B00B7H7M2E EBOK, page 14
In 1742, Bradley succeeded Halley as Astronomer Royal.
Figure 4.4
The arcsecond originated as an ancient Mesopotamian measurement. A circle has 360 degrees. Each degree can be divided into 60 minutes of arc or ‘arcminutes’. Each minute of arc can be divided into 60 seconds of arc or ‘arcseconds’.
The measurement of an arcsecond isn’t a measurement of true size. If you hold your finger up at arm’s length against the sky, its width covers about two degrees of arc. But this finger held at arm’s length would cover a branch on a nearby tree, the Concorde flying overhead, the entire Moon, or (out of sight with the naked eye) an enormous number of galaxies. Clearly not all objects in the sky that have the ‘angular size’ of two degrees of arc are the same true size. How ‘large’ two degrees of arc are depends upon how deep into space you’re looking. The Moon’s angular size is about half a degree of arc. The Sun’s angular size is approximately the same as the Moon. Yet these two bodies are definitely not the same true size.
In the picture below, each of the circles has the same angular size viewed from Earth, covering the same number of degrees of arc, yet they are not the same true size. (Recall Aristarchus’s study of the Sun and Moon, shown in Figure 1.4.)
One arcsecond is the angular size the width of your finger would have if you were able to hold your finger up about 5,000 feet (1,500 metres) above you.
The 18th century saw a rapid increase in the number of observatories in Europe. Among the sciences, only in medicine were there more people professionally involved in research. Not all of them were peering through telescopes, for the meticulous cataloguing of what others found required many clerical workers. Funding came from governments, universities, scientific bodies, even religious societies – the expense often justified in terms of the practical spin-off for navigation, mapping and surveying, and the prestige such institutions gave to their sponsors.
The educated public loved astronomy and followed it avidly. Travelling lecturers drew large audiences, less technical books were best-sellers, telescopes for amateur use sold well, as did globes. Natural theology – the argument that nature and the harmony of the universe are eloquent proof of the existence of God and tell us what God is like – was preached from many pulpits, given voice in hymns and secular poetry, and favourably discussed in academic circles. Though astronomy had ceased to be a required part of the curriculum in most universities, it was widely considered essential to a proper gentlemanly education.
In England, the Royal Observatory continued to be financed from government coffers, a considerable investment. The Observatory’s demand for equipment as well as the Royal Society’s great interest in the improvement of all scientific instruments, including telescopes, helped support and encourage a healthy local optical industry. The Industrial Revolution, which started in England in the 18th century, brought advances in the design and construction of machines and in precision engineering in general. Astronomy reaped enormous benefits from this progress and also, with the increasing expertise of its instrument-makers and demand for their products, contributed substantially to it. The finest telescopic instruments came from England, and English manufacturers were suppliers to all Europe, setting the standard and style of the profession. Earlier astronomers had often designed and built their own instruments, and some of the more notable among them would continue to do so, but increasingly there began to be a division between those who manufactured telescopes and those who used them. Telescope builders were not necessarily considered a lower breed than practising astronomers. Some were elected to the Royal Society.
In the early 19th century, the Industrial Revolution spread to Europe and the United States. London opticians were still producing reflecting telescopes, the type pioneered by Newton and others in the late 17th century (see Figure 4.5), at affordable prices. English amateurs were making some excellent instruments themselves. However, Britain’s Prime Minister William Pitt and his government dealt London’s optical industry an almost mortal blow by imposing a punitive tax first on windows and a little later on all glass. After Swiss glass-maker Pierre Guinand moved from Switzerland to Munich in 1804, bringing with him a new method of mixing molten glass, Germany took the lead in refining the art of telescope design and manufacture. Bavarian-born Josef von Fraunhofer, who had worked for a time as Guinand’s assistant, greatly improved the refracting telescope (again, see Figure 4.5). Friedrich Wilhelm Bessel pioneered the use of the meridian circle, which made it possible to measure two coordinates of a star at the same time, improving greatly the accuracy of observations, as did advances in the design of astronomical clocks. Mathematician Karl Friedrich Gauss, then only 18 years old, at Göttingen in 1804, invented the method of ‘least squares’ which enabled an astronomer to choose the best observations in a less arbitrary manner.
Figure 4.5
This sketch shows the basic difference between a refracting and a reflecting telescope. There are many varieties of each.
A refracting telescope.
The large lens (object glass) in one end gathers light from the stars and bends or ‘refracts’ it down the length of the tube to focus on a smaller magnifying lens (eyepiece).
A reflecting telescope.
A curved mirror at the bottom end of an empty tube gathers light from the stars and reflects it to focus on a second mirror suspended at the first mirror’s focal point. The second mirror reflects the image to the eyepiece.
It’s possible to make a reflecting telescope much larger than a refracting telescope, because the large mirror can be supported from the back as a lens cannot.
Finally, by the late 1830s, improved technology and theoretical understanding had converged to the extent that it was possible for three astronomers to detect annual stellar parallax. Clearly it was a discovery whose time had come. The three measurements occurred independently but almost simultaneously.
