S194_1

The Sun

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This free course provides a sample of level 1 study in Science http://www.open.ac.uk/courses/find/science

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Contents

- Introduction

- Learning outcomes

- 1 Observing the Sun

- 1.1 The Sun at visible wavelengths

- 1.3 Beyond visible light

- 1.4 The invisible Sun

- 2 Inside the Sun

- 3 Measuring the Sun

- 3.1 Angular size

- 3.2 Angular size, actual size and distance

- 4 course summary

- 2.6 End-of-course questions

- Conclusion

- Keep on learning

- Acknowledgements

Introduction

For astronomers, the Sun is fascinating because it is our nearest star. By studying the Sun, they can gain an insight into the workings of the other millions of stars that are visible in the night sky. Learning that the Sun is a star can be a little surprising. After all, the Sun is a brightly glowing, yellow object - so bright that it is dangerous to look at it directly, and so hot that we can feel its radiation warming the whole Earth. Stars, on the other hand, are mere silvery pinpoints of light that are visible only against the darkness of the night sky and with no discernible heating effect on Earth. How can they possibly be the same sort of object? The key to the answer lies in their distances.

In astronomical terms, the Sun is relatively close, being only about 150 million kilometres (93 million miles) from Earth. The stars that are visible at night are much further away: the nearest is about 40 million million kilometres from Earth, and most are much more distant than that. Imagine looking at a glowing light bulb first from very close up and then from a much greater distance. Close up, you would see the shape of the bulb but, from far away, it would be just a point of light.

This OpenLearn course provides a sample of level 1 study in Science

Learning outcomes

After studying this course, you should be able to:

- demonstrate knowledge of the electromagnetic spectrum and how it is used to infer properties of sources of radiation

- demonstrate knowledge of the range of sizes, distances and motions of objects in the Universe and how they can be measured

- demonstrate knowledge of the structure of, and the main processes operating in, the Sun

- comprehend concepts lying well outside everyday experience, including those that involve very large and very small distances, times, temperatures and energies, and those that are non-intuitive.

1 Observing the Sun

Safety warning

Never look directly at the Sun, either with the unaided eye or through spectacles, binoculars or a telescope. You risk permanently damaging your eyes if you do so.

1.1 The Sun at visible wavelengths

The Sun is seen as a blindingly bright, yellow object in the sky. The part of the Sun that you normally see is called the photosphere (meaning 'sphere of light'); this is best thought of as the 'surface' of the Sun, although it is very different from the surface of a planet such as Earth. Its diameter is about 1.4 million kilometres, making the Sun's volume roughly one million times that of the Earth. The photosphere is not solid. Rather, it is a thin layer of hot gaseous material, about 500 kilometres deep, with an average temperature of about 5500 °C (degrees Celsius).

Detailed studies of the body of the Sun usually require special equipment. However, the natural phenomenon known as a total eclipse of the Sun provides an opportunity to gain further insight into the nature of the Sun (see Figure 1 below). A total eclipse happens when the Moon passes in front of the Sun and blocks out the bright light from the photosphere.

When the Moon just eclipses the bright photosphere, it is often possible to see part of a narrow, pink-coloured ring that encircles the Sun. This is the chromosphere (meaning 'sphere of colour'), the lower or 'inner' part of the Sun's atmosphere. It is actually another layer of gaseous material, a few thousand kilometres thick, that sits on top of the photosphere. The lower parts of the chromosphere are cooler than the photosphere, while the higher parts are considerably hotter, but the chromospheric material is so thin that it emits relatively little light, and is therefore unseen under normal conditions.

Figure 1 A total eclipse of the Sun, revealing the outer part of the Sun's atmosphere, the corona, and the inner part, the chromosphere, which can just be seen as a reddish tinge on the upper right limb.

As a total solar eclipse proceeds, a third part of the Sun is seen - the corona (meaning 'crown'). This is the extremely tenuous (i.e. thin) upper atmosphere of the Sun that extends out to several times the Sun's photospheric radius. The corona seems to be composed of streamers or plumes, but its shape changes from eclipse to eclipse, although it will not usually show any changes during the few minutes of totality that characterise a typical total eclipse. The corona is very hot (temperatures of several million degrees Celsius are not unusual) but it is so thin that its pearly white light is very faint compared with the light from the photosphere.

Answering in-text questions

Throughout this course there are in-text questions marked by a bullet point, which are immediately followed by their answers. To gain maximum benefit from these questions you should think of your own response before clicking to reveal the answer. You will probably find it helpful to write down your answer, in note form at least, before reading the answer in the text.

Question 1

- The corona may be faint, but it does glow. Why are we not normally aware of the Sun's corona?

