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[1.0] The Invention Of The Telescope

v3.0.0 / chapter 1 of 5 / 01 nov 16 / greg goebel

* From ancient times astronomers had carefully watched the heavens, but though they developed ever more sophisticated tools to watch the skies, for millennia all their observations were performed with the unaided eye. The telescope was finally invented early 17th century, opening up the Universe to astronomers, and leading to an endless race to build more powerful telescopes.

Huygens' aerial telescope


[1.1] THE EYEBALL ASTRONOMERS
[1.2] THE FIRST TELESCOPES
[1.3] GALILEO'S TELESCOPIC OBSERVATIONS
[1.4] THE KEPLERIAN TELESCOPE
[1.5] THE LONG TELESCOPES
[1.6] CLOCKS AND THE ASTRONOMERS
[1.7] THE MICROMETER
[1.8] MAPPING THE SKY WITH THE TELESCOPE

[1.1] THE EYEBALL ASTRONOMERS

* Humans have been observing the night sky since prehistory, but before the scientific revolution, all their observations were by "eyeball". The positions and movements of various objects in the sky could be tracked with mechanical aids, such as sticks or arrangements of stones -- the famous structure known as Stonehenge in southern England was laid out with an eye to tracking the sky and the seasons -- but nobody had any better idea of what the objects in the sky were than what could be seen with the naked eye.

Of course, the Moon appeared to be another world of its own, but the stars didn't seem to be anything more than points of light, any more than were the planets that wandered through the otherwise fixed patterns of the sky. Every now and then a fuzzy "comet" would pass through the sky on a completely unpredictable basis, often causing public consternation. In the West, in the 2nd century CE a scholar named Claudius Ptolemaeus (~100:170 CE), better known as "Ptolemy", published a description of the cosmos, in which the stars were simply lights or holes on a distant sphere, with the planets arranged on transparent spheres below. All the spheres were perfectly circular. Since the planets had irregular motions, sometimes reversing their course in the sky for short times, the planets actually moved on an "epicyclic" arrangement of spheres-on-spheres that became increasingly complicated.

The basic concept had been originally devised by Aristotle (384:322 BCE), the most influential ancient Greek scholar, and extended by the 2nd century BCE Greek astronomer Hipparchus (~190:120 BCE), one of the greatest of the "eyeball" astronomers. The Ptolemaic system did account for the movements of the planets, though it was cumbersome and not very elegant even on its own terms. The problem was that nobody thought the Earth orbited around the Sun; certainly that would have seemed like a bizarre idea, since the Sun could be seen cycling around the Earth on a highly predictable daily basis, and the Earth underfoot seemed entirely immobile.

The early astronomers did achieve some other successes with "eyeball" methods. About 240 BCE, the Greek geographer Eratosthenes (276:195 BCE) managed to determine the diameter of the Earth -- even in ancient times, educated people knew the Earth was round, it could be seen to be curved from the way ships would disappear over the horizon. Eratosthenes, who worked in Alexandria, Egypt, observed that the Sun was 7 degrees off the zenith (the line straight up into the sky) at noon on 21 June, the day of the summer solstice. He learned that the Sun was directly overhead at what is now Aswan, well to the south up the Nile, at the same time, and a little simple geometry gave him the size of the Earth.

Hipparchus later leveraged off this knowledge to obtain the distance from the Earth to the Moon, as well as the size of the Moon. In 129 BCE, there was a total eclipse of the Moon. As is true with all total eclipses, they only occur along a single track across the Earth, with areas outside of the track observing a partial eclipse. Knowledge of the locations of where the eclipse was total and where it was partial, by a given amount, allowed determination of the distance to the Moon by a little trigonometry. Of course, once the distance was known, its size could be determined as well.

* Attempts to determine the distance from the Earth to the Sun and from the Earth to the planets didn't work out so well. Determining the distance to the stars was obviously impossible with the technology available. Still, astronomers continued to observe the heavens with "eyeball" methods. The tools they used could not provide magnification; they could only determine the celestial "longitude" and "latitude" of objects in the sky.

The "armillary" was one device used to measure celestial longitude. There were various forms, but a typical configuration involved a fixed ring mounted to parallel the Earth's equator. The ring was marked; the armillary included a second, movable ring or an arm to help pinpoint the position of a celestial object. The "quadrant" was one of the devices used to measure celestial latitudes. It consisted of a quarter of a circle, with markings along the rim, a plumbob to align the device to the vertical, and a moveable arm with sights that was used to target a celestial object. There were a number of variations on and combinations of these two schemes, but they were all functionally equivalent. It was also handy to have some sort of timepiece to match the celestial longitude of an object to a set time, but before the scientific revolution clocks were limited to sundials, water clocks, and primitive and inaccurate clockwork systems.

