlight that hits it – so it would be incorrect to conclude that the light we see coming from Saturn represents one billionth of the Sun’s light. Instead, he thought that Saturn probably reflects only about a quarter of the Sun’s light that hits it, which would mean that the reflected sunlight coming from Saturn gives us a good indication of what one part in four billion of the Sun’s light looks like. Following this line of thought, if a distant star seems to have the same brightness as Saturn, it follows that the light we are receiving from that star (not reflected sunlight; the star’s own light) is also equivalent to one part in four billion of the Sun’s light. What this means – if all stars’ brightnesses are the same as the Sun’s – is that a star that looks (from Earth) as bright as Saturn would have to be approximately a hundred thousand times further away from us than the Sun is.
Newton’s measurements of the distances to some of the nearest stars were not far wide of the mark, though this method was not dependable partly because stars do differ in their absolute magnitude (their ‘close-up’ brightness), and a star’s apparent magnitude (how bright it appears from Earth) alone can’t be used as a gauge of its distance. (See box below.) Some of the stars that look brightest in the night sky are very far away, while many nearer stars are rather inconspicuous.
In 1718, Newton’s younger friend Edmund Halley discovered an important new clue to star distances. He had become fascinated with Ptolemy’s writings and the star catalogues that ancient astronomer had compiled. Halley was particularly curious as to whether the stars had changed positions since the time of Hipparchus and Ptolemy. He took it upon himself to compare positions recorded in Ptolemy’s Almagest with positions in his own lifetime in the late 17th and early 18th century.
Halley was born in 1656 and while still an undergraduate at Oxford wrote and published a book on Kepler’s laws. His book came to the attention of Flamsteed, who had a great deal of influence as the first Astronomer Royal of England (though the position wasn’t called that yet) and first head of the Royal Observatory at Greenwich. Halley left Oxford without getting his degree and, at Flamsteed’s behest, was soon on the island of St Helena in the South Atlantic, mapping the sky as seen from the southern hemisphere. When he returned to England two years later he was elected to the Royal Society. He was only 22.
Even more eclectic in his interests than Newton, Halley spent the next 30 years in an astounding variety of pursuits. He travelled extensively to meet other scientists and astronomers; he assisted Flamsteed; he got married; he commanded a warship in the Royal Navy and captained a mutinous ship across the Atlantic; he went to Vienna on two secret diplomatic missions; he served as deputy to the controller of the Mint at Chester (a position Newton helped secure for him); he studied magnetism and the winds and tides; he prevailed upon Newton to publish the Principia, and he financed its publication. Of course the work which brought him most fame was his study of comets. ‘Halley’s Comet’ was named after him when it reappeared in 1758, after his death, at the time he had predicted. In 1703, Halley joined the faculty of the University of Oxford, where he had failed to complete his degree, as Galileo had done at the University of Pisa.
In 1718, Halley reported that three of the stars he was studying – Sirius, Arcturus and Aldebaran – had shifted over the centuries since Ptolemy. He strongly suspected that the discrepancies between the old charts and those of his own time were too large and too isolated to be attributed to errors in ancient measurement. Why should early astronomers have got everything else right but this? As a follow-up, Halley proceeded to measure the shift of Sirius during the 100 years since Tycho Brahe had observed it, a measurement that confirmed his suspicions. The change had been so gradual that it could only be noticed over a span of at least several human generations.
‘Proper motion’ is the name given to this movement of stars relative to one another over the centuries – an apparent movement across the sky when viewed from the Earth. Most stars are not moving only side-to-side, of course, as though the sky were a two-dimensional surface; they are likely at the same time to be getting closer to us or further away.
In 1720, at the age of 64, Halley succeeded Flamsteed as Astronomer Royal of England, which would not have pleased Flamsteed, for Halley had acquiesced in Newton’s poor treatment of the old man. It probably would have pleased Flamsteed that his widow whisked all the instruments out of the Royal Observatory. They were legally hers because the financial arrangement at the Observatory was such that the Astronomer Royal purchased equipment out of his salary. Halley had to set to work acquiring new equipment.
Edmund Halley died in 1742 at the age of 85. One of his most significant achievements didn’t come to fruition until nearly 20 years later.