View answer - Question 1

Sometimes in eclipses observers also see prominences - great spurts of hot material at the edge of the Sun, extending outwards from the solar surface for many thousands of kilometres. Prominences and the changing shape of the corona indicate that the Sun is an active body, not just a quietly glowing source of light. There is further evidence of this in the images that you will look at shortly. This will introduce you to other features of the visible Sun, including the seething pattern of granules seen all across the photosphere, and the relatively cool sunspots that appear as small dark patches on the photosphere. Individual granules come and go in a few minutes, often to be replaced by other granules. Sunspots are larger and longer-lived, typically surviving for a week or so, and sometimes for many weeks. The longer-lasting sunspots can be photographed repeatedly as they cross the face of the Sun. They can even be used to investigate the rate at which the Sun rotates.

Activity 1 Viewing images

0 hours 15 minutes

Briefly examine the images below. They are accompanied by a paragraph beneath the image, which provides further detail on the image. Read the descriptions carefully, paying particular attention to any reference to sunspots.

Figure 2 A sunspot

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26564

A false colour picture of a sunspot, taken with the National Solar Observatory's Vacuum Tower Telescope at the Sacramento Peak Observatory. The central dark area of the spot is called the umbra and the surrounding lighter region is called the penumbra. Solar granulation is clearly visible around the spot. The spot is about 25 000 kilometres in diameter; the smallest features seen in the picture are on a scale of about 100 kilometres. The umbra represents a depression in the solar surface, where the temperature is about 1600 degrees less than in the photosphere; in the penumbra the temperature is about 500 degrees below that of the surrounding photosphere. Well developed sunspots of the kind shown in the picture live for a few weeks, though some (particularly the larger ones) can persist for many weeks, or even a few months.

Figure 3 Movements below a sunspot

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26565

It has long been known that, in the penumbra of a sunspot, there is a generally outward flow of material, away from the centre of the spot. More recent research, based on the surface effects of sound waves travelling through the solar interior. has revealed the movement of material directly below a sunspot. This image shows a complicated flow of material that includes inward motion. "We discovered that the out-flowing material was just a surface feature," said one of the researchers. "If you can look a bit deeper, you find material rushing inward, like a planet-sized whirlpool or hurricane. This inflow pulls the magnetic fields together." The intense magnetic field below a sunspot strangles the normal up-flow of energy fiom the hot solar interior. As a result a sunspot is cooler and therefore darker than its surroundings.

Figure 4 A large sunspot group

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Sunspots often appear in pairs or groups. The members of a pair will typically have opposite magnetic polarity (one having north magnetic polarity, the other south). In more complex groups the magnetic field may also be arranged in a more complicated way. This picture, taken in September 2000 shows a large complex sunspot group covering 2,140 millionths of the visible solar surface, an area about a dozen times larger than the entire surface of the Earth.

Figure 5 Sunspots crossing the sun

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This sequence of images, each individually dated and timed, shows a number of sunspots crossing the face of the Sun. The observed motion is partly the result of the Earth's orbital motion around the Sun, but is mainly a consequence of the Sun's own rotation about its axis. Once the effect of the Earth's motion has been taken into account, such image sequences make it possible to measure the rate at which the Sun rotates. The measurements reveal that the Sun does not rotate as a solid body. Rather the time taken for any pan of the photosphere to make a complete rotation depends on its distance from the equator. At the equator, the Sun takes just under 26 days to complete a rotation. Near the poles, the rotation period is more like 36 days.

1.3 Beyond visible light

During the twentieth century, astronomers extended their capabilities by developing telescopes and detectors that were sensitive to radio waves, microwaves, infrared and ultraviolet radiation, X-rays and gamma rays. All these forms of electromagnetic radiation, along with visible light, are emitted by the Sun.

Figure 6 The electromagnetic spectrum

This is a good place to examine the electromagnetic spectrum in more detail and to review some of its features. Figure 6 shows the wavelength values in metres but only some of the marks are labelled. The marks go up in 'times ten' steps so, to the right of the 1 metre mark, the first (unlabelled) mark indicates a wavelength of 10 metres (10 m), the next 100 m and the third 1000 m. Going to the left of the 1 metre mark, the next mark is 0.1 m, then 0.01 m (which is 1 centimetre or 1 cm for short), 0.001 m (1 millimetre or 1 mm), and so on. Going further to the left involves putting more and more zeroes after the decimal point, so the wavelengths are sometimes measured in micrometres - millionths of a metre. One micrometre is 0.000 001 metres.

Question 2

- What is the definition of the wavelength of an electromagnetic wave?

View answer - Question 2

Question 3

- Roughly, what is the wavelength of visible light?

View answer - Question 3

Question 4

- What type of electromagnetic radiation has the longest wavelength? What, approximately, is its wavelength range?