One of the most famous and sophisticated of the "eyeball" astronomers was Tycho Brahe (1546:1601), a Dane who set up an astronomical observatory on the island of Uraniborg in the Baltic. His instruments were built to a high level of craftsmanship, and his measurements were very precise.

At the time Tycho was performing his observations, a scientific revolution in astronomy was brewing. The Polish astronomer Nikolas Copernicus (1473:1543) began the revolution by publishing a text that suggested the Earth orbited the Sun, not the reverse. Copernicus realized his "heliocentric" theory would be controversial and made sure the text was published posthumously, in fact on the day he died. Tycho Brahe was not fond of the idea, but his assistant Johannes Kepler (1571:1630) was intrigued, and after Tycho's death Kepler used his master's data to flesh out the concept.

Copernicus had not been willing to completely discard old ideas: although he envisioned the Earth orbiting the Sun, he retained the old epicyclic scheme, with the Earth riding on spheres on a sphere to account for idiosyncrasies in its motion. Kepler went farther and stated that the planets orbited the Sun in ellipses, with the Sun at one of the focal points. He was able to neatly match his model to the actual motions of the planets, lending considerable weight to his argument: it was so much cleaner than the old Ptolemaic system of epicycles. However, it was still a major conceptual leap: how could the obviously immobile Earth be orbiting around the Sun? By itself, Kepler's theory was a hard sell.

Incidentally, the Uraniborg observatory didn't survive to the present. After Tycho's death, it fell into disrepair and was gradually salvaged by locals until there was nothing left. As for Tycho's instruments, they were put into storage to be burned in the violence of the Thirty Years' War (1618:1648), and lost forever.

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[1.2] THE FIRST TELESCOPES

* As often happens with revolutions in technology, a number of separate elements came together at the same time to produce a greater effect than any one of them could on its own.

The ancient Greeks knew that water-filled glass globes could concentrate light and be used to start fires, and that knowledge had led to the construction of simple "convex" lenses -- discs of glass that were thick in the center and thin on the edges. If the lens was flat on one side, it was a "plano-convex" lens; if the lens was curved on both sides, it was a "biconvex" lens. The first person to perform a methodical analysis of the action of light and lenses was the brilliant Arab researcher Ibn al Haythen, known in Europe as Alhazen (~965:1038). His works were translated into Latin over a century after his death, and European researchers began to follow up on his ideas.

The most prominent early European studies on lenses and optics were performed by two Englishman, Robert Grosseteste (1175:1253) and his student, the famous Roger Bacon (1220:1292). Bacon used a lens as a magnifying glass to help him read, and suggested the concept of spectacles, as an aid for reading for older people and others with weak short-range vision. By the year 1300, spectacles were being manufactured and sold in Italy. They soon became popular and led to the first true optics industry.

Of course, manufacture of lenses led to further research and technical refinements. One was the development of "concave" lenses, which are thick on the edge and thin in the center. If such a lens was flat on one side, it was a "plano-concave" lens; if it was concave on both sides, it was a "biconcave" lens. While a convex lens magnifies an image, a concave lens reduces it in size. That might seem of limited usefulness, but it was helpful for people with weak long-range vision, and spectacles with concave lenses were in production by about the year 1450. This led in turn to "concavo-convex" lenses that were concave on one side and convex on another, with the lens shape tailored to provide better vision correction.

The Netherlands became a particular center for lens crafting. Hans Lippershey (1570:1619), a spectacle-maker in the Dutch of Middelburg, came up with the idea of using two lenses in series to magnify distant objects. As the story goes, in 1608 his apprentice was fiddling around with two lenses and noticed that when he held them in series, he could see distant objects up close. The apprentice told his master Lippershey about it; Lippershey fitted the two lenses into a tube and produced the world's first telescope.

Actually, the idea was so straightforward that anybody who had a collection of lenses sitting around the shop was likely to stumble on to it while playing around in an idle moment, and it appears that a number of different spectacle manufacturers developed the telescope roughly in parallel. One of Lippershey's local competitors, Zacharias Janssen (1580:1638) later claimed to have built a telescope in 1604. It's possible that Lippershey simply lifted the idea from Janssen or another competitor and claimed he had invented it himself -- but whatever the case, Lippershey was the most aggressive in promoting the idea, selling it to the Dutch government for military purposes.

