Astronomy

Adams, Fred and Greg Laughlin. The Five Ages of the Universe. New York: The Free Press, 1999. ISBN 0-684-85422-8.

April 2001 

Aratus of Soli. Phænomena. Edited, with introduction, translation, and commentary by Douglas Kidd. Cambridge: Cambridge University Press, [c. 275 B.C.] 1997. ISBN 0-521-58230-X.

September 2001 

Bjornson, Adrian. A Universe that We Can Believe. Woburn, Massachusetts: Addison Press, 2000. ISBN 0-9703231-0-7.

December 2001 

Carter, Bill and Merri Sue Carter. Latitude. Annapolis: Naval Institute Press, 2002. ISBN 1-55750-016-9.

Although I bought this book from Amazon, recently it's shown there as “out of stock”; you may want to order it directly from the publisher. Naturally, you'll also want to read Dava Sobel's 1995 Longitude, which I read before I began keeping this list.

March 2003 

Ekers, Ronald D. et al., eds. SETI 2020. Mountain View, CA: SETI Institute, 2002. ISBN 0-9666335-3-9.

March 2003 

Florence, Ronald. The Perfect Machine. New York: Harper Perennial, 1994. ISBN 978-0-06-092670-0.

George Ellery Hale was the son of a wealthy architect and engineer who made his fortune installing passenger elevators in the skyscrapers which began to define the skyline of Chicago as it rebuilt from the great fire of 1871. From early in his life, the young Hale was fascinated by astronomy, building his own telescope at age 14. Later he would study astronomy at MIT, the Harvard College Observatory, and in Berlin. Solar astronomy was his first interest, and he invented new instruments for observing the Sun and discovered the magnetic fields associated with sunspots.

His work led him into an academic career, culminating in his appointment as a full professor at the University of Chicago in 1897. He was co-founder and first editor of the Astrophysical Journal, published continuously since 1895. Hale's greatest goal was to move astronomy from its largely dry concentration on cataloguing stars and measuring planetary positions into the new science of astrophysics: using observational techniques such as spectroscopy to study the composition of stars and nebulæ and, by comparing them, begin to deduce their origin, evolution, and the mechanisms that made them shine. His own work on solar astronomy pointed the way to this, but the Sun was just one star. Imagine how much more could be learned when the Sun was compared in detail to the myriad stars visible through a telescope.

But observing the spectra of stars was a light-hungry process, especially with the insensitive photographic material available around the turn of the 20th century. Obtaining the spectrum of all but a few of the brightest stars would require exposure times so long they would exceed the endurance of observers to operate the small telescopes which then predominated, over multiple nights. Thus, Hale became interested in larger telescopes, and the quest for ever more light from the distant universe would occupy him for the rest of his life.

First, he promoted the construction of a 40 inch (102 cm) refractor telescope, accessible from Chicago at a dark sky site in Wisconsin. At the epoch, universities, government, and private foundations did not fund such instruments. Hale persuaded Chicago streetcar baron Charles T. Yerkes to pick up the tab, and Yerkes Observatory was born. Its 40 inch refractor remains the largest telescope of that kind used for astronomy to this day.

There are two principal types of astronomical telescopes. A refracting telescope has a convex lens at one end of a tube, which focuses incoming light to an eyepiece or photographic plate at the other end. A reflecting telescope has a concave mirror at the bottom of the tube, the top end of which is open. Light enters the tube and falls upon the mirror, which reflects and focuses it upward, where it can be picked off by another mirror, directly focused on a sensor, or bounced back down through a hole in the main mirror. There are a multitude of variations in the design of both types of telescopes, but the fundamental principles of refraction and reflection remain the same.

Refractors have the advantages of simplicity, a sealed tube assembly which keeps out dust and moisture and excludes air currents which might distort the image but, because light passes through the lens, must use clear glass free of bubbles, strain lines, or other irregularities that might interfere with forming a perfect focus. Further, refractors tend to focus different colours of light at different distances. This makes them less suitable for use in spectroscopy. Colour performance can be improved by making lenses of two or more different kinds of glass (an achromatic or apochromatic design), but this further increases the complexity, difficulty, and cost of manufacturing the lens. At the time of the construction of the Yerkes refractor, it was believed the limit had been reached for the refractor design and, indeed, no larger astronomical refractor has been built since.

In a reflector, the mirror (usually made of glass or some glass-like substance) serves only to support an extremely thin (on the order of a thousand atoms) layer of reflective material (originally silver, but now usually aluminium). The light never passes through the glass at all, so as long as it is sufficiently uniform to take on and hold the desired shape, and free of imperfections (such as cracks or bubbles) that would make the reflecting surface rough, the optical qualities of the glass don't matter at all. Best of all, a mirror reflects all colours of light in precisely the same way, so it is ideal for spectrometry (and, later, colour photography).

With the Yerkes refractor in operation, it was natural that Hale would turn to a reflector in his quest for ever more light. He persuaded his father to put up the money to order a 60 inch (1.5 metre) glass disc from France, and, when it arrived months later, set one of his co-workers at Yerkes, George W. Ritchey, to begin grinding the disc into a mirror. All of this was on speculation: there were no funds to build a telescope, an observatory to house it, nor to acquire a site for the observatory. The persistent and persuasive Hale approached the recently-founded Carnegie Institution, and eventually secured grants to build the telescope and observatory on Mount Wilson in California, along with an optical laboratory in nearby Pasadena. Components for the telescope had to be carried up the crude trail to the top of the mountain on the backs of mules, donkeys, or men until a new road allowing the use of tractors was built. In 1908 the sixty inch telescope began operation, and its optics and mechanics performed superbly. Astronomers could see much deeper into the heavens. But still, Hale was not satisfied.

Even before the sixty inch entered service, he approached John D. Hooker, a Los Angeles hardware merchant, for seed money to fund the casting of a mirror blank for an 84 inch telescope, requesting US$ 25,000 (around US$ 600,000 today). Discussing the project, Hooker and Hale agreed not to settle for 84, but rather to go for 100 inches (2.5 metres). Hooker pledged US$ 45,000 to the project, with Hale promising the telescope would be the largest in the world and bear Hooker's name. Once again, an order for the disc was placed with the Saint-Gobain glassworks in France, the only one with experience in such large glass castings. Problems began almost immediately. Saint-Gobain did not have the capacity to melt the quantity of glass required (four and a half tons) all at once: they would have to fill the mould in three successive pours. A massive piece of cast glass (101 inches in diameter and 13 inches thick) cannot simply be allowed to cool naturally after being poured. If that were to occur, shrinkage of the outer parts of the disc as it cooled while the inside still remained hot would almost certainly cause the disc to fracture and, even if it didn't, would create strains within the disc that would render it incapable of holding the precise figure (curvature) required by the mirror. Instead, the disc must be placed in an annealing oven, where the temperature is reduced slowly over a period of time, allowing the internal stresses to be released. So massive was the 100 inch disc that it took a full year to anneal.

When the disc finally arrived in Pasadena, Hale and Ritchey were dismayed by what they saw, There were sheets of bubbles between the three layers of poured glass, indicating they had not fused. There was evidence the process of annealing had caused the internal structure of the glass to begin to break down. It seemed unlikely a suitable mirror could be made from the disc. After extended negotiations, Saint-Gobain decided to try again, casting a replacement disc at no additional cost. Months later, they reported the second disc had broken during annealing, and it was likely no better disc could be produced. Hale decided to proceed with the original disc. Patiently, he made the case to the Carnegie Institution to fund the telescope and observatory on Mount Wilson. It would not be until November 1917, eleven years after the order was placed for the first disc, that the mirror was completed, installed in the massive new telescope, and ready for astronomers to gaze through the eyepiece for the first time. The telescope was aimed at brilliant Jupiter.

Observers were horrified. Rather than a sharp image, Jupiter was smeared out over multiple overlapping images, as if multiple mirrors had been poorly aimed into the eyepiece. Although the mirror had tested to specification in the optical shop, when placed in the telescope and aimed at the sky, it appeared to be useless for astronomical work. Recalling that the temperature had fallen rapidly from day to night, the observers adjourned until three in the morning in the hope that as the mirror continued to cool down to the nighttime temperature, it would perform better. Indeed, in the early morning hours, the images were superb. The mirror, made of ordinary plate glass, was subject to thermal expansion as its temperature changed. It was later determined that the massive disc took twenty-four hours to cool ten degrees Celsius. Rapid changes in temperature on the mountain could cause the mirror to misbehave until its temperature stabilised. Observers would have to cope with its temperamental nature throughout the decades it served astronomical research.