View answer - Question 4

1.4 The invisible Sun

Figure 7 shows an image of the Sun, taken when a huge prominence was visible (bottom left). The image was recorded using instruments that are sensitive to ultraviolet radiation rather than visible light, so the colours that you see are 'false'. They simply indicate different levels of intensity of ultraviolet radiation. The use of such false colour images is unavoidable when dealing with radiation that lies outside the range of visible wavelengths. None the less, the image shows that prominences emit copious amounts of ultraviolet radiation and are therefore observed easily at those wavelengths.

The Sun's radio waves carry much less energy than its visible light but can readily be detected with even a small radio telescope. Fortunately for us, the Earth's atmosphere shields us from the Sun's potentially harmful X-rays, so these can only be studied using telescopes put into orbit above the atmosphere.

Figure 7 A 'false colour' image of the Sun, taken at ultraviolet wavelengths.

A combination of ground-based and space-based instruments has enabled astronomers to observe the Sun over a wide range of wavelengths and to build up a clear picture of its various emissions.

Many solar observers are particularly interested in the Sun's active regions (see Figure 8), the nature and appearance of which depend on the locality and the wavelength being observed. When seen in the photosphere at visible wavelengths, active regions are often associated with groups of sunspots. Their counterparts in the chromosphere, sometimes observed at specific red, blue and ultraviolet wavelengths, are bright regions known as plage (which is French for 'beach'), while in the corona, X-ray astronomers can see transient regions of higher than usual temperature and pressure called coronal condensations. Active regions are generally caused by the Sun's magnetic field, which influences the flow of hot gaseous material on the Sun, and can sometimes rearrange itself on very short time-scales (seconds or minutes). Such sudden changes to the magnetic field in the corona are thought to be responsible for flares, one of the most energetic of all solar phenomena. Flares emit radiation of all wavelengths, from radio waves to gamma rays. Much of the energy is emitted very quickly at the start of the flare, although the flare will typically continue to radiate for several hours, even lasting a day in exceptional cases. Energetic particles are also emitted during a flare (fast-moving protons and electrons for instance), which certainly reach the Sun's surface and, sometimes, even the Earth.

Figure 8 An active region of the Sun, represented by a powerful flare (seen here as X-rays) associated with a large sunspot group.

Activity 2 Examining images of the invisible Sun

0 hours 20 minutes

Images from a variety of telescopes, representing various wavelengths of 'invisible' radiation, are included below. Some of these images enhance astronomers' knowledge of particular solar features (such as prominences or sunspot groups), while others help them to observe particular regions (such as X-ray images of the corona or ultraviolet images of the chromosphere). You should examine those images now, taking care not to be misled by their use of false colours.

Figure 9 The Sun at radio wavelengths

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26568

An image of the Sun recorded at the Nobeyama Radioheliograph in Japan, at a wavelength of 1.76 centimetre (which corresponds to a frequency of 17 gigahertz). The radioheliograph takes the form of a T shaped arrangement of 84 individual dish shaped antennas. The use of high speed computer analysis allows the radio heliograph to provide up to 20 images of the Sun per second. enough to follow rapidly developing eruptive processes. This image was recorded in 2001 at around the time of maximum activity in solar cycle 23. Signs of activity are readily apparent across the solar disc.

The image in Figure 7 was captured in September 1977 by the Extreme Ultra-violet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO) spacecraft. The image used radiation with a wavelength of 30.4 billionths of a metre, emitted by helium atoms that have lost one of their orbiting electrons. These emissions come mainly from the upper part of the chromosphere (the transition region), where the temperature is around 60 000 degrees. In addition to some bright plage regions on the disc, there are also some striking prominences extending out into the corona. Particularly noticeable is the enormous erupting prominence at the 7 o'clock position. The material in this prominence will be at a temperature of 60,000 - 80,000 degrees; much cooler than the surrounding corona, which is typically at temperatures above 1 million degrees.

Figure 10 A coronal hole in extreme ultra-violet radiation

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The dark shape sprawling across the face of the active Sun in this extreme ultraviolet image is a coronal hole - a low density region extending above the surface where the solar magnetic field opens freely into interplanetary space. Studied extensively from space since the 1960s at ultraviolet and x-ray wavelengths, coronal holes are known to be the source of the high-speed solar wind, atoms and electrons which flow outward along the open magnetic field lines. During periods of low solar activity, coronal holes typically cover regions just above the Sun's poles. But this large coronal hole extends from the Sun's South Pole (bottom) well into northern hemisphere. Coronal holes like this one may last for a few solar rotations before the magnetic fields shift and change configuration. Shown in false-colour, this picture of the Sun was recorded by the EIT instrument on board the space-based SOHO observatory using radiation with a wavelength of 28.4 billionths of a metre, from iron atoms that have lost fourteen of their orbiting electrons.

