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«Men at some time are masters of their fates: The fault, dear Brutus, is not in our stars, But in ourselves, that we are underlings. – Cassius, from ...»

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Geoff Andersen: The Telescope

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permissions@pupress.princeton.edu Chapter 1

Men at some time are masters of their fates:

The fault, dear Brutus, is not in our stars, But in ourselves, that we are underlings.

– Cassius, from Julius Caesar (Act I, Scene ii) by William Shakespeare If you live in a big city, you have no doubt heard talk of stars. Next time you are driving across country at night or any time you are away from the city lights, stop for a while and take a good look at the sky.

How many stars do you think you can see? Generally speaking, if you are in a dark enough location, you should be able to see around 1000 stars at any given time. As the Earth rotates throughout the night and stars rise in the east and others set in the west, you can increase your count to 2000, then 2001 when the Sun rises. The total number will grow further over the course of a year, with the slow motion of the Earth around the Sun. With a visit to other latitudes to see objects otherwise hidden below the horizon, the total would come to around 6000, depending on how good your eyesight is. Some of these ‘stars’ are in fact nebulae or even one of the five planets visible to the naked eye. The total number of objects is only slightly increased by throwing in one Moon and three galaxies. Including the odd comet and closely passing asteroid, the rare supernova, the occasional Earth-orbiting satellite, that’s the entire list of objects beyond the Earth you can hope to see with the naked eye.

Given that our galaxy alone has some 10 billion stars in it, you might think that we are missing out on a lot. But our eye is doing a remarkable job even to present this view of our universe, and it is the result of much evolutionary modification. It has been theorised that the development of vision was responsible for the Cambrian evolutionary explosion some 540 million years ago. For around 3.5 billion years, life on Earth developed into just three phyla (a taxonomic grouping of plants or animals). Then, after a burst of evolutionary development lasting possibly as little as 5 million years, there were 38 phyla (which later extinctions reduced to the 35 we see today). It just so happens that natural light-sensitive receptors began to develop around this same period. Vision provides a huge selective pressure on animals to detect predators, prey, food, mates and the surrounding environment. Not surprisingly, then, eyes have developed in many different forms. Some animals are sensitive to ultraviolet or infrared radiation that we cannot see, while others have eyes specially designed for low light levels or polarised light. Even the different structures of eyes demonstrate a wide diversity: from the multi-lensed fly to the lobster, which produces images by reflection. Some creatures have zoom lenses, others have scanning optics while yet others have simple eyes which act like pinhole cameras. The eye is a remarkable piece of natural engineering, and in the case of humans, by far the most powerful of our senses.

–  –  –

Figure 1.1: The human eye.

Our best imaging takes place for light falling on the fovea which is populated mostly with colour-sensitive cones.

The human eye has many parts, but the basic design can be broken down into four major sections, as shown in Figure 1.1. There is a cornea for protection, an iris to alter the amount of incoming light and a focusable lens which forms an image onto the light-sensitive retina.

The retina has two types of light-sensitive receptors, namely cones and rods. There are about 5 million colour-sensitive cones, predominantly The naked-eye universe located within a 1.5-mm diameter region called the fovea. These provide sharp imaging over a small field of view under good lighting conditions. The 100 million rods are distributed over the rest of the retina and while not able to distinguish colours, provide most of our peripheral and low-light vision.

Overall the eye is able to image at wavelengths of light (in effect defining the ‘visible spectrum’) from around 400 nm (violet) to 700 nm (red).1 Individual cones are sensitive to a narrow range of colours centred approximately over the violet-blue, green and greenish-yellow portions of the spectrum. The actual colour of incoming light is inferred by the amount of activity triggered in each type of cone. For example, if the brain senses an equal output signal from neighbouring blue- and green-sensitive cones, then a colour lying midway between the two (something like aqua or turquoise) would be what the brain ‘sees’. The cones are separated by about 2.5 micrometres (2.5 μm) in the fovea, so the smallest angle we can resolve under ideal conditions is around 1 arcminute (or around a thirtieth of the angle subtended by the full Moon). To put it another way, this means we should just be able to make out two distinct headlights on a car around 3 km away.

As a slight diversion at this point, it is often said that the Great Wall of China is the only man-made object visible from space. This is complete nonsense, as can easily be demonstrated. From the height of the International Space Station (350 km), an angle of 1 arcminute translates to 100 m on the ground. There are, of course, a multitude of structures larger than this. For example, the Great Pyramid of Giza, at 230 m on a side would be easily visible and appear quite separate to other pyramids nearby. On the other hand, the Great Wall is a little less obvious and most astronauts, including Chinese astronaut Yang Liwei, have said it was not visible. We will address this issue in greater detail later on, but the fact that the wall is quite long (over 6000 km) means nothing – the more important factor is that it is only 15 m wide. Under the right lighting conditions, it may show up against the background, just as we see stars at night but cannot resolve them.