Of course, word began to spread and within a few years telescopes were widely available. They weren't called "telescopes" at the time, however; they were given various names such as "looker", "far-seer", "cylinder", "perspective", and so on, in various languages. In 1612, a Greek mathematician named Ioannes Dimisiani suggested the name "telescope", Greek for "far-seer", and by the end of the century that name would become effectively universal for the device.

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[1.3] GALILEO'S TELESCOPIC OBSERVATIONS

* In 1609, the great Italian scientist Galileo Galilei (1654:1642), then at the University of Padua, heard about the telescope, and decided to build his own. After a troublesome search for usable glass, he ground a plano-convex lens and a plano-concave lens, both 4.2 centimeters in diameter, and fitted them into a lead tube. He looked through the concave lens, which was the "eyepiece", with the convex lens, the "objective", admitting light into the front of the tube. It could magnify about three times. He demonstrated it to officials of the city-state of Venice, who were suitably impressed, and saw to it that the university granted him academic tenure -- just as or more valued then as it is now -- and a raise in salary.

Galileo continued to build telescopes, constructing one with a magnifying power of 33, and then turned it on the skies. It was a revelation. Although anyone could see with the naked eye that the Moon had surface details of sorts, nobody had ever made them out clearly before. Galileo saw mountains, craters, and vast dark plains that suggested seas ("maria"). In other words, it really was a world like the Earth, at least in a general sense, and not merely a perfect heavenly sphere painted with cryptic markings.

He then turned his telescopes elsewhere in the sky, and found the numbers of stars vastly increased. The bright star cluster known as the "Pleiades" revealed an order of magnitude more stars through the telescope than could be seen by the naked eye. The Milky Way, the stream of faint light running through the heavens, turned out to be made up of almost countless stars. The five planets known to the ancients -- Mercury, Venus, Mars, Jupiter, and Saturn -- could sometimes be seen as discs through the telescope, not simple points of light, suggesting they were distant worlds in themselves.

Galileo's observations of the planet Jupiter led to a particularly breathtaking discovery. On 7 January 1610, he was observing Jupiter and noticed that it was flanked by three small starlike dots in a straight line. He continued his observations on following nights, watching the dots move towards and away from Jupiter. On 13 January, he spotted a fourth shiny dot. He concluded that Jupiter had four moons and produced simple plots of their orbits.

Galileo published the results of his observations in March 1610 in a small pamphlet titled SIDEREUS NUNCIUS (Latin for "Messenger From The Stars"). Galileo's observations were so revolutionary that he was denounced as a fraud and worse. The notion that Jupiter had moons was particularly distressing, because it implied there were other centers to the Universe than the Earth. However, a German astronomer named Simon Marius (1570:1624) used his Dutch-built telescope to observe the four moons as well, and even claimed he had spotted them before Galileo did. That might possibly have been true, but then as now priority went to the researcher who published first, and so Galileo rightly gets the credit.

Marius did manage to put his own stamp on the discovery. Although Galileo wanted to call the four moons of Jupiter the "Medician stars" to court favor with the powerful Medici family, Marius named them (in the order from the innermost to the outermost moon) "Io", "Europa", "Ganymede", and "Callisto". Theses names would stick, though they would become known as the "Galilean moons" in honor of Galileo. They are actually substantial worlds of their own, and would even be visible to the naked eye if Jupiter's light didn't drown them out.

Galileo continued his own observations, observing that Saturn seemed to one large planet that was flanked by two smaller bodies; he was puzzled when the two smaller bodies shrank and finally disappeared over the next two years. He also observed the phases of Venus. There was no way the phases of Venus were consistent with the Ptolemaic scheme, and his observations provided another item of proof for the heliocentric theory.

In 1611, Galileo performed observations of the Sun, presumably when it was low in the sky and shining through fog, but almost certainly damaging his eyes in the process. However, he did observe that the Sun had spotted markings. That was another outrageous concept, since up to that time the Sun had been regarded as a perfect body. A German astronomer named Christophe Scheiner (1579:1650) suggested that they might be small objects in the line of sight between Earth and Sun, but Galileo observed that the spots appeared shortened when they reached the Sun's "limb", the edges of its disc, and that would not be the case unless they were part of the Sun's surface. He believed they were some sort of cloud in the Sun's atmosphere, and published his new findings in 1613.