Figure 11 The Sun at soft X-ray wavelengths

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26570

An image of the Sun recorded in soft X-rays, using the Soft X-ray Telescope (SXT) on the Japanese Yohkoh satellite. The SXT gathers radiation in the wavelength range from 0.8 to 5 billionths of a metre. Only the corona emits in this range. The large dark region at the top of the image is a coronal hole. where the Sun's magnetic field opens out into interplanetary space. High temperature regions of the corona can be seen as bright spots in this false colour image. Accounting for the high temperature of the corona is a major challenge. The average temperature of the photosphere is between 5000 and 6000 degrees Celsius, so the million degree temperatures observed in the corona cannot be due to radiation from the photosphere, other heating mechanisms must be involved. Sound waves and magnetic effects are plausible candidates, but the details are still disputed.

Figure 12 An active region

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26571

This false-colour ultra-violet image shows an active region near the edge of the Sun. Hot material is seen travelling along loops defined by the Sun's magnetic field. The red regions are particularly hot, indicating that some magnetic field loops carry hotter gas than others. These active loops are so large that the Earth could easily fit under them. Active regions are often associated with sunspot groups in the photosphere, with plage in the chromosphere, and with coronal condensations in the corona. They are also sometimes associated with flares, one of which was responsible for the outburst shown in this image. This image was obtained from space using the telescope onboard the Transition Region and Coronal Explorer. The transition region is a thin and very irregular layer of the Sun's atmosphere that separates the hot corona from the much cooler chromosphere. Heat flows down from the corona into the chromosphere and in the process produces the transition region where the temperature changes rapidly from 1,000,000°C down to about 20,000°C.

Using the internet for updates

The Sun is constantly being watched from a variety of observatories. You can usually find recent images by searching the internet, using terms such as 'solar image' or modifications such as 'solar image, X-ray'. Some particularly useful websites are given below. These sites have been chosen partly because of their reliability. By all means look for other websites but be aware that there are few guarantees of quality or reliability on the internet. Always ask yourself how much you should rely on any particular source. University websites are generally fairly reliable but even there you should exercise caution.

University of Hawaii Institute of Astronomy

Solar and Heliospheric Observatory

The European Space Agency

2 Inside the Sun

To account for its brightness and activity, the Sun must contain a power source. However, the nature of that power source was a great puzzle in the nineteenth and early twentieth centuries. Fossil records and ideas about evolution were beginning to provide firm evidence that the Earth must be at least hundreds of millions of years old, rather than thousands of years as was previously thought, and the Sun must be at least as old as the Earth. The only fuels known at the time were coal, wood, oil, gas, and so on. It was fairly easy to calculate that, even if the Sun were made entirely of one of these fuels, and could get the necessary oxygen from its surroundings, it could burn for only a few thousand years at most while producing its current output of heat and light - not nearly long enough to sustain life on Earth over millions of years.

The problem of the Sun's fuel baffled many of the world's best scientists until nuclear reactions were discovered in the early twentieth century. Such reactions provided a totally new type of energy source. Rather than burning like coal or gas, nuclear reactions need no oxygen and produce vastly more heat and light for a given amount of fuel. Nuclear reactions give 'atomic' weapons their great destructive power but are harnessed more productively in electricity generation. The type of reactions that power the Sun - so-called fusion reactions involving hydrogen - are similar to those that occur in a hydrogen bomb, but in the Sun they proceed steadily rather than as an explosion.

Figure 13 Sir Arthur Eddington (1882-1944), astronomer and mathematician: one of the first astronomers to understand the internal constitution of stars.

The British astronomer Arthur Eddington (Figure 13) calculated that, if the Sun were made mainly of hydrogen undergoing nuclear reactions, it could last for millions of years while producing a more-or-less steady heat and light output. Furthermore, its outward appearance would closely resemble that of the actual Sun. We now know that hydrogen nuclear reactions will sustain the Sun for about ten thousand million years. The Sun is currently about half-way through the hydrogen-fuelled phase of its life.

Everything that is known about nuclear reactions is based on experiments performed in laboratories on Earth. Eddington's great triumph was being able to take that knowledge and work out what would happen if nuclear reactions happened on a far larger scale than was possible on Earth, and to relate his deductions to what was known about the Sun. This example illustrates an important feature of astronomy: everything that is known about the Universe beyond our Earth and Moon (apart from a few planets that space probes have visited) must be deduced by observing from a very great distance. Astronomers have two main strands to their quest to understand such distant objects. One strand involves the observations themselves: studying the appearance and movement of distant objects and analysing the radiation received from them. The other strand involves finding out how objects behave on Earth and using that knowledge to interpret and account for the observations.

Scientists have used what they know about nuclear reactions and about how very hot materials behave, together with detailed observations of the Sun, to piece together a model (that is, a mental picture) of what the Sun must be like deep inside. This is shown schematically in Figure 14 and described in the caption. The Sun does indeed consist largely of hydrogen and it is fluid throughout. The nuclear reactions occur only in the Sun's core - that is, deep in its centre -because the hydrogen fuel needs to be at a temperature of over 10 million °C before nuclear reactions can begin. Energy is carried away from the core by radiation that is repeatedly absorbed and re-emitted as it travels through the radiative zone. Closer to the surface, energy is transferred by a different process, known as convection, in which material, heated from below, expands and floats upwards, displacing cooler material that sinks downwards through the convection zone.