When Halley had been on St Helena in his early twenties he had seen and timed a transit of Mercury across the Sun. He was the first man ever to observe both Mercury’s first entry on to the Sun’s disc and its final exit. Halley knew of a suggestion from James Gregory that a transit would provide an opportunity to use parallax in a new way to measure distances in the solar system. The passage of a planet across the Sun shows up as a tiny black dot passing across the Sun’s face, and observers at different locations on the Earth’s surface see the planet first touch the Sun’s disc at different times.
Halley put little faith in earlier measurements of the Sun’s and the planets’ parallaxes and distances, including those of Cassini and Flamsteed, although his friend Newton came to agree with them. Newton also measured the orbits and the distances of the planets from the Sun, using not astronomical observations but the dynamics of the system as the basis for his calculation. He concluded that Cassini’s and Flamsteed’s results were better than his own. But as of 1700, the only real agreement among astronomers when it came to the Sun’s distance was that it was at least 55 million miles away. Halley was convinced that the transit of Venus would be a chance to make much more definitive measurements.
A transit is a relatively rare event, but Halley knew there would be a transit of Venus across the Sun in 1761. He also knew he wouldn’t be alive to witness it unless he lived to be 105. So he wrote and published detailed instructions on the best way to use observations of the transit from different parts of the world.
Sixteen years after Halley’s death, with the return of the comet he’d seen in 1682, his name became a household word. In 1761 there was indeed considerable effort, much due to his prestige, to study the transit of Venus, and similar excitement about a second transit in 1769. Both times, the globe was studded with observing parties, who knew the opportunity wouldn’t be repeated again until 1874. There are colourful stories connected with this venture which indicate that many astronomers at the time were less denizens of the ivory tower cum telescope than they were prototypes of Indiana Jones.
Frenchman Guillaume le Gentil planned to observe the 1761 transit from Pondicherry, near Madras in India. He arrived to find the town occupied by British forces. This was during the Seven Years War, England and France were enemies, and le Gentil was not welcome in Pondicherry. Rather than turn around and head for home, he settled nearby for eight years, supporting himself in part by trading while he waited for the next transit. By then the British had ceased to be an obstacle, but nature had no mercy on le Gentil. The Sun shone brightly before and after the transit. During the transit, alas, it was hidden by a cloud.
Jean d’Auteroche led another French observing team in Russia in 1761, and in what is now southern California in 1769. The party of four astronomers trekked overland across Mexico to reach their California observing location. D’Auteroche and two of the others died of disease shortly after their arrival. That left the fourth to undertake the treacherous return journey alone, but he brought back with him the dearly bought records of the observation.
The Reverend Nevil Maskelyne, sent by the Royal Society to St Helena to observe the 1761 transit, had a much better time of it. Maskelyne’s expenditures were in the neighbourhood of £292, out of which £141 went on his personal liquor supply.
David Rittenhouse, in America, worked for months before the 1769 transit building a temporary log observatory at Norriton, near Philadelphia. He used a collection of instruments there that included telescopes from Europe and others he had built himself, and also his own eight-day clock that ‘does not stop when wound up, beats dead seconds, and is kept in motion by a weight of five pounds’.
Charles Mason and Jeremiah Dixon, who would later establish the Mason-Dixon Line in North America, headed up another team sponsored by the Royal Society. That august body threatened them with disgrace and possible legal action if they failed to continue with their expedition to the Cape of Good Hope to observe the 1761 transit, after a French frigate attacked their ship in the English Channel and 11 crew members died. Evidently the captain of the French frigate had been unaware that in spite of the ongoing Seven Years War, Englishmen and Frenchmen were collaborating in this scientific endeavour.
Maximilian Hell, a Viennese Jesuit astronomer, observed the 1769 transit from Norway and suffered devastating damage to his reputation when Jerome Lalande insinuated that Hell had fiddled his observations to make them consistent with those reported by others. Karl von Littrow supported Lalande’s allegation, claiming to have found proof in the form of different ink colours in Hell’s report. Hell’s good name wasn’t restored until 1883, after there had been another transit. Among other things, it was discovered that von Littrow had been colour blind.
Sadly, the results of all this effort were less definitive than Halley and these astronomers had hoped. Precise determination of the instant the planet touched the Sun’s disc was much more difficult than anticipated. Because of the Sun’s corona and the atmosphere of Venus, Venus’s image at the beginning and end of the transit was blurry. Calculations based on the results of these observations put the distance from the Earth to the Sun at about 95 million miles or 153 million kilometres, as compared with Cassini’s measurement in 1672 of 87 million miles or 140 million kilometres, and our modern measurement of 93 million miles or 149.5 million kilometres.