By that time, the Copernican system and Galileo's findings were coming under fire from the established authorities, and over the next two decades the quarrel grew increasingly bitter. Finally, in 1633 the Church forced Galileo to recant and put him under house arrest.

Galileo rightly remains a symbol of independence and rationality against superstitious authority -- but the story is muddied on closer inspection by the fact that Galileo did much to bring misfortune down on himself. He was vain, arrogant, petty-minded, quarrelsome, inclined to pour sarcasm on lesser intellects, and he thoughtlessly made many enemies who wished to put him in his place. When one of his writings featured a simple-minded character who could be interpreted as representing the Pope himself, they moved in on him. Galileo was brought to trial, humiliated, forced him to recant, and placed under house arrest. However, the success of his enemies backfired magnificently: in a grand Zen irony they made him into a hero for all history, an honor the disagreeable Galileo couldn't have achieved on his own.

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[1.4] THE KEPLERIAN TELESCOPE

* The limited nature of the persecution of Galileo was emphasized by the fact that new discoveries about the heavens continued to pour in with little or no official obstruction. The telescope provided such an expanded vision that astronomers hardly knew what to make of all their new discoveries. They were helped by an improved telescope design devised by Johannes Kepler.

Kepler obtained a telescope in 1610. He quickly grasped its principles and came up with ideas for how it might be improved. Galileo's telescope featured a convex objective lens and a concave eyepiece; light rays passed through both the objective and the eyepiece before coming to a focus. Kepler proposed building a longer telescope with a convex objective and a convex eyepiece, with the image obtained by the objective lens passing through its focus before reaching the eyepiece lens. The Keplerian design permitted the construction of telescopes with a wider field of view and greater magnification than the Galilean design. It did have the disadvantage that it flipped the image upside-down, but that wasn't much of a problem for heavenly objects.

Kepler's eyesight was poor and he didn't have mechanical aptitude to build a telescope himself, but the Keplerian telescope was such an advance that it quickly became the tool of choice for astronomers. In the 1640s, an Italian astronomer named Franciscus Fontana used a Keplerian telescope to observe that the surface of Jupiter was marked by "belts", and that Mars had indistinct markings as well. Another Italian astronomer, Giovanni Battista Riccioli (1598:1671), observed the shadows of the moons of Jupiter on their mother planet, confirming that most or all of Jupiter's light was reflected sunlight and not generated by the planet itself.

The Polish astronomer Johannes Hevelius (1611:1687) published the first detailed map of the Moon in 1647. Hevelius assigned names to prominent features, but though his names for mountains and maria caught on, most of the craters were named by Riccioli. Riccioli thought that craters should honor astronomers -- no wonder his scheme caught on -- and named the brightest crater "Tycho" in honor of his hero Tycho Brahe. Riccioli also discovered the first "double star" in 1650. Other observers discovered faint fuzzy objects in the fixed field of stars that were sometimes reminiscent of comets; they would be named "nebulas", from the Latin for "cloud".

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[1.5] THE LONG TELESCOPES

* The Keplerian design still left room for improvement. For example, there was the matter of the inverted image. In 1645, a Bohemian astronomer, Anton Maria Schyrle, invented a multi-lens eyepiece that would flip the image back rightside-up. There were other problems that weren't as easy to fix. Kepler had performed an analysis of lenses and concluded that the existing way of grinding the lenses, so that they had a surface that matched a section of a sphere, didn't work very well: it didn't bring all the light rays to the same focus. This error became known as "spherical aberration". There was another error, in which images were surrounded by colored halos. This error was called "chromatic aberration".

Nobody understood enough about light at the time to make much sense out of chromatic aberration, but researchers quickly got a handle, or at least half of one, on spherical aberration. The Dutch mathematician Willebroerd Snellius, better known as Snell (1591:1626), observed that if light passed from one medium with a given index of refraction into another with a different index of refraction, the angle of the path of the light relative to the perpendicular of the plane of the interface between the two mediums would change. This had been known for a long time in itself. What Snell brought to the party was the realization that the ratio of the indexes of refraction would be same as the sines of the angles of the path of light relative to the perpendicular.

"Snell's law", as it came to be known, was popularized by the French mathematician Rene Descartes (1596:1650) in a document published in 1638. Snell's law provided the theoretical tools for designing better lenses, but unfortunately the technology didn't exist to grind a lens in a predictable way that had anything but a spherical section. The law did suggest that if the section of the sphere were small enough -- that is, the lens had very shallow curvature -- then the effects of spherical aberration would be minimized. Chromatic aberration would be reduced as well, but it wouldn't go away.