As the 1920s progressed, driven in large part by work done on the 100 inch Hooker telescope on Mount Wilson, astronomical research became increasingly focused on the “nebulæ”, many of which the great telescope had revealed were “island universes”, equal in size to our own Milky Way and immensely distant. Many were so far away and faint that they appeared as only the barest smudges of light even in long exposures through the 100 inch. Clearly, a larger telescope was in order. As always, Hale was interested in the challenge. As early as 1921, he had requested a preliminary design for a three hundred inch (7.6 metre) instrument. Even based on early sketches, it was clear the magnitude of the project would surpass any scientific instrument previously contemplated: estimates came to around US$ 12 million (US$ 165 million today). This was before the era of “big science”. In the mid 1920s, when Hale produced this estimate, one of the most prestigious scientific institutions in the world, the Cavendish Laboratory at Cambridge, had an annual research budget of less than £ 1000 (around US$ 66,500 today). Sums in the millions and academic science simply didn't fit into the same mind, unless it happened to be that of George Ellery Hale. Using his connections, he approached people involved with foundations endowed by the Rockefeller fortune. Rockefeller and Carnegie were competitors in philanthropy: perhaps a Rockefeller institution might be interested in outdoing the renown Carnegie had obtained by funding the largest telescope in the world. Slowly, and with an informality which seems unimaginable today, Hale negotiated with the Rockefeller foundation, with the brash new university in Pasadena which now called itself Caltech, and with a prickly Carnegie foundation who saw the new telescope as trying to poach its painfully-assembled technical and scientific staff on Mount Wilson. By mid-1928 a deal was in hand: a Rockefeller grant for US$ 6 million (US$ 85 million today) to design and build a 200 inch (5 metre) telescope. Caltech was to raise the funds for an endowment to maintain and operate the instrument once it was completed. Big science had arrived.

In discussions with the Rockefeller foundation, Hale had agreed on a 200 inch aperture, deciding the leap to an instrument three times the size of the largest existing telescope and the budget that would require was too great. Even so, there were tremendous technical challenges to be overcome. The 100 inch demonstrated that plate glass had reached or exceeded its limits. The problems of distortion due to temperature changes only increase with the size of a mirror, and while the 100 inch was difficult to cope with, a 200 inch would be unusable, even if it could be somehow cast and annealed (with the latter process probably taking several years). Two promising alternatives were fused quartz and Pyrex borosilicate glass. Fused quartz has hardly any thermal expansion at all. Pyrex has about three times greater expansion than quartz, but still far less than plate glass.

Hale contracted with General Electric Company to produce a series of mirror blanks from fused quartz. GE's legendary inventor Elihu Thomson, second only in reputation to Thomas Edison, agreed to undertake the project. Troubles began almost immediately. Every attempt to get rid of bubbles in quartz, which was still very viscous even at extreme temperatures, failed. A new process, which involved spraying the surface of cast discs with silica passed through an oxy-hydrogen torch was developed. It required machinery which, in operation, seemed to surpass visions of hellfire. To build up the coating on a 200 inch disc would require enough hydrogen to fill two Graf Zeppelins. And still, not a single suitable smaller disc had been produced from fused quartz.

In October 1929, just a year after the public announcement of the 200 inch telescope project, the U.S. stock market crashed and the economy began to slow into the great depression. Fortunately, the Rockefeller foundation invested very conservatively, and lost little in the market chaos, so the grant for the telescope project remained secure. The deepening depression and the accompanying deflation was a benefit to the effort because raw material and manufactured goods prices fell in terms of the grant's dollars, and industrial companies which might not have been interested in a one-off job like the telescope were hungry for any work that would help them meet their payroll and keep their workforce employed.

In 1931, after three years of failures, expenditures billed at manufacturing cost by GE which had consumed more than one tenth the entire budget of the project, and estimates far beyond that for the final mirror, Hale and the project directors decided to pull the plug on GE and fused quartz. Turning to the alternative of Pyrex, Corning glassworks bid between US$ 150,000 and 300,000 for the main disc and five smaller auxiliary discs. Pyrex was already in production at industrial scale and used to make household goods and laboratory glassware in the millions, so Corning foresaw few problems casting the telescope discs. Scaling things up is never a simple process, however, and Corning encountered problems with failures in the moulds, glass contamination, and even a flood during the annealing process before the big disc was ready for delivery.

Getting it from the factory in New York to the optical shop in California was an epic event and media circus. Schools let out so students could go down to the railroad tracks and watch the “giant eye” on its special train make its way across the country. On April 10, 1936, the disc arrived at the optical shop and work began to turn it into a mirror.

With the disc in hand, work on the telescope structure and observatory could begin in earnest. After an extended period of investigation, Palomar Mountain had been selected as the site for the great telescope. A rustic construction camp was built to begin preliminary work. Meanwhile, Westinghouse began to fabricate components of the telescope mounting, which would include the largest bearing ever manufactured.

But everything depended on the mirror. Without it, there would be no telescope, and things were not going well in the optical shop. As the disc was ground flat preliminary to being shaped into the mirror profile, flaws continued to appear on its surface. None of the earlier smaller discs had contained such defects. Could it be possible that, eight years into the project, the disc would be found defective and everything would have to start over? The analysis concluded that the glass had become contaminated as it was poured, and that the deeper the mirror was ground down the fewer flaws would be discovered. There was nothing to do but hope for the best and begin.

Few jobs demand the patience of the optical craftsman. The great disc was not ready for its first optical test until September 1938. Then began a process of polishing and figuring, with weekly tests of the mirror. In August 1941, the mirror was judged to have the proper focal length and spherical profile. But the mirror needed to be a parabola, not a sphere, so this was just the start of an even more exacting process of deepening the curve. In January 1942, the mirror reached the desired parabola to within one wavelength of light. But it needed to be much better than that. The U.S. was now at war. The uncompleted mirror was packed away “for the duration”. The optical shop turned to war work.

In December 1945, work resumed on the mirror. In October 1947, it was pronounced finished and ready to install in the telescope. Eleven and a half years had elapsed since the grinding machine started to work on the disc. Shipping the mirror from Pasadena to the mountain was another epic journey, this time by highway. Finally, all the pieces were in place. Now the hard part began.

The glass disc was the correct shape, but it wouldn't be a mirror until coated with a thin layer of aluminium. This was a process which had been done many times before with smaller mirrors, but as always size matters, and a host of problems had to be solved before a suitable coating was obtained. Now the mirror could be installed in the telescope and tested further. Problem after problem with the mounting system, suspension, and telescope drive had to be found and fixed. Testing a mirror in its telescope against a star is much more demanding than any optical shop test, and from the start of 1949, an iterative process of testing, tweaking, and re-testing began. A problem with astigmatism in the mirror was fixed by attaching four fisherman's scales from a hardware store to its back (they are still there). In October 1949, the telescope was declared finished and ready for use by astronomers. Twenty-one years had elapsed since the project began. George Ellery Hale died in 1938, less than ten years into the great work. But it was recognised as his monument, and at its dedication was named the “Hale Telescope.”

The inauguration of the Hale Telescope marked the end of the rapid increase in the aperture of observatory telescopes which had characterised the first half of the twentieth century, largely through the efforts of Hale. It would remain the largest telescope in operation until 1975, when the Soviet six metre BTA-6 went into operation. That instrument, however, was essentially an exercise in Cold War one-upmanship, and never achieved its scientific objectives. The Hale would not truly be surpassed before the ten metre Keck I telescope began observations in 1993, 44 years after the Hale. The Hale Telescope remains in active use today, performing observations impossible when it was inaugurated thanks to electronics undreamt of in 1949.

This is an epic recounting of a grand project, the dawn of “big science”, and the construction of instruments which revolutionised how we see our place in the cosmos. There is far more detail than I have recounted even in this long essay, and much insight into how a large, complicated project, undertaken with little grasp of the technical challenges to be overcome, can be achieved through patient toil sustained by belief in the objective.