Figure 14 The solar interior. Temperature and density increase rapidly with depth inside the Sun, but only in the central core are the conditions right for nuclear reactions to occur. Beyond the core there are zones where energy is transported to the surface by processes involving radiation and convection (hot material rises while cooler material sinks to replace it).

As rising columns of hot material approach the top of the convection zone, the material above becomes thinner, increasing the chance of any emitted light escaping into space. This 500-kilometre thick region constitutes the photosphere, and the rising and falling columns of solar material account for the seething pattern of granules mentioned in Section 1.

Our understanding of the solar interior depends very much on our ability to understand the laws of physics that govern its behaviour. However, there are observations, based particularly on solar neutrinos and solar oscillations, that support and guide our theories. These are explored in the section of images below devoted to 'the solar interior', which you should look at in the next activity.

Activity 3 Describing the Sun

0 hours 30 minutes

At the start of this course, the Sun was referred to as a 'blindingly bright, yellow object'. From what you have read and studied so far, you now know rather more about the Sun than that simple description. Spend a few minutes looking through the text and the relevant pictures and captions below, including those concerning 'the solar interior'. Summarise what you have learned about the Sun's appearance and about its interior. Your summary should be in the form of a labelled sketch (maybe based on Figure 14). Try to make your summary as precise as possible: for example, include sizes and temperatures of the various parts of the Sun where you can.

Figure 15 A view of the solar interior

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26574

This diagram shows the major features of the solar interior; the core, the radiative zone and the convective zone; along with external features such as the photosphere, the chromosphere and the corona. Also indicated are some of the waves that make it possible to learn about the interior by studying the motion of the solar surface.

Figure 16 A mode of solar oscillation

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https://www.open.edu/openlearn/ocw/mod/resource/view.php?id=26576

This colour picture is a computer representation of one of nearly ten million different modes of solar oscillation. These modes are comparable to the vibrations of a ringing bell, or a plucked guitar string. Each part of a plucked string moves up and down in a certain period of time, and a snapshot of the string would capture some parts that were moving upwards while other parts were moving down. In a similar way, this picture shows regions of the Sun that are expanding and contracting within a period of about five minutes; regions caught in a state of contraction are shown in red tones and expanding regions in blue. While having observable surface effects, the vibrations also penetrate deeply into the solar interior and are therefore sensitive to the condition there. Many such modes of oscillation combine to create the observed movement of the solar surface. By measuring the strengths and frequencies of those modes arid using theoretical models, solar astronomers can infer much about the internal structure and dynamics of the Sun. This technique is called helioseismology because of its similarities to terrestrial seismology (the study of earthquakes and other terrestrial vibrations). Helioseismology is at the heart of the research programme of the Global Oscillation Network Group (GONG), which continuously monitors solar oscillations by operating an international network of instrument stations that always has at least one station in daylight.

Figure 17 Describing modes of solar oscillation

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This image shows three more modes of solar oscillation. Each mode is partly characterized by an arrangement of intersecting planes. The planes consist of points that are left unaffected by the movements that contribute to the mode they characterize. The arrangement of these planes can be specified by two numbers (designated l and m) that help define the mode concerned.

Figure 18 The solar interior

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This image shows differences in the speed of rotation of material inside the Sun. The false colours represent speed; red material is rotating the fastest, dark blue the slowest. The inner 70% or so of the Sun rotates at nearly the same rate. However there is marked differential rotation in the outer 30%, which corresponds to the solar convection zone where the energy is carried upwards by convection rather than by radiation. Note that the equator rotates much faster than the poles.

View answer - Activity 3 Describing the Sun

3 Measuring the Sun

Section 2 referred to observations that can only be made using sophisticated telescopes, but this section turns to an observation you can do yourself. There are two reasons for this: one is to give you experience in scientific measuring and the other is to introduce some terminology that astronomers use frequently.

3.1 Angular size

Figure 19 A total eclipse of the Sun, revealing the outer part of the Sun's atmosphere, the corona, and the inner part, the chromosphere, which can just be seen as a reddish tinge on the upper right limb.

The image shown in Figure 1 at the start of this course (repeated above), was taken during a total eclipse of the Sun, in which the Moon blocked out light from the Sun's photosphere, enabling the chromosphere and the corona to be seen. This happens because of a remarkable coincidence. The Sun is very much bigger than the Moon - about 400 times bigger in diameter - but it is also very much further away, by almost exactly the same factor. This means that the Sun and the Moon appear the same size in the sky: that is, the Sun and the Moon have the same angular size. Figure 20 illustrates this idea by showing lines drawn from an observer's eye to the extreme edges of objects at various distances. The angle between the lines determines the angular size of the objects, which would be 10° in all three cases, according to the shown observer. Angular size thus depends on an object's actual size and its distance from the observer's eye.