The problem with using lenses with such shallow curvature was that it meant a really long focal length and so a long, unwieldy telescope. The second half of the 17th century led to a race to develop longer and longer telescopes. The race was set off by the Dutch scholar Christiaan Huygens (1629:1695), who built a telescope in 1655 that had an objective lens 5 centimeters in diameter, a length of 3.6 meters, and a magnifying factor of about 50 times. Huygens was particularly interested in Saturn and the mysterious "handles" reported by Galileo. When Huygens turned his new telescope on the planet, however, he couldn't see the "handles" -- but he did find a starlike object in the close vicinity of the planet that he ultimately determined went around it every 16 days. In 1656 he announced that Saturn had a moon, which would ultimately be named "Titan". Centuries later, the first space probe to be sent to Titan was named "Huygens" by the European Space Agency (ESA) in his honor.

Huygens kept on building longer and more powerful telescopes, reaching one that had a length of 37 meters! He finally began to spot the "handles" reported by Galileo, and in 1659 announced that Saturn was surrounded by a ring. The reason the ring had seemed to disappear was because it was about edge-on to the Earth's line of sight when Huygens began his observations, and it took a few years for the viewing angle to change enough to make it visible again.

Hevelius built an even longer telescope with a length of 46 meters. It featured a wooden frame and was all but impossible to use, requiring a troop of assistants to keep it on target, when it could be done at all. Some astronomers speculated about telescopes over 300 meters long, but Hevelius was pushing the practical limits of the technology. Huygens did invent an unorthodox "dodge" to address some of the problems, in the form of the "aerial telescope". This featured an objective lens assembly on a platform that could be raised or lowered by rope on the side of a pole, and a separate eyepiece assembly linked to the objective lens by a taut cord. The observer could move the eyepiece assembly around and the cord would, in principle, allow the objective lens assembly to "track" it. It was one of those inventions that in hindsight seems half-brilliant, half-mad, but it did make the long telescope somewhat easier to handle.

The English researcher Robert Hooke (1635:1703) came up with a conceptually more elegant solution, what would now be called "folded optics". He envisioned a Keplerian long-focus telescope built in the form of a long box that had the objective lens on one side, the eyepiece on the other, and a set of mirrors in between that bounced the light back and forth. It was a slick idea -- but unfortunately, the technology for building nice flat mirrors was no more advanced at the time than the technology for grinding lenses, and it couldn't be made to work for the moment.

Easy to handle or not, astronomers would be stuck with the long telescope well into the next century, and used it to make significant discoveries. Giovanni Domenico Cassini (1625:1712), an Italian-born astronomer who worked mostly in France, discovered what would be known as the "Great Red Spot" of Jupiter in 1664; it is now known to be a very long-lived cyclonic storm. Another Italian astronomer, Francesco Maria Grimaldi (1618:1663), observed that Saturn was slightly flattened at the poles. Cassini corroborated this observation and also found that Jupiter was similarly flattened. This was another shock to the old ways of thinking, since it showed the planets weren't perfect heavenly spheres.

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[1.6] CLOCKS AND THE ASTRONOMERS

* Cassini went on two discover four new moons of Saturn -- Iapetus, Rhea, Tethys, and Dione -- as well as the "gap" in Saturn's ring that is now known as "Cassini's division", showing the ring to actually be a system of rings. The first Saturn orbiter probe was named "Cassini" in his honor by the ESA; it carried the Huygens Titan lander. However, Cassini's most significant contribution to astronomy was arguably not from his observations, but from his use of mechanical clocks in astronomy.

Mechanical clocks had been around since the 1300s. Early mechanical clocks were driven by a weight on a chain that turned the clockwork around; these devices were highly inaccurate and were only fitted with one hand, which timed through quarter hours. Something needed to be added to allow them to keep better time. The key was Galileo's discovery that a pendulum of a given length had a period of oscillation proportional to its length, no matter how long or short the swing of the pendulum was. Galileo didn't carry the concept much farther than that, but in 1656 Huygens began work on a pendulum clock. It was a tricky job -- the period of a pendulum of a given length is not precisely constant for different lengths of swing, and Huygens had to figure out schemes to minimize the variations.