A PBS documentary, The Journey to Palomar, is based upon this book. It is available on DVD or a variety of streaming services.

In the Kindle edition, footnotes which appear in the text are just asterisks, which are almost impossible to select on touch screen devices without missing and accidentally turning the page. In addition, the index is just a useless list of terms and page numbers which have nothing to do with the Kindle document, which lacks real page numbers. Disastrously, the illustrations which appear in the print edition are omitted: for a project which was extensively documented in photographs, drawings, and motion pictures, this is inexcusable.

October 2016 

Gingerich, Owen. The Book Nobody Read. New York: Penguin Books, 2004. ISBN 0-14-303476-6.

There is something about astronomy which seems to invite obsession. Otherwise, why would intelligent and seemingly rational people expend vast amounts of time and effort to compile catalogues of hundreds of thousands of stars, precisely measure the positions of planets over periods of decades, travel to the ends of the Earth to observe solar eclipses, get up before the crack of noon to see a rare transit of Mercury or Venus, or burn up months of computer time finding every planetary transit in a quarter million year interval around the present? Obsession it may be, but it's also fascinating and fun, and astronomy has profited enormously from the labours of those so obsessed, whether on a mountain top in the dead of winter, or carrying out lengthy calculations when tables of logarithms were the only computational tool available.

This book chronicles one man's magnificent thirty-year obsession. Spurred by Arthur Koestler's The Sleepwalkers, which portrayed Copernicus as a villain and his magnum opus De revolutionibus “the book that nobody read”—“an all time worst seller”, followed by the discovery of an obviously carefully read and heavily annotated first edition in the library of the Royal Observatory in Edinburgh, Scotland, the author, an astrophysicist and Harvard professor of the history of science, found himself inexorably drawn into a quest to track down and examine every extant copy of the first (Nuremberg, 1543) and second (Basel, 1566) editions of De revolutionibus to see whether and where readers had annotated them and so determine how widely the book, of which about a thousand copies were printed in these editions—typical for scientific works at the time—was read. Unlike today, when we've been educated that writing in a book is desecration, readers in the 16th and 17th centuries often made extensive annotations to their books, even assigning students and apprentices the task of copying annotations by other learned readers into their copies.

Along the way Gingerich found himself driving down an abandoned autobahn in the no man's land between East and West Germany, testifying in the criminal trial of a book rustler, discovering the theft of copies which librarians were unaware were missing, tracking down the provenance of pages in “sophisticated” (in the original sense of the word) copies assembled from two or more incomplete originals, attending the auction at Sotheby's of a first edition with a dubious last leaf which sold for US$750,000 (the author, no impecunious naïf in the rare book game, owns two copies of the second edition himself), and discovering the fate of many less celebrated books from that era (toilet paper). De revolutionibus has survived the vicissitudes of the centuries quite well—out of about 1000 original copies of the first and second editions, approximately six hundred exemplars remain.

Aside from the adventures of the Great Copernicus Chase, there is a great deal of information about Copernicus and the revolution he discovered and sparked which dispels many widely-believed bogus notions such as:

• Copernicus was a hero of secular science against religious fundamentalism. Wrong!   Copernicus was a deeply religious doctor of church law, canon of the Roman Catholic Varmian Cathedral in Poland. He dedicated the book to Pope Paul III.
• Prior to Copernicus, astronomers relying on Ptolemy's geocentric system kept adding epicycles on epicycles to try to approximate the orbits of the planets. Wrong!   This makes for a great story, but there is no evidence whatsoever for “epicycles on epicycles”. The authoritative planetary ephemerides in use in the age of Copernicus were calculated using the original Ptolemaic system without additional refinements, and there are no known examples of systems with additional epicycles.
• Copernicus banished epicycles from astronomy. Wrong!   The Copernican system, in fact, included thirty-four epicycles! Because Copernicus believed that all planetary motion was based on circles, just like Ptolemy he required epicycles to approximate motion which wasn't known to be actually elliptical prior to Kepler. In fact, the Copernican system was no more accurate in predicting planetary positions than that of Ptolemy, and ephemerides computed from it were no better.
• The Roman Catholic Church was appalled by Copernicus's suggestion that the Earth was not the centre of the cosmos and immediately banned his book. Wrong!   The first edition of De revolutionibus was published in 1543. It wasn't until 1616, more than seventy years later, that the book was placed on the Index Librorum Prohibitorum, and in 1620 it was permitted as long as ten specific modifications were made. Outside Italy, few copies even in Catholic countries were censored according to these instructions. In Spain, usually thought of as a hotbed of the Inquisition, the book was never placed on the Index at all. Galileo's personal copy has the forbidden passages marked in boxes and lined through, permitting the original text to be read. There is no evidence of any copy having been destroyed on the orders of the Church, and the Vatican library has three copies of both the first and second editions.

Obviously, if you're as interested as I in eccentric topics like positional astronomy, rare books, the evolution of modern science, and the surprisingly rapid and efficient diffusion of knowledge more than five centuries before the Internet, this is a book you're probably going to read if you haven't already. The only flaw is that the colour plates (at least in the UK paperback edition I read) are terribly reproduced—they all look like nobody bothered to focus the copy camera when the separations were made; plates 4b, 6, and 7a through 7f, which show annotations in various copies, are completely useless because they're so fuzzy the annotations can barely be read, if at all.

November 2005 

Gott, J. Richard. The Cosmic Web. Princeton: Princeton University Press, 2016. ISBN 978-0-691-15726-9.

Some works of popular science, trying to impress the reader with the scale of the universe and the insignificance of humans on the cosmic scale, argue that there's nothing special about our place in the universe: “an ordinary planet orbiting an ordinary star, in a typical orbit within an ordinary galaxy”, or something like that. But this is wrong! Surfaces of planets make up a vanishingly small fraction of the volume of the universe, and habitable planets, where beings like ourselves are neither frozen nor fried by extremes of temperature, nor suffocated or poisoned by a toxic atmosphere, are rarer still. The Sun is far from an ordinary star: it is brighter than 85% of the stars in the galaxy, and only 7.8% of stars in the Milky Way share its spectral class. Fully 76% of stars are dim red dwarves, the heavens' own 25 watt bulbs.

What does a typical place in the universe look like? What would you see if you were there? Well, first of all, you'd need a space suit and air supply, since the universe is mostly empty. And you'd see nothing. Most of the volume of the universe consists of great voids with few galaxies. If you were at a typical place in the universe, you'd be in one of these voids, probably far enough from the nearest galaxy that it wouldn't be visible to the unaided eye. There would be no stars in the sky, since stars are only formed within galaxies. There would only be darkness. Now look out the window: you are in a pretty special place after all.

One of the great intellectual adventures of the last century is learning our place in the universe and coming to understand its large scale structure. This book, by an astrophysicist who has played an important role in discovering that structure, explains how we pieced together the evidence and came to learn the details of the universe we inhabit. It provides an insider's look at how astronomers tease insight out of the messy and often confusing data obtained from observation.

It's remarkable not just how much we've learned, but how recently we've come to know it. At the start of the 20th century, most astronomers believed the solar system was part of a disc of stars which we see as the Milky Way. In 1610, Galileo's telescope revealed that the Milky Way was made up of a multitude of faint stars, and since the galaxy makes a band all around the sky, that the Sun must be within it. In 1918, by observing variable stars in globular clusters which orbit the Milky Way, Harlow Shapley was able to measure the size of the galaxy, which proved much larger than previously estimated, and determine that the Sun was about half way from the centre of the galaxy to its edge. Still, the universe was the galaxy.

There remained the mystery of the “spiral nebulæ”. These faint smudges of light had been revealed by photographic time exposures through large telescopes to be discs, some with prominent spiral arms, viewed from different angles. Some astronomers believed them to be gas clouds within the galaxy, perhaps other solar systems in the process of formation, while others argued they were galaxies like the Milky Way, far distant in the universe. In 1920 a great debate pitted the two views against one another, concluding that insufficient evidence existed to decide the matter.