Figure 20 The observed angular size of an object depends on the size of the object and its distance from the observer.

You are probably familiar with angles measured in degrees (360° for a full circle, 90° for a right angle, and so on). However, although the objects studied by astronomers are very large, they are at such vast distances that their angular sizes are often very small. These small angles could be written as fractions of a degree or their decimal equivalents but, in practice, subdivisions of degrees are used, known as minutes of arc (or arcmin) and seconds of arc (or arcsec). A degree can be divided into 60 minutes of arc, and a minute of arc can be further divided into 60 seconds of arc. A single tick mark is used to represent arcmin, so 1/60 of a degree is written 1′. A double tick mark denotes arcsec, so 1/3600 of a degree (1/60 of an arcmin) is written 1″.

Angular size is a very useful quantity in astronomy, since angular sizes are very much easier to measure than actual sizes because they refer simply to how large an object appears in the sky. The Sun and the Moon both have an angular size of about half a degree, which is about 30 arcmin or 30′.

Question 5

- How would you define the angular size of the Moon?

View answer - Question 5

3.2 Angular size, actual size and distance

The angular size of an object is determined uniquely by its actual size and its distance from the observer. For an object of fixed size, the larger the distance, the smaller the angular size. For objects at a fixed distance, the larger the actual size of an object, the larger its angular size. For objects with small angular sizes, such as typical astronomical objects, the precise relationship between angular size, actual size and distance is well approximated by the equation:

angular size = (actual size ÷ distance)

However, when using this equation you must be very careful about the units in which quantities are measured. If the actual size and the distance are measured in the same units (metres or kilometres, or anything else as long as it is used for both quantities), the angular size that you calculate will be in measured units called radians. A radian is equal to a little more than 57° so, in order to obtain angular sizes in degrees, the following approximation can be used (as long as the angular size is not too great):

angular size = 57 × (actual size ÷ distance)

The next question asks you to apply this expression to Figure 20.

Question 6

- Calculate 57 × (actual size ÷ distance) for each of the objects in Figure 20.

View answer - Question 6

Units, numbers and physical quantities

Much of astronomy concerns quantities such as temperatures, distances, diameters and angular sizes. In all of these cases, units of measurement are important. Physical quantities are generally the result of multiplying together a number and a unit of measurement. Thus a distance such as 5.2 kilometres is really the result of multiplying the number 5.2 by the unit of distance known as the kilometre. There are many units of measurement in common use, so, whenever you quote the value of a physical quantity, you should always take care to include the unit as well as the number multiplying that unit. It is no use being told that a distance is 5.2 if you don't know whether that means 5.2 centimetres or 5.2 kilometres. The unit is at least as important as the number.

In scientific work there are several internationally agreed conventions for the definition of units and the way in which units should be used and represented when writing down the values of physical quantities. The most widely adopted system of units is known as SI, which stands for Systeme International. This is based on seven carefully defined units that include the metre (for length), the second (for time) and the kilogram (for mass). The other four base units relate to luminous intensity (i.e. brightness), quantity of matter, electric current and temperature, the unit of which is the same size as the degree Celsius but starts from a different zero value and is called the kelvin.

The recognised abbreviations for the metre, the second and the kilogram are m, s and kg, respectively. In all cases, units should be written in the singular form, so it should really be 5.2 kilometre or 5.2 km, rather than 5.2 kilometres, and certainly never 5.2 kms, since that might be misinterpreted as 5.2 × 1 km × 1 s.

In calculations, units should be treated in the same way as numbers, so the result of dividing 6.0 km by 3.0 s is 2.0 km/s, which can be read as 2.0 kilometre per second.

Units, such as km/s, that result from combining the base units are called derived units. The most common derived units are sometimes given their own names and symbols. The angular unit known as a radian is an example, since angular size can be equated to the result of dividing one length (a diameter) by another length (a distance). The more familiar unit of angle - the degree - is said to be a supplementary unit since it is defined as a specific fraction (a little less than 1/57) of a radian.

To do the next activity, you need to know that the Moon's diameter is 3476 km. You may wonder how this can be measured from the Earth. In principle, it is a surprisingly easy measurement to make. First, you have to find the diameter of the Earth, which can be worked out by measuring how much its surface curves. You may be surprised to learn that this measurement was made in about 235 BC by the Greek astronomer Eratosthenes, and that his value was quite close to our modern measurement of 12756 km (for the equatorial diameter, which is slightly bigger than the polar diameter). The sizes of the Earth and the Moon can be compared by looking at the Earth's shadow on the Moon's surface during a partial eclipse of the Moon (see Figure 21). A careful measurement of this kind reveals that the Earth's diameter is 3.67 times that of the Moon.