By 1659, Huygens had a working pendulum clock. In 1670, an English clockmaker named William Clement used a longer pendulum with a period of a second, with the clockwork mechanism driven by a falling weight, and enclosed the mechanism in a case to keep it from being disturbed by air currents. Clement had invented the "grandfather clock". Clocks would also be built using pendulums spinning on a wire, which had a similar periodicity as they spun one way, then spun back the other. In both cases, the speed of the clockwork mechanism was regulated by a toothed "escapement wheel" and a "pivot" that was connected to the pendulum on one end and meshed with the escapement wheel with two teeth on the other. The pivot would shift back and forth along with the pendulum, only allowing the escapement wheel to advance a tooth at a time, while the escapement wheel provided a little force in return to keep the pendulum oscillating.

Pendulums weren't generally useful for clocks on the move, but an equivalent scheme was discovered, involving a loosely-wound spiral "hairspring" inside of a relatively massive ring or "balance wheel", functionally equivalent to a spinning pendulum: the balance wheel drew up the hairspring, which then sent it spinning back in the other direction. The result was the pocket watch, which was driven by a tightly-coiled "mainspring" through an assembly of clockwork gears. In either case, clocks could now be built with minute hands -- and ultimately even second hands -- that actually meant something.

Since one of the functions of astronomers since antiquity had been to track the timing of celestial motions, once relatively accurate clocks were available, astronomical observatories quickly acquired them. Jean Picard (1620:1682), who ran the Paris Observatory, bought clocks for his establishment, and Cassini made good use of them in his work there, in particular finding out in 1665 that Jupiter rotated once every 9 hours 56 minutes.

* Clocks also helped give the first proper estimates of the size of the Solar System. Although nobody had an accurate measurement of the absolute distances of the known planets from the Sun at the time, Kepler's analysis of planetary orbits allowed astronomers to determine the relative distances with fair accuracy. That meant that if the distance from the Earth to another planet were known, everything would fall into place.

In 1670, Picard and Cassini decided to determine the absolute distance from the Earth to Mars, which would give the other absolute planetary distances as well. They intended to use a "parallax" measurement, observing Mars during its closest approach to Earth from two different and widely-separated locations at the same time; determining the angle of line of sight from Earth to Mars at each location; and then using simple trigonometry to give the distance.

Of course, parallax measurement works better if the "baseline" between the two observing sites is wide, and so the astronomer Jean Richer (1630:1696) was dispatched to the French colony of Cayenne, in what is now French Guiana in equatorial South America, to make one measurement while Cassini made the other. Cayenne was about 6,500 kilometers over the surface of the Earth from Paris, or (more relevantly for purposes of parallax measurement) about 6,000 kilometers in a straight line bored through the surface of the Earth. Taking such a long sea trip at the time was very troublesome and difficult, and tropic lands were full of diseases that gave visits to such places by Europeans a level of risk roughly on the same order as that of playing the modern game of Russian roulette -- but Richer made the trip, arriving in Cayenne in 1671.

Performing simultaneous parallax measurements in the two remote locations meant synchronizing the observations with clocks: Mars had to be observed at the same time in both locations to get proper results. Richer performed astronomical observations to set his clock precisely -- more on this concept below -- though he ran into an odd anomaly, finding the clock seemed to be keeping slightly slower time than it did in Paris. He had no idea why this was so, but we now know it was because the Earth isn't a perfect sphere, it bulges at the equator, the bulge results in very slightly lower gravity, and a longer pendulum beat, just enough to throw off measurements. In any case, Richer essentially shrugged, figured out the size of the discrepancy, and compensated for it.

When Richer returned safely to Paris in 1673, Cassini used the sets of measurements to calculate the distance to Mars. Although his results weren't very accurate by modern standards, they were definitely in the ballpark, with the Earth being judged about 140 million kilometers from the Sun, about 4% less than its actual value. This was an absolute shock to scientists of the time, since such distances were all but unimaginable. Saturn, for example, was well over a billion kilometers away. The Sun turned out to have a diameter a hundred times that of Earth, while Jupiter was 11 times wider than the Earth.

* The use of clocks in astronomy led to another surprising, and closely related, discovery, though the story is roundabout. Galileo had tinkered with the idea that the movements of the moons of Jupiter could be used as a kind of "universal clock". All he had to do in principle was develop tables of the times they would disappear behind the planet -- be eclipsed by it, in other words -- and then the movements of these moons could be used as a standard time reference by any observatory in the world.