That evidence would not be long in coming. Shortly thereafter, using the new 100 inch telescope on Mount Wilson in California, Edwin Hubble was able to photograph the Andromeda Nebula and resolve it into individual stars. Just as Galileo had done three centuries earlier for the Milky Way, Hubble's photographs proved Andromeda was not a gas cloud, but a galaxy composed of a multitude of stars. Further, Hubble was able to identify variable stars which allowed him to estimate its distance: due to details about the stars which were not understood at the time, he underestimated the distance by about a factor of two, but it was clear the galaxy was far beyond the Milky Way. The distances to other nearby galaxies were soon measured.

In one leap, the scale of the universe had become breathtakingly larger. Instead of one galaxy comprising the universe, the Milky Way was just one of a multitude of galaxies scattered around an enormous void. When astronomers observed the spectra of these galaxies, they noticed something odd: spectral lines from stars in most galaxies were shifted toward the red end of the spectrum compared to those observed on Earth. This was interpreted as a Doppler shift due to the galaxy's moving away from the Milky Way. Between 1929 and 1931, Edwin Hubble measured the distances and redshifts of a number of galaxies and discovered there was a linear relationship between the two. A galaxy twice as distant as another would be receding at twice the velocity. The universe was expanding, and every galaxy (except those sufficiently close to be gravitationally bound) was receding from every other galaxy.

The discovery of the redshift-distance relationship provided astronomers a way to chart the cosmos in three dimensions. Plotting the position of a galaxy on the sky and measuring its distance via redshift allowed building up a model of how galaxies were distributed in the universe. Were they randomly scattered, or would patterns emerge, suggesting larger-scale structure?

Galaxies had been observed to cluster: the nearest cluster, in the constellation Virgo, is made up of at least 1300 galaxies, and is now known to be part of a larger supercluster of which the Milky Way is an outlying member. It was not until the 1970s and 1980s that large-scale redshift surveys allowed plotting the positions of galaxies in the universe, initially in thin slices, and eventually in three dimensions. What was seen was striking. Galaxies were not sprinkled at random through the universe, but seemed to form filaments and walls, with great voids containing little or no galaxies. How did this come to be?

In parallel with this patient observational work, theorists were working out the history of the early universe based upon increasingly precise observations of the cosmic microwave background radiation, which provides a glimpse of the universe just 380,000 years after the Big Bang. This ushered in the era of precision cosmology, where the age and scale of the universe were determined with great accuracy, and the tiny fluctuations in temperature of the early universe were mapped in detail. This led to a picture of the universe very different from that imagined by astronomers over the centuries. Ordinary matter: stars, planets, gas clouds, and you and me—everything we observe in the heavens and the Earth—makes up less than 5% of the mass-energy of the universe. Dark matter, which interacts with ordinary matter only through gravitation, makes up 26.8% of the universe. It can be detected through its gravitational effects on the motion of stars and galaxies, but at present we don't have any idea what it's composed of. (It would be more accurate to call it “transparent matter” since it does not interact with light, but “dark matter” is the name we're stuck with.) The balance of the universe, 68.3%, is dark energy, a form of energy filling empty space and causing the expansion of the universe to accelerate. We have no idea at all about the nature of dark energy. These three components: ordinary matter, dark matter, and dark energy add up to give the universe a flat topology. It is humbling to contemplate the fact that everything we've learned in all of the sciences is about matter which makes up less than 5% of the universe: the other 95% is invisible and we don't know anything about it (although there are abundant guesses or, if you prefer, hypotheses).

This may seem like a flight of fancy, or a case of theorists making up invisible things to explain away observations they can't otherwise interpret. But in fact, dark matter and dark energy, originally inferred from astronomical observations, make predictions about the properties of the cosmic background radiation, and these predictions have been confirmed with increasingly high precision by successive space-based observations of the microwave sky. These observations are consistent with a period of cosmological inflation in which a tiny portion of the universe expanded to encompass the entire visible universe today. Inflation magnified tiny quantum fluctuations of the density of the universe to a scale where they could serve as seeds for the formation of structures in the present-day universe. Regions with greater than average density would begin to collapse inward due to the gravitational attraction of their contents, while those with less than average density would become voids as material within them fell into adjacent regions of higher density.

Dark matter, being more than five times as abundant as ordinary matter, would take the lead in this process of gravitational collapse, and ordinary matter would follow, concentrating in denser regions and eventually forming stars and galaxies. The galaxies formed would associate into gravitationally bound clusters and eventually superclusters, forming structure at larger scales. But what does the universe look like at the largest scale? Are galaxies distributed at random; do they clump together like meatballs in a soup; or do voids occur within a sea of galaxies like the holes in Swiss cheese? The answer is, surprisingly, none of the above, and the author explains the research, in which he has been a key participant, that discovered the large scale structure of the universe.

As increasingly more comprehensive redshift surveys of galaxies were made, what appeared was a network of filaments which connected to one another, forming extended structures. Between filaments were voids containing few galaxies. Some of these structures, such as the Sloan Great Wall, at 1.38 billion light years in length, are 1/10 the radius of the observable universe. Galaxies are found along filaments, and where filaments meet, rich clusters and superclusters of galaxies are observed. At this large scale, where galaxies are represented by single dots, the universe resembles a neural network like the human brain.

As ever more extensive observations mapped the three-dimensional structure of the universe we inhabit, progress in computing allowed running increasingly detailed simulations of the evolution of structure in models of the universe. Although the implementation of these simulations is difficult and complicated, they are conceptually simple. You start with a region of space, populate it with particles representing ordinary and dark matter in a sea of dark energy with random positions and density variations corresponding to those observed in the cosmic background radiation, then let the simulation run, computing the gravitational attraction of each particle on the others and tracking their motion under the influence of gravity. In 2005, Volker Springel and the Virgo Consortium ran the Millennium Simulation, which started from the best estimate of the initial conditions of the universe known at the time and tracked the motion of ten billion particles of ordinary and dark matter in a cube two billion light years on a side. As the simulation clock ran, the matter contracted into filaments surrounding voids, with the filaments joined at nodes rich in galaxies. The images produced by the simulation and the statistics calculated were strikingly similar to those observed in the real universe. The behaviour of this and other simulations increases confidence in the existence of dark matter and dark energy; if you leave them out of the simulation, you get results which don't look anything like the universe we inhabit.

At the largest scale, the universe isn't made of galaxies sprinkled at random, nor meatballs of galaxy clusters in a sea of voids, nor a sea of galaxies with Swiss cheese like voids. Instead, it resembles a sponge of denser filaments and knots interpenetrated by less dense voids. Both the denser and less dense regions percolate: it is possible to travel from one edge of the universe to another staying entirely within more or less dense regions. (If the universe were arranged like a honeycomb, for example, with voids surrounded by denser walls, this would not be possible.) Nobody imagined this before the observational results started coming in, and now we've discovered that given the initial conditions of the universe after the Big Bang, the emergence of such a structure is inevitable.

All of the structure we observe in the universe has evolved from a remarkably uniform starting point in the 13.8 billion years since the Big Bang. What will the future hold? The final chapter explores various scenarios for the far future. Because these depend upon the properties of dark matter and dark energy, which we don't understand, they are necessarily speculative.

The book is written for the general reader, but at a level substantially more difficult than many works of science popularisation. The author, a scientist involved in this research for decades, does not shy away from using equations when they illustrate an argument better than words. Readers are assumed to be comfortable with scientific notation, units like light years and parsecs, and logarithmically scaled charts. For some reason, in the Kindle edition dozens of hyphenated phrases are run together without any punctuation.

May 2016 

Hawking, Stephen. The Universe in a Nutshell. New York: Bantam Books, 2001. ISBN 0-553-80202-X.

January 2002 

Hirshfeld, Alan W. Parallax. New York: Henry Holt, 2001. ISBN 0-8050-7133-4.

December 2003 

Hirshfeld, Alan W. Parallax. New York: Dover, [2001] 2013. ISBN 978-0-486-49093-9.

“Eppur si muove.” As legend has it, these words were uttered (or muttered) by Galileo after being forced to recant his belief that the Earth revolves around the Sun: “And yet it moves.” The idea of a heliocentric model, as opposed to the Earth being at the center of the universe (geocentric model), was hardly new: Aristarchus of Samos had proposed it in the third century B.C., as a simplification of the prevailing view that the Earth was fixed and all other heavenly bodies revolved around it. This seemed to defy common sense: if the Earth rotated on its axis every day, why weren't there strong winds as the Earth's surface moved through the air? If you threw a rock straight up in the air, why did it come straight down rather than being displaced by the Earth's rotation while in flight? And if the Earth were offset from the center of the universe, why didn't we observe more stars when looking toward it than away?