Halley’s discovery of proper motion was also destined to bear fruit far beyond his lifetime. It so happens that the three stars whose proper motion he first measured – Sirius, Arcturus and Aldebaran – are some of the brightest in the sky. Was this mere coincidence? A star might look brighter than others because it really is brighter, or it might look brighter because it is closer. Halley’s discovery of proper motion gave astronomers a new clue.
Objects moving across our line of vision close to us appear to move more rapidly against the background than those further away. A child on a tricycle near us can easily outrace a car driving at a good clip off on the horizon. Logic tells us that the same will be true with stars that are moving across our line of vision. Unless stars are all the same distance, we ought to find the nearer stars appearing to move against a background of more distant stars. Most stars, in fact the vast majority of them, show no change of position since Ptolemy for a viewer on the Earth. Does that mean they are far more distant than those that have changed position?
Sixty-six years after Halley’s discovery, astronomer William Herschel, the discoverer of the planet Uranus, studied the proper motions of a number of stars and the way those proper motions relate to one another, and from that he was able to plot the Sun’s motion through our part of the Galaxy. Still later, the German astronomer Friedrich Wilhelm Bessel, suspecting that proper motion, rather than brightness, might be the most significant indicator of which stars are nearest us, used it as a basis for choosing which stars to try to measure with the parallax method.
The stellar parallax shift (see box above) that ancient Greek and Hellenistic astronomers could not find does exist, just as astronomers around 1700 were sure it must. Stars do have a parallax shift produced by the Earth’s yearly journey around the Sun. But the shift is extremely tiny and difficult to detect. Certainly it isn’t possible to see it with the naked eye, so the astronomers in antiquity can’t be blamed for missing it. Telescopes of Galileo’s and Cassini’s time weren’t refined enough to reveal it either.
One man who attempted to detect stellar parallax – making other important discoveries in the process – was James Bradley, born in England in 1693. The star Gamma Draconis passes almost directly overhead in London, and Bradley and his friend Samuel Molyneux, a wealthy amateur astronomer, decided to try to measure its parallax motion. They attached a 24-foot-long telescope to a stack of brick chimneys on the building where Molyneux was living. By using a screw, they could adjust the telescope to keep it tilted towards the star. The result was puzzling. Instead of having to adjust the tilt most in December and June, as they had expected, the adjustment was most extreme in March and September and was so large that, even if it had occurred at the right time of year, it was highly unlikely to be caused by parallax. Bradley took advantage of an exceptionally understanding aunt, who allowed him to cut holes in her roof and floors and install a larger and more sophisticated telescope. Observations with this instrument only repeated his and Molyneux’s earlier baffling findings.
The explanation dawned on Bradley, so the story goes, while he was taking a cruise on the Thames. When the boat changed direction, a weathervane on the mast shifted. It wasn’t the wind direction that had changed, however. It was the boat’s direction in relation to the direction from which the wind was blowing. Bradley realized that the displacement of the stars he was studying was similarly caused by the changing motion of the Earth. Just as the wind direction seemed to shift according to the direction the boat was moving, so starlight seemed to shift according to the direction of the Earth’s motion.
Bradley knew he had not found stellar parallax. What his observations demonstrated was that the Earth orbits the Sun and the speed of light is not infinite, both of which were already well accepted. Bradley named the effect he had found ‘aberration’ and announced the discovery to the Royal Society in 1729. Aberration produces a 20½ arcsecond shift (see Figure 4.4) in the apparent positions of stars over a year. Bradley also found that the Earth wobbles due to the fact that its shape is not perfectly spherical, and he gave the wobble the name ‘nutation’. Aberration and nutation were not what Bradley had set out to find; but these discoveries were actually helpful steps on the road to discovering the tiny displacement of true annual stellar parallax. In any search for annual stellar parallax, one needed to take into account these other reasons why the positions of stars change with the seasons. The negative side of Bradley’s discoveries was even more significant. He had shown that the parallaxes of stars could not be more than one second of arc. Had they been as large as one arcsecond, he knew he would have been able to detect them. This meant stars were much further away than was generally supposed.