This leads to another property of the eye which is truly remarkable – its sensitivity to a wide range of light levels. The eye’s response to luminous flux is logarithmic, which permits us to accommodate both very bright and very dim scenes, often without even being aware of the difference. For example, you can comfortably read this book in direct sunlight, or by the light of a half-full Moon – a reduction in light levels by a factor of one million! By comparison, manufacturers of photographic film are happy with a film which can accommodate a range one thousand times smaller. Even the most advanced digital sensors would find it difficult to accommodate these extremes. Of course, the human eye cheats a little by using cones for bright light and rods for low light levels. For astronomy then, rods are the more important detector in the retina, and they lie outside our direct field of vision (the fovea). This means that to see the faintest stars it is often best to use averted vision. That is, you should look to one side of the star so that the light does not fall on the fovea, which is predominately populated with less sensitive cones. The problem with rods, of course, is that they have no colour sensitivity. This is fairly evident when you look at a nighttime scene dimly lit by the Moon, where everything loses its colour and the scene appears in shades of grey. The colours are still there – you simply can’t see them.

Beyond just collecting light, the human eye forms images of distant objects. These images are produced on the retina by the lens, in precisely the same way as a camera lens forms images on film. We’ll come back to the concept of imaging later, but for now we should note that by changing the tension in muscles surrounding the lens of our eye, the shape of the lens can be stretched or compressed in order to maintain focus over a wide range of viewing distances. The retinal image is actually produced upside down, but the brain does its own correction to this unreal situation and inverts everything back to normal. The brain then combines the light from two eyes which look at a scene from slightly different angles (parallax) to give us a sense of three dimensions. In summary, the human eye can be used to detect colours, shades, shapes, dimensions and distances. From an engineering point of view, the eye is a truly remarkable instrument;

even more so given that it is the result of millions of years of random trial and error.

Of course, the human eye does have some limitations. We cannot see radio waves, microwaves, infrared, ultraviolet, X-rays or gammarays. The refresh rate of the visual signal processing (called persistence) is around 20 times a second and changes occurring faster than this cannot be seen. At the same time, we cannot brighten the image of a dim object by staring at it for a long period of time in the same manner as a time-lapse exposure on film. Another difference between the eye and cameras is that there is no way of recording our retinal views on a permanent medium for others to see. The eye is susceptible to fatigue, disease and aging, which can affect resolution, focusing and The naked-eye universe sensitivity. On top of this, the eye (or more correctly, the brain) can also be confused and fooled by certain arrangements of objects. In spite of these limitations, though, the eye is a remarkably versatile instrument.

Often when considering a telescope, people will be prompted to ask: ‘Just how far can it see?’ Later in this book it will become clear just how meaningless this question is, but for now consider applying the same question to our eye. You can see objects sitting right in front of your face, but at the same time you can see a mountain dozens of kilometres away. Alpha Centauri is around 40 trillion kilometres away, and Andromeda Galaxy, also visible to the naked eye in dark skies, is nearly a million times more distant than this. So really, whether the eye can see an object comes down to how big and bright the object is, not how far away it is. Of course, seeing light from a star is not the same as forming an image of it – after all, a point of light is not an illuminated disk, so this is where it becomes meaningless to consider these sorts of issues. In fact, it is because we cannot see any of their details that cosmic objects have always held such a fascination for us.

As you look at the stars, try to imagine yourself as an Egyptian sailor on the Mediterranean Sea some four-and-a-half thousand years ago.

From an early age, you would have been taught how to find the dim star Thuban. Throughout the entire night, it would serve as an unwavering beacon by which to navigate. Even after the most disorientating of storms, this star always lay to the north. It is no wonder, then, that Pharaoh Khufu aligned his Great Pyramid to this most important of stars. It is in contemplating the history of naked-eye observations of the sky that we begin to appreciate why such observations have had such a powerful effect on mankind throughout the ages.

Every star (except the Sun) rises and sets around four minutes earlier every night. Over 365 days, this amounts to a complete day, so the rising or setting of a particular star at a particular time can be used as a measure of a year. The same Egyptian sailor, as a long-time observer of the heavens, would know that the rising of certain groupings of stars at dusk indicates the onset of particular seasons. This knowledge could be used to anticipate the annual flooding of the Nile and for planning harvests and plantings. To nomadic civilisations, accurate timekeeping was equally important for following migratory animals and preparing for the harsh environmental conditions of particular seasons. As civilisations developed, crop rotations and agricultural storage requirements were determined by a ‘calendar’ which was essentially a measure of the motion of the stellar sphere.

Naturally it was easy to believe that these groupings of stars were not simply passive markers of time, but exerted an active influence over life on Earth. These groupings (asterisms or constellations) were associated with physical objects or gods as long ago as 4000 BCE, and from there it was a small step to anthropomorphising their forms. The constellations thus became powerful gods influencing our lives, which inevitably led to religious and superstitious rituals and beliefs. Temples were built and offerings and sacrifices were made to influence the gods to provide bountiful harvests and improve living conditions. These gods were regarded as powerful enough to control human existence, so they were not to be trifled with. The intertwining of superstitions and religion continued even into the modern era. For example, the Catholic Church used astrological charts until well into the eighteenth century.

While many people still believe in astrology today, it clearly makes no sense. The constellations used for astrological ‘signs’ are merely apparent groupings of stars which are actually unrelated and lie at completely different distances. They have no physical existence – you could never ‘visit’ a constellation. Furthermore, there are three planets which are used in present-day astrology whose existence was not even known before the eighteenth century, so those who purport to be using ‘ancient mystical knowledge’ are relying more on the gullibility of the uneducated than on any secrets of civilisations past. It is also worth mentioning that there are in fact 13 Zodiacal constellations, with Ophiuchus lying between Libra and Sagittarius.

While the stars appear to move around us, their motions are really only telling us where we are and what time it is.

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