By Galileo's time, many of these objections had been refuted, in part by his own work on the laws of motion, but the fact remained that there was precisely zero observational evidence that the Earth orbited the Sun. This was to remain the case for more than a century after Galileo, and millennia after Aristarchus, a scientific quest which ultimately provided the first glimpse of the breathtaking scale of the universe.

Hold out your hand at arm's length in front of your face and extend your index finger upward. (No, really, do it.) Now observe the finger with your right eye, then your left eye in succession, each time closing the other. Notice how the finger seems to jump to the right and left as you alternate eyes? That's because your eyes are separated by what is called the interpupillary distance, which is on the order of 6 cm. Each eye sees objects from a different perspective, and nearby objects will shift with respect to distant objects when seen from different eyes. This effect is called parallax, and the brain uses it to reconstruct depth information for nearby objects. Interestingly, predator animals tend to have both eyes on the front of the face with overlapping visual fields to provide depth perception for use in stalking, while prey animals are more likely to have eyes on either side of their heads to allow them to monitor a wider field of view for potential threats: compare a cat and a horse.

Now, if the Earth really orbits the Sun every year, that provides a large baseline which should affect how we see objects in the sky. In particular, when we observe stars from points in the Earth's orbit six months apart, we should see them shift their positions in the sky, since we're viewing them from different locations, just as your finger appeared to shift when viewed from different eyes. And since the baseline is enormously larger (although in the times of Aristarchus and even Galileo, its absolute magnitude was not known), even distant objects should be observed to shift over the year. Further, nearby stars should shift more than distant stars, so remote stars could be used as a reference for measuring the apparent shift of those closest to the Sun. This was the concept of stellar parallax.

Unfortunately for advocates of the heliocentric model, nobody had been able to observe stellar parallax. From the time of Aristarchus to Galileo, careful observers of the sky found the positions of the stars as fixed in the sky as if they were painted on a distant crystal sphere as imagined by the ancients, with the Earth at the center. Proponents of the heliocentric model argued that the failure to observe parallax was simply due to the stars being much too remote. When you're observing a distant mountain range, you won't notice any difference when you look at it with your right and left eye: it's just too far away. Perhaps the parallax of stars was beyond our ability to observe, even with so long a baseline as the Earth's distance from the Sun. Or, as others argued, maybe it didn't move.

But, pioneered by Galileo himself, our ability to observe was about to take an enormous leap. Since antiquity, all of our measurements of the sky, regardless of how clever our tools, ultimately came down to the human eye. Galileo did not invent the telescope, but he improved what had been used as a “spyglass” for military applications into a powerful tool for exploring the sky. His telescopes, while crude and difficult to use, and having a field of view comparable to looking through a soda straw, revealed mountains and craters on the Moon, the phases of Venus (powerful evidence against the geocentric model), the satellites of Jupiter, and the curious shape of Saturn (his telescope lacked the resolution to identify its apparent “ears” as rings). He even observed Neptune in 1612, when it happened to be close to Jupiter, but he didn't interpret what he had seen as a new planet. Galileo never observed parallax; he never tried, but he suggested astronomers might concentrate on close pairs of stars, one bright and one dim, where, if all stars were of comparable brightness, one might be close and the other distant, from which parallax could be teased out from observation over a year. This was to inform the work of subsequent observers.

Now the challenge was not one of theory, but of instrumentation and observational technique. It was not to be a sprint, but a marathon. Those who sought to measure stellar parallax and failed (sometimes reporting success, only to have their results overturned by subsequent observations) reads like a “Who's Who” of observational astronomy in the telescopic era: Robert Hooke, James Bradley, and William Herschel all tried and failed to observe parallax. Bradley's observations revealed an annual shift in the position of stars, but it affected all stars, not just the nearest. This didn't make any sense unless the stars were all painted on a celestial sphere, and the shift didn't behave as expected from the Earth's motion around the Sun. It turned out to be due to the aberration of light resulting from the motion of the Earth around the Sun and the finite speed of light. It's like when you're running in a rainstorm:

Raindrops keep fallin' in my face,
More and more as I pick up the pace…

Finally, here was proof that “it moves”: there would be no aberration in a geocentric universe. But by Bradley's time in the 1720s, only cranks and crackpots still believed in the geocentric model. The question was, instead, how distant are the stars? The parallax game remained afoot.

It was ultimately a question of instrumentation, but also one of luck. By the 19th century, there was abundant evidence that stars differed enormously in their intrinsic brightness. (We now know that the most luminous stars are more than a billion times more brilliant than the dimmest.) Thus, you couldn't conclude that the brightest stars were the nearest, as astronomers once guessed. Indeed, the distances of the four brightest stars as seen from Earth are, in light years, 8.6, 310, 4.4, and 37. Given that observing the position of a star for parallax is a long-term project and tedious, bear in mind that pioneers on the quest had no idea whether the stars they observed were near or far, nor the distance to the nearest stars they might happen to be lucky enough to choose.

It all came together in the 1830s. Using an instrument called a heliometer, which was essentially a refractor telescope with its lens cut in two with the ability to shift the halves and measure the offset, Friedrich Bessel was able to measure the parallax of the star 61 Cygni by comparison to an adjacent distant star. Shortly thereafter, Wilhelm Struve published the parallax of Vega, and then, just two months later, Thomas Henderson reported the parallax of Alpha Centauri, based upon measurements made earlier at the Cape of Good Hope. Finally, we knew the distances to the nearest stars (although those more distant remained a mystery), and just how empty the universe was.

Let's put some numbers on this, just to appreciate how great was the achievement of the pioneers of parallax. The parallax angle of the closest star system, Alpha Centauri, is 0.755 arc seconds. (The parallax angle is half the shift observed in the position of the star as the Earth orbits the Sun. We use half the shift because it makes the trigonometry to compute the distance easier to understand.) An arc second is 1/3600 of a degree, and there are 360 degrees in a circle, so it's 1/1,296,000 of a full circle.

Now let's work out the distance to Alpha Centauri. We'll work in terms of astronomical units (au), the mean distance between the Earth and Sun. We have a right triangle where we know the distance from the Earth to the Sun and the parallax angle of 0.755 arc seconds. (To get a sense for how tiny an angle this is, it's comparable to the angle subtended by a US quarter dollar coin when viewed from a distance of 6.6 km.) We can compute the distance from the Earth to Alpha Centauri as:

1 au / tan(0.755 / 3600) = 273198 au = 4.32 light years

Parallax is used to define the parsec (pc), the distance at which a star would have a parallax angle of one arc second. A parsec is about 3.26 light years, so the distance to Alpha Centauri is 1.32 parsecs. Star Wars notwithstanding, the parsec, like the light year, is a unit of distance, not time.

Progress in instrumentation has accelerated in recent decades. The Earth is a poor platform from which to make precision observations such as parallax. It's much better to go to space, where there are neither the wobbles of a planet nor its often murky atmosphere. The Hipparcos mission, launched in 1989, measured the parallaxes and proper motions of more than 118,000 stars, with lower resolution data for more than 2.5 million stars. The Gaia mission, launched in 2013 and still underway, has a goal of measuring the position, parallax, and proper motion of more than a billion stars.

It's been a long road, getting from there to here. It took more than 2,000 years from the time Aristarchus proposed the heliocentric solar system until we had direct observational evidence that eppur si muove. Within a few years, we will have in hand direct measurements of the distances to a billion stars. And, some day, we'll visit them.

I originally read this book in December 2003. It was a delight to revisit.

July 2016 

Hoyle, Fred, Geoffrey Burbridge, and Jayant V. Narlikar. A Different Approach to Cosmology. Cambridge: Cambridge University Press, 2000. ISBN 0-521-66223-0.

March 2001 

Johnson, George. Miss Leavitt's Stars. New York: W. W. Norton, 2005. ISBN 978-0-393-32856-1.