The scheme could be also used to determine geographic location. Although determining latitude is fairly easy -- in the northern latitudes, all it requires is a measurement of the angle of the Pole Star above the horizon -- finding longitude is substantially trickier. Longitude can be determined from the difference between the time of high noon in one location and the time of high noon at the longitudinal meridian ("zero longitude"), which runs through Greenwich, England. If an astronomical observatory were set up at a remote location, astronomers could observe the eclipses of the moons of Jupiter, set a clock accordingly to Greenwich time, then observe the difference between that and local high noon to get the exact longitude. This was the sort of observation that Richer performed to calibrate his clock; the same sort of scheme was considered for maritime navigation, but it was far too difficult to perform on a vessel at sea to be workable.

There was also a problem in that the times of these eclipses tended to vary off schedule by some number of minutes one way or another, with the eclipses lagging when the Earth was relatively far away from Jupiter and catching back up again as the Earth came closer to Jupiter. In hindsight, the answer was obvious: the time lags were due to the fact that light had a finite speed.

Galileo had tried to determine the speed of light by signaling an assistant on a distant hill with lamps, but all he could determine was that if light had a finite speed, it was much too fast to be measured using such a method. Ironically, it was his observations of the moons of Jupiter that led to the actual answer. In 1675, using the solar system dimensions provided by Cassini and company, a Danish astronomer named Olaus Roemer (1644:1710) analyzed the variations in time and concluded that it took light 22 minutes to pass from one side of the Earth's orbit to the other. He managed to calculate a value of the speed of light of about 227,000 kilometers per second, not a bad initial estimate compared to its actual value of about 300,000 kilometers per second. Scientists were beginning to think in terms of larger and larger numbers of zeroes.

Incidentally, the maritime navigation problem was solved by an English clockmaker named John Harrison (1693:1776) after an epic intellectual struggle. In 1759, he built what amounted to a large, precisely-engineered pocket-watch that kept highly accurate time. Ships could synchronize such a "chronometer" to Greenwich time before leaving port, and then refer to it at sea to help determine their longitude.

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[1.7] THE MICROMETER

* In the first decades of observing the sky with telescopes, all astronomers actually did was look at things. That was fine in and of itself, but science is based on measurements and simple observations aren't really enough.

In 1638, the English astronomer William Gascoigne (1612:1644) invented the "micrometer" -- a simple device, consisting of two strips of metal placed at the focal point of a telescope that could be pivoted together or apart with turns of a screw. By placing the edges of the strips up against the bounds of a celestial object, the angular size of that object could be estimated.

Gascoigne didn't publicize his invention, and the English Civil War disrupted scientific research in the country; Gascoigne himself was killed in action at the Battle of Marston Moor in 1644, and his invention was forgotten. In 1658, Huygens tinkered with devices for measuring the angular size of celestial objects but went nowhere with the effort. It wasn't until 1666 that the micrometer was properly re-invented by the French astronomer Adrien Azout (1622:1691) -- though he used hairlines instead of metal edges, creating the "filar micrometer". Hooke also invented a micrometer at about the same time, and records of Gascoigne's work also resurfaced.

In 1667, Picard used a telescope with a micrometer to perform very precise distance measurements by triangulation of locations around the city of Paris. His goal was actually to determine the deviation of a triangle due to the curvature of the surface of the Earth: the sum of all the interior angles of a triangle drawn on a ball is more than 180 degrees, and increases as the curvature increases. Picard used this information to obtain an improved estimate of the diameter of the Earth reasonably close to its modern value. The English physicist Isaac Newton (1642:1727) used this value to work out contradictions he had encountered in calculating the orbit of the Moon using the older, much less accurate value for the diameter of the Earth.

Picard, who as mentioned was also a pioneer in the astronomical use of clocks, came up with an idea for linking the clock and the micrometer. He suggested the construction of a telescope mounted so it could be pivoted up and down at precise angles along the line of longitude, the "local meridian", at a location, but could not be turned from side to side to observe any other line of longitude. The telescope would have a micrometer that would be used, in conjunction with a clock, to precisely mark the time a celestial object passed the local meridian. That would allow a very precise reckoning of the exact "celestial coordinates" of the object, or in other words its "grid location" in the sphere of the heavens above. Picard didn't live long enough to build such a "transit instrument", but Olaus Roemer built one in Copenhagen in 1684.

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[1.8] MAPPING THE SKY WITH THE TELESCOPE

* The micrometer gave astronomers the tool they needed to build new, more accurate sky maps. Tycho's maps of the stars were still "state of the art" in the 1670s, even though they had been constructed strictly by eyeball and had an accuracy of only about one minute of arc (a sixtieth of a degree).