Friedrich Wilhelm Bessel, in Königsburg, Germany, was the first to announce his findings, in 1838. Reasoning that proper motion, rather than brightness, might be the most significant indicator of which stars are nearest, he chose 61 Cygni, a dim star with a large proper motion (5.2 arcseconds a year). (See Figure 4.4.) The figure at which he arrived for its annual parallax was 0.3136 arcseconds. Knowing the distance the Earth had travelled in its orbit in order to produce this displacement allowed him to calculate the distance from the Earth to the star – 3.4 parsecs (11.2 light years) – which is, for comparison, 600,000 times greater than the distance from the Earth to the Sun. Bessel’s measurement was a considerable step up on the cosmic distance ladder.
Meanwhile Thomas Henderson from Scotland, observing from South Africa, chose to study Alpha Centauri. He made his choice on the basis of brightness rather than proper motion. Alpha Centauri is the third brightest star in the night sky. Though Henderson actually measured Alpha Centauri’s parallax before Bessel measured 61 Cygni’s, Henderson didn’t announce his results until he got back to Britain early in 1839 – thus losing out to Bessel in the pages of history. A year later, Friedrich von Struve, born in Germany but working in Tallin (now in Estonia), announced that he had measured the parallax for Alpha Lyrae (aka Vega), the fifth brightest star in the night sky.
The parallaxes measured for all three of these stars were small:
For 61 Cygni, a parallax of 0.3136 arcseconds (see Figure 4.4), a distance from us of 3.4 parsecs (11.2 light years). We now know that 61 Cygni is a double star.
For Alpha Centauri, about 1 arcsecond parallax – a figure later refined to 0.76. The Alpha Centauri star system (for we now know it consists of three stars) is 1.3 parsecs away (4.3 light years). The star that we call Proxima Centauri is one of that trio and at the moment is the solar system’s closest neighbour. It revolves around its mates Centauri A and B every 500,000 years.
For Alpha Lyrae (Vega), a parallax of 0.2613 arcseconds, a distance of 8.3 parsecs (26 light years).
How far away they are! And yet these are some of the nearest stars. With their measurement, it began to sink home how profoundly alone our little solar system community is. After Cassini and Flamsteed it had seemed so huge. Now it became tiny compared to the enormous emptiness we would have to cross to reach anything else beyond. You have to multiply the distance from the Sun to Pluto (the planet furthest from the Sun) by nine thousand to reach Proxima Centauri – the next break in the darkness.
The successful measurement of the distance to the nearest stars strengthened an impression that had existed since the 18th century that ‘celestial mechanics’, the marriage of mathematics and astronomy, was the highest of all the sciences and the most valuable for deepening human understanding of the laws of nature. Another achievement crowned this reputation even more spectacularly. Soon after Bessel, Henderson and von Struve’s measurements, Urbain Jean Joseph Leverrier, who was the virtual dictator of the Royal Observatory in Paris and scorned and discouraged any intellectual pursuit that wasn’t celestial mechanics, studied the orbit of the planet Uranus. He came to the conclusion that certain mysterious irregularities in the orbit that do not accord with Newton’s laws must be caused by the gravitational pull of another undiscovered planet. On 23 September 1846, Johann Gottfried Galle at the Berlin Observatory, looking for that unknown planet where Leverrier had predicted it should be, and working with records kept by British astronomer John Couch Adams, discovered Neptune. Leverrier’s prediction had been astoundingly close to right – quite by coincidence, actually, for he had not chosen correctly among several possible solutions for the orbit. The discovery was a public sensation. A miracle! Indeed, more of a miracle than the public knew, given Leverrier’s wrong choice.
At mid-century, astronomy and celestial mechanics did indeed seem to be moving from triumph to triumph. They had also suffered one setback, for knowing the distances to a few stars gave astronomers a way to calculate their absolute magnitudes and erased forever any hope that the absolute magnitude of all stars is the same. The elephants on the plain came in a variety of sizes, and we could measure directly the distance to only a few of them. How could we possibly judge the size or distance of the others?
One way to approach the problem would be to take another look at this category we’ve been calling ‘elephant’ and see whether we can break it down. Maybe there are Indian elephants and African elephants, and some way to tell them apart. If all elephants aren’t the same size, perhaps all Indian elephants are.
The trick would be to find characteristics that (unlike apparent size) won’t change with distance, such as distinctive ears. We could call these strange-eared animals Group A elephants. Suppose we do have a way of measuring the actual distance to a few of the Group A elephants and having done so discover that their size doesn’t vary greatly. It seems fairly safe to assume that those Group A elephants too far away for direct measurement are also that size. With that assumption, we can take the exercise further. If another animal is standing near a Group A elephant in the distance, drinking from the same waterhole, we can judge the size of that second animal by comparing it to the elephant. Suppose the second animal is spotted and has an extraordinarily long neck. We name it a giraffe. Now if we go on watching elephants and giraffes out there and conclude that all giraffes are about the same size, we have a potential way of calculating the distance to any other animal that shares giraffe characteristics. One measurement builds on another. Of course if there is a mistake somewhere along the line – maybe Group A elephants come in two sizes, or maybe the animal we think is near the elephant is actually fifty feet beyond it – then the whole measurement structure begins to collapse and has to be recalibrated.