Henrietta Swan Leavitt was a computer. No, this is not a tale of artificial intelligence, but rather of the key discovery which allowed astronomers to grasp the enormity of the universe. In the late 19th century it became increasingly common for daughters of modestly prosperous families to attend college. Henrietta Leavitt's father was a Congregational church minister in Ohio whose income allowed him to send his daughter to Oberlin College in 1885. In 1888 she transferred to the Society for the Collegiate Instruction of Women (later Radcliffe College) in Cambridge Massachusetts where she earned a bachelor's degree in 1892. In her senior year, she took a course in astronomy which sparked a lifetime fascination with the stars. After graduation, she remained in Cambridge and the next year was volunteering at the Harvard College Observatory and was later put on salary.

The director of the observatory, Edward Pickering, realised that while at the time it was considered inappropriate for women to sit up all night operating a telescope, much of the work of astronomy consisted of tedious tasks such as measuring the position and brightness of stars on photographic plates, compiling catalogues, and performing analyses based upon their data. Pickering realised that there was a pool of college educated women (especially in the Boston area) who were unlikely to find work as scientists but who were perfectly capable of doing this office work so essential to the progress of astronomy. Further, they would work for a fraction of the salary of a professional astronomer and Pickering, a shrewd administrator as well as a scientist, reasoned he could boost the output of his observatory by a substantial factor within the available budget. So it was that Leavitt was hired to work full-time at the observatory with a job title of “computer” and a salary of US$ 0.25 per hour (she later got a raise to 0.30, which is comparable to the U.S. federal minimum wage in 2013).

There was no shortage of work for Leavitt and her fellow computers (nicknamed “Pickering's Harem”) to do. The major project underway at the observatory was the creation of a catalogue of the position, magnitude, and colour of all stars visible from the northern hemisphere to the limiting magnitude of the telescope available. This was done by exposing glass photographic plates in long time exposures while keeping the telescope precisely aimed at a given patch of the sky (although telescopes of era had “clock drives” which approximately tracked the apparent motion of the sky, imprecision in the mechanism required a human observer [all men!] to track a guide star through an eyepiece during the long exposure and manually keep the star centred on the crosshairs with fine adjustment controls). Since each plate covered only a small fraction of the sky, the work of surveying the entire hemisphere was long, tedious, and often frustrating, as a cloud might drift across the field of view and ruin the exposure.

But if the work at the telescope was seemingly endless, analysing the plates it produced was far more arduous. Each plate would contain images of thousands of stars, the position and brightness (inferred from the size of the star's image on the plate) of which had to be measured and recorded. Further, plates taken through different colour filters had to be compared, with the difference in brightness used to estimate each star's colour and hence temperature. And if that weren't enough, plates taken of the same field at different times were compared to discover stars whose brightness varied from one time to another.

There are two kinds of these variable stars. The first consist of multiple star systems where one star periodically eclipses another, with the simplest case being an “eclipsing binary”: two stars which eclipse one another. Intrinsic variable stars are individual stars whose brightness varies over time, often accompanied by a change in the star's colour. Both kinds of variable stars were important to astronomers, with intrinsic variables offering clues to astrophysics and the evolution of stars.

Leavitt was called a “variable star ‘fiend’ ” by a Princeton astronomer in a letter to Pickering, commenting on the flood of discoveries she published in the Harvard Observatory's journals. For the ambitious Pickering, one hemisphere did not suffice. He arranged for an observatory to be established in Arequipa Peru, which would allow stars visible only from the southern hemisphere to be observed and catalogued. A 24 inch telescope and its accessories were shipped around Cape Horn from Boston, and before long the southern sky was being photographed, with the plates sent to Harvard for measurement and cataloguing. When the news had come to Harvard, it was the computers, not the astronomers, who scrutinised them to see what had been discovered.

Now, star catalogues of the kind Pickering was preparing, however useful they were to astronomers, were essentially two-dimensional. They give the position of the star on the sky, but no information about how distant it is from the solar system. Indeed, only the distances of few dozen of the very closest stars had been measured by the end of the 19th century by stellar parallax, but for all the rest of the stars their distances were a complete mystery and consequently also the scale of the visible universe was utterly unknown. Because the intrinsic brightness of stars varies over an enormous range (some stars are a million times more luminous than the Sun, which is itself ten thousand times brighter than some dwarf stars), a star of a given magnitude (brightness as observed from Earth) may either be a nearby star of modest brightness or an brilliant supergiant star far away.

One of the first intrinsic variable stars to be studied in depth was Delta Cephei, found to be variable in 1784. It is the prototype Cepheid variable, many more of which were discovered by Leavitt. Cepheids are old, massive stars, which have burnt up most of their hydrogen fuel and vary with a characteristic sawtooth-shaped light curve with periods ranging from days to months. In Leavitt's time the mechanism for this variability was unknown, but it is now understood to be due to oscillations in the star's radius as the ionisation state of helium in the star's outer layer cycles between opaque and transparent states, repeatedly trapping the star's energy and causing it to expand, then releasing it, making the star contract.

When examining the plates from the telescope in Peru, Leavitt was fascinated by the Magellanic clouds, which look like little bits of the Milky Way which broke off and migrated to distant parts of the sky (we now know them to be dwarf galaxies which may be in orbit around the Milky Way). Leavitt became fascinated by the clouds, and by assiduous searches on multiple plates showing them, eventually published in 1908 a list of 1,777 variable stars she had discovered in them. While astronomers did not know the exact nature of the Magellanic clouds, they were confident of two things: they were very distant (since stars within them of spectral types which are inherently bright were much dimmer than those seen elsewhere in the sky), and all of the stars in them were about the same distance from the solar system, since it was evident the clouds must be gravitationally bound to persist over time.

Leavitt's 1908 paper contained one of the greatest understatements in all of the scientific literature: “It is worthy of notice that the brightest variables have the longer periods.” She had discovered a measuring stick for the universe. In examining Cepheids among the variables in her list, she observed that there was a simple linear relationship between the period of pulsation and how bright the star appeared. But since all of the Cepheids in the clouds must be at about the same distance, that meant their absolute brightness could be determined from their periods. This made the Cepheids “standard candles” which could be used to chart the galaxy and beyond. Since they are so bright, they could be observed at great distances.

To take a simple case, suppose you observe a Cepheid in a star cluster, and another in a different part of the sky. The two have about the same period of oscillation, but the one in the cluster has one quarter the brightness at Earth of the other. Since the periods are the same, you know the inherent luminosities of the two stars are alike, so according to the inverse-square law the cluster must be twice as distant as the other star. If the Cepheids have different periods, the relationship Leavitt discovered can be used to compute the relative difference in their luminosity, again allowing their distances to be compared.

This method provides a relative distance scale to as far as you can identify and measure the periods of Cepheids, but it does not give their absolute distances. However, if you can measure the distance to any single Cepheid by other means, you can now compute the absolute distance to all of them. Not without controversy, this was accomplished, and for the first time astronomers beheld just how enormous the galaxy was, that the solar system was far from its centre, and that the mysterious “spiral neublæ” many had argued were clouds of gas or solar systems in formation were entire other galaxies among a myriad in a universe of breathtaking size. This was the work of others, but all of it was founded on Leavitt's discovery.

Henrietta Leavitt would not live to see all of these consequences of her work. She died of cancer in 1921 at the age of 53, while the debate was still raging over whether the Milky Way was the entire universe or just one of a vast number of “island universes”. Both sides in this controversy based their arguments in large part upon her work.

She was paid just ten cents more per hour than a cotton mill worker, and never given the title “astronomer”, never made an observation with a telescope, and yet working endless hours at her desk made one of the most profound discoveries of 20th century astronomy, one which is still being refined by precision measurements from the Earth and space today. While the public hardly ever heard her name, she published her work in professional journals and eminent astronomers were well aware of its significance and her part in creating it. A 66 kilometre crater on the Moon bears her name (the one named after that Armstrong fellow is just 4.6 km, albeit on the near side).

This short book is only in part a biography of Leavitt. Apart from her work, she left few traces of her life. It is as much a story of how astronomy was done in her days and how she and others made the giant leap in establishing what we now call the cosmic distance ladder. This was a complicated process, with many missteps and controversies along the way, which are well described here.