In 1676, the English astronomer Edmund Halley (1656:1742) decided to construct the first telescopic sky map. Since such sky maps as were then available of the southern skies were far inferior to those of the northern skies, Halley decided to perform his sky survey of the southern skies. He went to the island of Saint Helena, where Napoleon Bonaparte would live out his life in exile much later, which was 16 degrees south of the equator in the Atlantic. Halley was equipped with a refracting telescope 7.3 meters long with a micrometer, as well as precision clocks. The weather in Saint Helena tends toward the damp, which is not favorable for astronomy, but in two years Halley managed to put together a map of 341 stars in the southern skies.

Back in England, an astronomer named John Flamsteed (1646:1719) decided to draw up a telescopic sky map of the northern skies. He had been appointed the first astronomer royal by King Charles II in 1675. Incidentally, the primary function of the Royal Observatory was to provide astronomical data for navigational purposes, with pure research a strictly secondary objective.

Flamsteed set up an observatory at Greenwich in the London area. He had few resources, but he managed to scrounge up a useful if unspectacular collection of equipment. He was single-minded in the work on his sky map, taking every pain to make sure it was correct. Edmund Halley grew impatient with Flamsteed's perfectionism, and decided to publish Flamsteed's data on his own initiative in 1712, which led to considerable friction between the two men. Flamsteed would not be hurried; and in fact the authorized version of his star map, the HISTORIA COELISTIS in three volumes, wasn't published until 1725, years after his death. It was generally worth the wait. It listed 3,000 stars and gave their positions to within ten seconds of arc, six times more accurate than Tycho's map.

* The new star maps provided yet another startling revelation about the skies. In 1718, Halley announced that the positions of three bright stars, Sirius, Arcturus, and Aldebaran, were well off those given by the ancient Greek eyeball astronomers. The discrepancies seemed unlikely to have due to human error: different sky maps created by different Greek astronomers all more or less gave the same positions of these stars, and the bulk of the stars in the old maps were still in the same positions, within the limits of the "error boxes" of the old measurements.

Halley's suggestion was that the "fixed" stars were not simply fixed lights in the heavens: they were distant suns that they had a "proper motion" of their own through the sky, one star going in one direction, another going in another. The closer of these distant suns could be assumed, as a very rough first approximation, to be generally brighter in the night sky than more distant suns, and so their proper motions would be most visible. Halley calculated the distance of Sirius by assuming it was the same brightness as the Sun, and came up with a value in modern terms of about two light-years.

Sirius is actually well brighter than the Sun and this value is less than a quarter of the actual distance of 8.8 light-years, though it was still another big leap of scale for the astronomers of the period. Halley understood that Sirius might well be well dimmer or brighter than our Sun, but he had no way of determining by how much, and so his assumption was reasonable. Determining the actual distance to Sirius would require a parallax measurement, checking the angle of the line of sight to the star over a period of six months, when the Earth was at the opposite extremes of its orbit. Halley also understood that obtaining such a precise measurement was pushing the state of the art of astronomical technology.

* Of course, there were bold souls who took a shot at determining "stellar parallax" anyway. In 1725, an Irishman named Samuel Molyneux (1689:1728) set up a long telescope as a fixed transit instrument alongside the chimney of his house in Yew, in the London area. He planned to use it to observe transits of the star gamma Draconis in order to determine its parallax. His day work at the British Admiralty got the better of him, however, and he had to pass the project on to his associate in matters astronomical, James Bradley (1693:1762).

Bradley began his observations of gamma Draconis late in 1725. Over the next three years he discovered that the position of the star seemed to shift by 40 seconds of arc over the course of a year. However, other stars showed this same shift, which suggested that something was not quite right.

As it turned out, the shift Bradley observed had nothing to do with stellar parallax. It was simply due to the motion of the Earth in its orbit. Suppose Alice is walking in a rainstorm with an umbrella. Even if the rain is falling straight down, her forward motion will cause the rain to fall under the forward edge of the umbrella and behind the rear edge of the umbrella. The umbrella needs to be tilted forward slightly to make sure she stays dry. The same is true of a telescope: it needs to be tilted ever so slightly to compensate for the motion of the Earth.

Bradley knew that the observed aberration of light did not give the distance to gamma Draconis, but understood that it did give the ratio of the speed of light to the speed of the Earth in its orbit around the Sun. Since the speed of the Earth was relatively well known at the time, he was able to come up with a velocity of light of 301,000 kilometers per second, very close to the real value and a much better estimate than Roemer had provided decades earlier. Bradley published his results in 1729. It was a significant discovery in fundamental physics, but it didn't bring anyone very much closer to determining stellar parallax for the time being.

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