Even before the first stellar parallax measurements, astronomers had begun to hope that, upon closer scrutiny, stars would turn out to have different characteristics that would allow them to be grouped into categories or ‘families’. If stars don’t all share the same absolute magnitude, perhaps those within certain recognizable ‘families’ do.
There had been some developments that would lead to a better understanding of stars. At the beginning of the 19th century, it had been generally assumed that it would never be possible to discover the chemical composition of stars or their physical make-up, because researchers couldn’t get near enough to examine them. The French philosopher Auguste Comte pointed to the chemical composition of stars as an example of ‘unobtainable knowledge’. Not everyone shared this pessimism. Researchers were soon to find that starlight carries with it an enormous amount of information about its source, if you can crack the code.
Since Isaac Newton’s study of optics, scientists and the general public had known how to use a glass prism to break a ray of light into its component parts. When white light passes through the prism, the colours of which the light is composed spread out in an ordered sequence – the spectrum – the familiar rainbow. The order is always the same: red, orange, yellow, green, blue, indigo and violet. The acronym for that is ‘Roy G. Biv’.
We refer to position in the spectrum by colours (‘the red end of the spectrum’ or ‘the violet end of the spectrum’), or more precisely by wavelengths, because each colour is produced by a different wavelength of light. The longer waves are the red. The waves grow shorter as we move across the spectrum to violet. See Figure 4.6.
Figure 4.6 The Electromagnetic Spectrum
Light that human eyes can see – the visible spectrum – is only a small part of the much larger ‘electromagnetic spectrum’. What is out beyond red on the one hand and violet on the other is invisible to us, but there is a great deal out there – infrared light, ultraviolet light, gamma rays, X-rays and radio waves, all of them forms of electromagnetic radiation, with wavelengths either too short or too long to be within the visible spectrum.
When light passes through a prism, the resulting spectrum gives us information about the light source, even when that source is billions of light years away.
An incandescent, solid light-source radiates all colours, and the spectrum is continuous from violet to red (and beyond the visible spectrum in either direction).
An incandescent gas radiates only a few isolated colours and each different kind of gas has its own pattern, called an emission spectrum.
When an incandescent solid (or its equivalent) is surrounded by a cooler gas, the result is a spectrum in which a continuous background (such as the spectrum an incandescent solid would produce) is interrupted by dark spaces – called ‘absorption lines’. See Figure 4.7. In this case the gas surrounding the original light source has absorbed from that light those colours which the gas would radiate itself. By looking at the pattern of the absorption lines and noting where they fall within the spectrum, it’s possible to discern which gas or gases are responsible for the absorption.
Much of our understanding of light and spectra stems from the pioneering work of Josef von Fraunhofer, born in Staubing, Bavaria, in 1787. Von Fraunhofer was the eleventh and youngest child of a master glazier and worker in decorative glass. Orphaned at 12, he became the apprentice of a mirror-maker and glass-cutter in Munich who paid him nothing, offered minimal instruction, and made it impossible for him to attend the Sunday Holiday School which offered apprentices a little schooling outside their trade. Fraunhofer’s luck turned for the better when he was 14 and his master’s house collapsed, burying the boy in the ruins. His escape – he was injured but protected from death by a crossbeam – became a news item in Munich and reached the ears of the Elector Maximilian. Maximilian, touched, gave young Fraunhofer some money which he used wisely, purchasing a little equipment for himself and buying out of his apprenticeship. He had to return only temporarily when his own business (engraving visiting cards) failed to support him. Fraunhofer’s miraculous survival in the collapsing house also drew the attention of a wealthy Munich lawyer and financier named Utzschneider, who soon hired Fraunhofer to work at his glass-making establishment. Such was Fraunhofer’s innate ability and zeal for his craft that when he was in his early twenties Utzschneider had already put him in sole charge of the glassworks.
Figure 4.7 Absorption Spectra
When an incandescent solid is surrounded by a cooler gas, the result is a spectrum in which a continuous background is interrupted by dark spaces – called ‘absorption lines’ – that occur because the gas has absorbed from the light those colours which the gas would radiate itself.
Fraunhofer was one of a handful of men in the early 19th century who rose from working-class backgrounds to become leaders in astronomy. In a short lifetime, he designed and built increasingly fine telescopes, among the best in the world at that time, and he was responsible for a number of inventions that made their use more effective. Bessel and von Struve were using Fraunhofer telescopes when they first measured stellar parallax.
Fraunhofer’s discoveries about light led to some of the most significant developments of the 19th and 20th centuries, making him one of the most important figures in the history of optics. He was the first to study and map the absorption lines of the Sun’s spectrum.