Figure 21 A partial eclipse of the Moon.

Activity 4 The distance to the Moon

0 hours 30 minutes

This activity needs to be done when the Moon is clearly visible in the sky. (It need not be done at night and, in fact, can be easier in the day or at twilight.)

DO NOT ATTEMPT THIS ACTIVITY ON THE SUN.

You will need the following items:

- a selection of coins (e.g. 1p, 5p and 10p);

- a straight rod (e.g. a piece of dowelling or a garden cane) at least 2 m long;

- a tape measure at least 2 m long;

- a ruler marked in centimetres and millimetres;

- some Blu-Tack® or plasticine;

- a pocket calculator.

Set up an arrangement with a coin fixed to a rod so that the coin just 'eclipses' the Moon. Figure 22 shows one possible set-up.

Figure 22 One possible arrangement for eclipsing the Moon.

Observing from one end of the rod, try different coins until you find one that is the right size to eclipse the Moon when fixed somewhere on the rod. Then adjust the position of the coin until it just blocks your view of the Moon. (This is less easy than it sounds, as there will always be some haze visible around the edge of the coin - try to get the best match.)

Measure the distance from the coin to the end of the rod where you have placed your eye, and measure the coin's diameter. Record your values like this:

Diameter of coin = .................... mm

Distance of coin = .................... mm

You now have the measurements that will enable you to calculate the angular size of a coin that has the same angular size as the Moon.

Use your two measurements on the coin to calculate its angular size in degrees, using the formula introduced earlier, adapted to the current case, i.e.:

angular size of coin = 57° × (diameter of coin ÷ distance of coin) = ....................

Your answer should be about half a degree (0.5°). Any value between 0.4° and 0.6° is fine. This is also your measurement of the angular size of the Moon. So, write down:

angular size of Moon in degrees = ....................

The next step is to calculate the distance to the Moon. Just as for the coin:

angular size of Moon = 57° × (diameter of coin ÷ distance of Moon) = ....................

This equation can be rearranged to give:

distance of Moon = 57° × (diameter of Moon ÷ angular size of Moon in degrees).

(Take this on trust if you cannot see it.) Now calculate the distance to the Moon, using your value for its angular size and 3476 km for its diameter.

Distance of Moon = 57° × (.................... ÷ ....................) = ....................km..

You might like to compare your result with the accurately measured value of the Moon's distance: 384 500 km. It is unlikely that you would have got very close to this answer, but even with such a quick and fairly rough measurement, your answer should show that the Moon's distance is a few hundred thousand km.

View answer - Activity 4 The distance to the Moon

The technique used in Activity 4 could also be used to work out the Sun's distance if you knew its size. However, under no circumstances should you try Activity 4 on the Sun because it would seriously damage your eyes.

4 course summary

The essential points of this course are as follows.

1. The Sun is a star, emitting all types of electromagnetic radiation. The light that reaches Earth from the Sun comes mainly from the photosphere, although on its way to Earth it must pass through the chromosphere and the corona. Each of these parts of the Sun shows signs of magnetically driven activity.

2. Electromagnetic radiation consists of waves that can travel through empty space and cover a huge range of wavelengths.

3. The Sun is powered by nuclear reactions in its hot core which enable it to release energy steadily over thousands of millions of years. The energy released in the core is transported to the surface by radiation and then convection, passing through radiative and convection zones on the way.

4. The Sun and the Moon have approximately the same angular size when viewed from the Earth.

5. The angular size of an object depends on its actual size and its distance from the observer.

2.6 End-of-course questions

Question 1

What is the approximate wavelength range (in metres) of microwaves?

View answer - Question 1

Question 2

What are the main modes of energy transfer that participate in the transport of energy from the Sun's core to the Earth's surface?

View answer - Question 2

Question 3

In a sentence or two, explain why the problem of the Sun's fuel puzzled scientists, and say how the discovery of nuclear reactions solved the puzzle.

View answer - Question 3

Question 4

The Sun is about 150 million km from the Earth. Use information from Section 4 about the angular diameters of the Sun and the Moon to calculate the Sun's approximate diameter. You should note the approximate relationship:

actual size = (angular size in degrees × distance) ÷ 57°.

(Do not spend more than a few minutes trying to answer this. There is a second way of tackling this question - see whether you can find it.)

View answer - Question 4

Question 5

A large sunspot is observed to have an angular size one-twentieth that of the Sun. Taking the Sun's angular size to be 0.5°, what is the angular size of the sunspot? Express your answer in (a) arcmin and (b) arcsec.

View answer - Question 5

Conclusion

This free course provided an introduction to studying Science. It took you through a series of exercises designed to develop your approach to study and learning at a distance, and helped to improve your confidence as an independent learner.

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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Course image: Charles Roffey in Flickr made available under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence.