In the Kindle edition (as viewed on the iPad) the quotations at the start of each chapter are mis-formatted so each character appears on its own line. The index contains references to page numbers in the print edition and is useless because the Kindle edition contains no page numbers.

May 2014 

Levenson, Thomas. The Hunt for Vulcan. New York: Random House, 2015. ISBN 978-0-8129-9898-6.

The history of science has been marked by discoveries in which, by observing where nobody had looked before, with new and more sensitive instruments, or at different aspects of reality, new and often surprising phenomena have been detected. But some of the most profound of our discoveries about the universe we inhabit have come from things we didn't observe, but expected to.

By the nineteenth century, one of the most solid pillars of science was Newton's law of universal gravitation. With a single equation a schoolchild could understand, it explained why objects fall, why the Moon orbits the Earth and the Earth and other planets the Sun, the tides, and the motion of double stars. But still, one wonders: is the law of gravitation exactly as Newton described, and does it work everywhere? For example, Newton's gravity gets weaker as the inverse square of the distance between two objects (for example, if you double the distance, the gravitational force is four times weaker [2² = 4]) but has unlimited range: every object in the universe attracts every other object, however weakly, regardless of distance. But might gravity not, say, weaken faster at great distances? If this were the case, the orbits of the outer planets would differ from the predictions of Newton's theory. Comparing astronomical observations to calculated positions of the planets was a way to discover such phenomena.

In 1781 astronomer William Herschel discovered Uranus, the first planet not known since antiquity. (Uranus is dim but visible to the unaided eye and doubtless had been seen innumerable times, including by astronomers who included it in star catalogues, but Herschel was the first to note its non-stellar appearance through his telescope, originally believing it a comet.) Herschel wasn't looking for a new planet; he was observing stars for another project when he happened upon Uranus. Further observations of the object confirmed that it was moving in a slow, almost circular orbit, around twice the distance of Saturn from the Sun.

Given knowledge of the positions, velocities, and masses of the planets and Newton's law of gravitation, it should be possible to predict the past and future motion of solar system bodies for an arbitrary period of time. Working backward, comparing the predicted influence of bodies on one another with astronomical observations, the masses of the individual planets can be estimated to produce a complete model of the solar system. This great work was undertaken by Pierre-Simon Laplace who published his Mécanique céleste in five volumes between 1799 and 1825. As the middle of the 19th century approached, ongoing precision observations of the planets indicated that all was not proceeding as Laplace had foreseen. Uranus, in particular, continued to diverge from where it was expected to be after taking into account the gravitational influence upon its motion by Saturn and Jupiter. Could Newton have been wrong, and the influence of gravity different over the vast distance of Uranus from the Sun?

In the 1840s two mathematical astronomers, Urbain Le Verrier in France and John Couch Adams in Britain, working independently, investigated the possibility that Newton was right, but that an undiscovered body in the outer solar system was responsible for perturbing the orbit of Uranus. After almost unimaginably tedious calculations (done using tables of logarithms and pencil and paper arithmetic), both Le Verrier and Adams found a solution and predicted where to observe the new planet. Adams failed to persuade astronomers to look for the new world, but Le Verrier prevailed upon an astronomer at the Berlin Observatory to try, and Neptune was duly discovered within one degree (twice the apparent size of the full Moon) of his prediction.

This was Newton triumphant. Not only was the theory vindicated, it had been used, for the first time in history, to predict the existence of a previously unknown planet and tell the astronomers right where to point their telescopes to observe it. The mystery of the outer solar system had been solved. But problems remained much closer to the Sun.

The planet Mercury orbits the Sun every 88 days in an eccentric orbit which never exceeds half the Earth's distance from the Sun. It is a small world, with just 6% of the Earth's mass. As an inner planet, Mercury never appears more than 28° from the Sun, and can best be observed in the morning or evening sky when it is near its maximum elongation from the Sun. (With a telescope, it is possible to observe Mercury in broad daylight.) Flush with his success with Neptune, and rewarded with the post of director of the Paris Observatory, in 1859 Le Verrier turned his attention toward Mercury.

Again, through arduous calculations (by this time Le Verrier had a building full of minions to assist him, but so grueling was the work and so demanding a boss was Le Verrier that during his tenure at the Observatory 17 astronomers and 46 assistants quit) the influence of all of the known planets upon the motion of Mercury was worked out. If Mercury orbited a spherical Sun without other planets tugging on it, the point of its closest approach to the Sun (perihelion) in its eccentric orbit would remain fixed in space. But with the other planets exerting their gravitational influence, Mercury's perihelion should advance around the Sun at a rate of 526.7 arcseconds per century. But astronomers who had been following the orbit of Mercury for decades measured the actual advance of the perihelion as 565 arcseconds per century. This left a discrepancy of 38.3 arcseconds, for which there was no explanation. (The modern value, based upon more precise observations over a longer period of time, for the perihelion precession of Mercury is 43 arcseconds per century.) Although small (recall that there are 1,296,000 arcseconds in a full circle), this anomalous precession was much larger than the margin of error in observations and clearly indicated something was amiss. Could Newton be wrong?

Le Verrier thought not. Just as he had done for the anomalies of the orbit of Uranus, Le Verrier undertook to calculate the properties of an undiscovered object which could perturb the orbit of Mercury and explain the perihelion advance. He found that a planet closer to the Sun (or a belt of asteroids with equivalent mass) would do the trick. Such an object, so close to the Sun, could easily have escaped detection, as it could only be readily observed during a total solar eclipse or when passing in front of the Sun's disc (a transit). Le Verrier alerted astronomers to watch for transits of this intra-Mercurian planet.

On March 26, 1859, Edmond Modeste Lescarbault, a provincial physician in a small town and passionate amateur astronomer turned his (solar-filtered) telescope toward the Sun. He saw a small dark dot crossing the disc of the Sun, taking one hour and seventeen minutes to transit, just as expected by Le Verrier. He communicated his results to the great man, and after a visit and detailed interrogation, the astronomer certified the doctor's observation as genuine and computed the orbit for the new planet. The popular press jumped upon the story. By February 1860, planet Vulcan was all the rage.

Other observations began to arrive, both from credible and unknown observers. Professional astronomers mounted worldwide campaigns to observe the Sun around the period of predicted transits of Vulcan. All of the planned campaigns came up empty. Searches for Vulcan became a major focus of solar eclipse expeditions. Unless the eclipse happened to occur when Vulcan was in conjunction with the Sun, it should be readily observable when the Sun was obscured by the Moon. Eclipse expeditions prepared detailed star charts for the vicinity of the Sun to exclude known stars for the search during the fleeting moments of totality. In 1878, an international party of eclipse chasers including Thomas Edison descended on Rawlins, Wyoming to hunt Vulcan in an eclipse crossing that frontier town. One group spotted Vulcan; others didn't. Controversy and acrimony ensued.

After 1878, most professional astronomers lost interest in Vulcan. The anomalous advance of Mercury's perihelion was mostly set aside as “one of those things we don't understand”, much as astronomers regard dark matter today. In 1915, Einstein published his theory of gravitation: general relativity. It predicted that when objects moved rapidly or gravitational fields were strong, their motion would deviate from the predictions of Newton's theory. Einstein recalled the moment when he performed the calculation of the motion of Mercury in his just-completed theory. It predicted precisely the perihelion advance observed by the astronomers. He said that his heart shuddered in his chest and that he was “beside himself with joy.”

Newton was wrong! For the extreme conditions of Mercury's orbit, so close to the Sun, Einstein's theory of gravitation is required to obtain results which agree with observation. There was no need for planet Vulcan, and now it is mostly forgotten. But the episode is instructive as to how confidence in long-accepted theories and wishful thinking can lead us astray when what might be needed is an overhaul of our most fundamental theories. A century hence, which of our beliefs will be viewed as we regard planet Vulcan today?

January 2016 

Manly, Peter L. Unusual Telescopes. Cambridge: Cambridge University Press, 1991. ISBN 0-521-48393-X.

May 2003 

Vilenkin, Alexander. Many Worlds in One. New York: Hill and Wang, 2006. ISBN 0-8090-9523-8.