Grateful acknowledgement is made to the following sources for permission to reproduce material in this course:

Figure 1 Dr J Durst, Schonenberg, Switzerland;

Figure 7 Courtesy of SOHO. SOHO is aproject of international cooperation between ESA and NASA;

Figure 8 US National Oceanic and Atmospheric Administration;

Figure 13 © The Royal Astronomical Society;

Figure 21 Dennis di cicco/Sky Publishing.

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Question 1

Answer

The bright light from the Sun's photosphere is scattered by the Earth's atmosphere. This makes the sky blue and generally rather bright. As a result, we cannot observe the much fainter light from the corona (rather as the light from a dim torch is unnoticeable on a bright sunny day).

Back

Question 2

Answer

It is the distance between successive peaks of the wave.

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Question 3

Answer

It is about 0.000 001 metres (actually, 0.000 000 4 to 0.000 000 7 metres).

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Question 4

Answer

Radio waves are the longest: in Figure 6, the shortest radio waves lie about one step to the left of the 1 m mark, which denotes a wavelength of 0.1 m. The band representing radio waves extends to the far right of the chart. The furthest mark on the right represents a wavelength of 1000 m (three steps to the right of the 1 m mark), so the figure shows that radio waves can have wavelengths of over 1 kilometre. (Such wavelengths are typical of radio stations still broadcasting in the 'long wave' band.)

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Activity 3 Describing the Sun

Answer

Figure 19 shows our summary description of the Sun. Yours may be presented in a different way but should include similar information.

Figure 19 A possible drawing for Activity 3.

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Question 5

Answer

It is the angle between two imaginary lines drawn from an observer's eye to the extremities of the disc of the Moon. (More formally, it is the angle subtended at the eye of the observer by the diameter of the Moon.)

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Question 6

Answer

The values are 57 × (1 m ÷ 5.7 m), 57 × (2 m ÷ 11.4 m), 57 × (3 m ÷ 17.1 m), which is 10° in each case (as expected).

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Activity 4 The distance to the Moon

Answer

Here are some typical results from this activity:

- diameter of coin = 1.7 cm (UK 5 pence coin)

- distance of coin = 182 cm

- distance ÷ diameter = 107.058 82 on a calculator (near enough 107).

So, for something whose angular size is that of the Moon (half a degree):

- distance = 107 × diameter

- diameter of Moon = 3476 km.

Therefore, distance of Moon = 107 × 3476 km, i.e. distance of Moon = 371 932 km (near enough 372 000 km).

To eclipse the Moon, the distance of the coin needs to be roughly one hundred times its diameter. If you tried using a coin larger than 2 cm diameter, it would need to be more than 2 m from your eye and would not fit on a 2 m rod.

Our result is quite close to the accurately measured value of 384 500 km; yours may be closer, or not quite so close. Provided you got a value of a few hundred thousand kilometres, that is reasonable. If your value was very different, check back through your calculations to see whether you have made a mistake, and look again at your measurements.

Back

Question 1

Answer

The range is from about 1 m down to a little less than 0.001 m (see Figure 6).

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Question 2

Answer

Energy released by nuclear reactions in the Sun's core is initially carried away by radiation. Although repeatedly absorbed and re-emitted, it is radiation that carries the energy through the radiative zone. It is absorbed at the bottom of the convective zone, where it causes the convective flows that are largely responsible for transporting energy up to the photosphere. Radiation takes over again in the photosphere; the radiation emitted there escapes from the Sun and may transport energy to the Earth's surface where it can be absorbed.

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Question 3

Answer

Conventional fuels could maintain the Sun's output of light and heat for only a few thousand years, which is not nearly long enough to sustain the evolution of life on Earth over the millions of years deduced from fossil records. Nuclear reactions produce much more energy output for a given amount of fuel, enabling the Sun to emit a steady output over thousands of millions of years.

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Question 4

Answer

There are two methods for answering this question.

Method 1

The expression given is:

actual size = (angular size in degrees × distance) ÷ 57.

This can be rewritten as:

diameter of Sun = (angular size of Sun in degrees × distance of Sun) ÷ 57.

The angular size of the Sun is about the same as that of the Moon, i.e. 0.5°, so:

diameter of Sun = (0.5 × 150 million km) ÷ 57 = 1.32 million km.

Method 2

The Sun's diameter is about 400 times the diameter of the Moon. Therefore, if the Moon is 3476 km in diameter, the Sun must have a diameter of about 400 × 3476 km = 1.39 million km. {This is not as accurate as in Method 1, because the diameter of the Sun is about 400 times the diameter of the Moon.}

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Question 5

Answer

(a) There are 60 arcmin in one degree (1°), so the Sun's angular size is 30 arcmin. The angular size of the sunspot is:

30 arcmin ÷ 20 = 1.5 arcmin

(b) 1.5 arcmin = 90 arcsec

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