From the dawn of the human species until a time within the memory of many people younger than I, the origin of the universe was the subject of myth and a topic, if discussed at all within the academy, among doctors of divinity, not professors of physics. The advent of precision cosmology has changed that: the ultimate questions of origin are not only legitimate areas of research, but something probed by satellites in space, balloons circling the South Pole, and mega-projects of Big Science. The results of these experiments have, in the last few decades, converged upon a consensus from which few professional cosmologists would dissent:

1. At the largest scale, the geometry of the universe is indistinguishable from Euclidean (flat), and the distribution of matter and energy within it is homogeneous and isotropic.
2. The universe evolved from an extremely hot, dense, phase starting about 13.7 billion years ago from our point of observation, which resulted in the abundances of light elements observed today.
3. The evidence of this event is imprinted on the cosmic background radiation which can presently be observed in the microwave frequency band. All large-scale structures in the universe grew from gravitational amplification of scale-independent quantum fluctuations in density.
4. The flatness, homogeneity, and isotropy of the universe is best explained by a period of inflation shortly after the origin of the universe, which expanded a tiny region of space, smaller than a subatomic particle, to a volume much greater than the presently observable universe.
5. Consequently, the universe we can observe today is bounded by a horizon, about forty billion light years away in every direction (greater than the 13.7 billion light years you might expect since the universe has been expanding since its origin), but the universe is much, much larger than what we can see; every year another light year comes into view in every direction.

Now, this may seem mind-boggling enough, but from these premises, which it must be understood are accepted by most experts who study the origin of the universe, one can deduce some disturbing consequences which seem to be logically unavoidable.

Let me walk you through it here. We assume the universe is infinite and unbounded, which is the best estimate from precision cosmology. Then, within that universe, there will be an infinite number of observable regions, which we'll call O-regions, each defined by the volume from which an observer at the centre can have received light since the origin of the universe. Now, each O-region has a finite volume, and quantum mechanics tells us that within a finite volume there are a finite number of possible quantum states. This number, although huge (on the order of 10¹⁰¹²³ for a region the size of the one we presently inhabit), is not infinite, so consequently, with an infinite number of O-regions, even if quantum mechanics specifies the initial conditions of every O-region completely at random and they evolve randomly with every quantum event thereafter, there are only a finite number of histories they can experience (around 10¹⁰¹⁵⁰). Which means that, at this moment, in this universe (albeit not within our current observational horizon), invoking nothing as fuzzy, weird, or speculative as the multiple world interpretation of quantum mechanics, there are an infinite number of you reading these words scribbled by an infinite number of me. In the vast majority of our shared universes things continue much the same, but from time to time they d1v3r93 r4ndtx#e~—….

Reset . . .
Snap back to universe of origin . . .
Reloading initial vacuum parameters . . .
Restoring simulation . . .
Resuming from checkpoint.

What was that? Nothing, I guess. Still, odd, that blip you feel occasionally. Anyway, here is a completely fascinating book by a physicist and cosmologist who is pioneering the ragged edge of what the hard evidence from the cosmos seems to be telling us about the apparently boundless universe we inhabit. What is remarkable about this model is how generic it is. If you accept the best currently available evidence for the geometry and composition of the universe in the large, and agree with the majority of scientists who study such matters how it came to be that way, then an infinite cosmos filled with observable regions of finite size and consequently limited diversity more or less follows inevitably, however weird it may seem to think of an infinity of yourself experiencing every possible history somewhere. Further, in an infinite universe, there are an infinite number of O-regions which contain every possible history consistent with the laws of quantum mechanics and the symmetries of our spacetime including those in which, as the author noted, perhaps using the phrase for the first time in the august pages of the Physical Review, “Elvis is still alive”.

So generic is the prediction, there's no need to assume the correctness of speculative ideas in physics. The author provides a lukewarm endorsement of string theory and the “anthropic landscape” model, but is clear to distinguish its “multiverse” of distinct vacua with different moduli from our infinite universe with (as far as we know) a single, possibly evolving, vacuum state. But string theory could be completely wrong and the deductions from observational cosmology would still stand. For that matter, they are independent of the “eternal inflation” model the book describes in detail, since they rely only upon observables within the horizon of our single “pocket universe”.

Although the evolution of the universe from shortly after the end of inflation (the moment we call the “big bang”) seems to be well understood, there are still deep mysteries associated with the moment of origin, and the ultimate fate of the universe remains an enigma. These questions are discussed in detail, and the author makes clear how speculative and tentative any discussion of such matters must be given our present state of knowledge. But we are uniquely fortunate to be living in the first time in all of history when these profound questions upon which humans have mused since antiquity have become topics of observational and experimental science, and a number of experiments now underway and expected in the next few years which bear upon them are described.

Curiously, the author consistently uses the word “google” for the number 10¹⁰⁰. The correct name for this quantity, coined in 1938 by nine-year-old Milton Sirotta, is “googol”. Edward Kasner, young Milton's uncle, then defined “googolplex” as 10¹⁰¹⁰⁰. “Google^™” is an Internet search engine created by megalomaniac collectivists bent on monetising, without compensation, content created by others. The text is complemented by a number of delightful cartoons reminiscent of those penned by George Gamow, a physicist the author (and this reader) much admires.

October 2006 

Webb, Stephen. If the Universe Is Teeming with Aliens…Where Is Everybody?. New York: Copernicus, 2002. ISBN 0-387-95501-1.

October 2003 

Woodbury, David O. The Glass Giant of Palomar. New York: Dodd, Mead, [1939, 1948] 1953. LCCN 53000393.

I originally read this book when I was in junior high school—it was one of the few astronomy titles in the school's library. It's one of the grains of sand dropping on the pile which eventually provoked the avalanche that persuaded me I was living in the golden age of engineering and that I'd best spend my life making the most of it.

Seventy years after it was originally published (the 1948 and 1953 updates added only minor information on the final commissioning of the telescope and a collection of photos taken through it), this book still inspires respect for those who created the 200 inch Hale Telescope on Mount Palomar, and the engineering challenges they faced and overcame in achieving that milestone in astronomical instrumentation. The book is as much a biography of George Ellery Hale as it is a story of the giant telescope he brought into being. Hale was a world class scientist: he invented the spectroheliograph, discovered the magnetic fields of sunspots, founded the Astrophysical Journal and to a large extent the field of astrophysics itself, but he also excelled as a promoter and fund-raiser for grand-scale scientific instrumentation. The Yerkes, Mount Wilson, and Palomar observatories would, in all likelihood, not have existed were it not for Hale's indefatigable salesmanship. And this was an age when persuasiveness was all. With the exception of the road to the top of Palomar, all of the observatories and their equipment promoted by Hale were funded without a single penny of taxpayer money. For the Palomar 200 inch, he raised US$6 million in gold-backed 1930 dollars, which in present-day paper funny-money amounts to US$78 million.

It was a very different America which built the Palomar telescope. Not only was it never even thought of that money coercively taken from taxpayers would be diverted to pure science, anybody who wanted to contribute to the project, regardless of their academic credentials, was judged solely on their merits and given a position based upon their achievements. The chief optician who ground, polished, and figured the main mirror of the Palomar telescope (so perfectly that its potential would not be realised until recently thanks to adaptive optics) had a sixth grade education and was first employed at Mount Wilson as a truck driver. You can make of yourself what you have within yourself in America, so they say—so it was for Marcus Brown (p. 279). Milton Humason who, with Edwin Hubble, discovered the expansion of the universe, dropped out of school at the age of 14 and began his astronomical career driving supplies up Mount Wilson on mule trains. You can make of yourself what you have within yourself in America, or at least you could then. Now we go elsewhere.

Is there anything Russell W. Porter didn't do? Arctic explorer, founder of the hobby of amateur telescope making, engineer, architect…his footprints and brushstrokes are all over technological creativity in the first half of the twentieth century. And he is much in evidence here: recruited in 1927, he did the conceptual design for most of the buildings of the observatory, and his cutaway drawings of the mechanisms of the telescope demonstrate to those endowed with contemporary computer graphics tools that the eye of the artist is far more important than the technology of the moment.

This book has been out of print for decades, but used copies (often, sadly, de-accessioned by public libraries) are generally available at prices (unless you're worried about cosmetics and collectability) comparable to present-day hardbacks. It's as good a read today as it was in 1962.

October 2009