Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.atnf.csiro.au/outreach/education/teachers/resources/conceptscosmicenginestw2006.pdf Äàòà èçìåíåíèÿ: Wed Jan 22 10:05:18 2014 Äàòà èíäåêñèðîâàíèÿ: Mon Apr 11 17:51:09 2016 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: microwave background

Science Teachers' Workshop 2006

Concepts for The Cosmic Engine
Robert Hollow CSIRO Australia Telescope National Facility Robert.Hollow@csiro.au

Introduction
This workshop will provide you with some simple ideas, demonstrations and analogies that consolidate a conceptual grasp of the theory and skills in module 8.5 The Cosmic Engine of the NSW Stage 6 Physics syllabus. Concepts addressed, in varying depths, include historical perspectives, the expansion of space and the Big Bang, colour and temperature of stars, luminosity and the Hertzsprung-Russell diagram. Despite the seeming lack of practical investigative work in the revised version of the Cosmic Engine unit, there are many simple demonstrations and analogies that are effective in engaging and challenging students. This paper aims to provide teachers with a range of ideas and activities plus some useful data with which to cover the syllabus requirements. It is not intended to provide a detailed theoretical background on the concepts as this is better covered in the various references but rather it aims to clarify some key teaching points and misconceptions about them. Some of the material included in this paper may be found in The Cosmic Engine section of the Australia Telescope Outreach and Education website; http://outreach.atnf.csiro.au/education/senior/cosmicengine/. Other material has been incorporated and updated from papers presented at previous Science Teacher Association of NSW workshops by the author.

Syllabus Requirements
This paper uses in this paper ap (pages 35 ­ 37 syllabus. It can the amended NSW Board of Studies Stage 6 Physics Syllabus of October 2002. The three areas targeted proximately relate to the syllabus outcomes in bold points 1, 2, and 3 in module 8.5 The Cosmic Engine of the printed edition). It is recommended that you read the paper with access to a current copy of the be obtained online from the Board of Studies at http://www.boardofstudies.nsw.edu.au/syllabus_hsc/.

Historical Models
Astronomy is the oldest western Europe show e understanding of seasons observations of the night of sciences. Numerous ancient sites such as many of the megalithic stone circles of northvidence of astronomical alignment. The growth of agricultural communities required an and time keeping. Ancient Egyptian and Babylonian records provide evidence of systematic sky.

Figure 1: Stonehenge at around Midwinter sunrise © R. Hollow Five planets, Mercury, Venus, Mars, Jupiter and Saturn plus the Sun and Moon were visible to the unaided eyes of the ancient astronomers. The planets could be distinguished from stars in that through regular observation they were seen to move relative to the stars. The very word planet derives from the classical Greek term for wandering star. Unlike stars, planets also varied their brightness over time. A final complication in the observed behaviour of planets was that of retrograde motion. This is where a planet seemed to back track on its path across the sky through the constellations before reverting to its normal direction. Figure 2 on the next page clearly shows this for the planet Mars in late 2003.

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Figure 2. Retrograde motion of Mars (Image was generated using Starry Night Pro software). The first section of The Cosmic Engine module requires students to outline the historical development of models from Aristotle to Newton and to assess one of these models and its limitations with respect to the technology available at the time. Given the time constraints for the module it is unrealistic to expect students to study the models in great depth or probe all of the subtle intricacies of, for instance, the Ptolemaic model. There are several useful websites, some listed in the references at the end of this paper, that provide an effective overview and from which students can extract relevant details on a specific model. Rather than just let students choose randomly which model to investigate it may be worthwhile to assign a different model to each student or group and have them report back to the whole class in chronological sequence so as to provide some sense of historical narrative.

Personal Cosmology
Before even starting on an investigation of a specific model, an effective approach is to ask your students to construct their own personal cosmology. An example of a worksheet for this approach is included in McNamara et al (1997). In this task ask your student to imagine that their entire Universe is what they can see from their classroom, their world. When prompted to do this many students will be bemused so may need some prompting. They have to describe their "world view" based purely upon what they can observe from their seat. If they have a view out of a window they may be able to see the Sun or they may only be able to see that the outside region can be blue, grey/white (ie cloudy) or dark. Sometimes external objects may seem to move or shake (trees blowing in the wind) or change (deciduous trees in the winter). Ask students as to what they would make of this world if they could not go outside the room and actually examine objects closely? Could they develop a model to account for observations? This, in essence, is what the early astronomers and philosophers had to do and indeed modern astronomers are still largely dependent upon. Forcing students to adopt this approach may make them less critical and more understanding of the problems facing their predecessors. It also illustrates the fact that astronomy is primarily an observational rather than an experimental science. If you have the time and capable students you scenarios developed by Dr Paul Francis from Astrophysics at Mount Stromlo. If you visit Understanding the Sky Exercise for 1st Year A can the his stro explore this approach in more depth by using one of the role-playing Australian National University's Research School of Astronomy and website http://www.mso.anu.edu.au/~pfrancis/roleplay.html use the nomy Students exercise.

Impact of Technologies on Historical Models
Many students have a poor understanding or appreciation of historical timelines and associated technologies. It is useful to explicitly refer to sates and intervals for historical periods. A scale timeline or chart in the classroom can be effective as a tool for ready reference. In discussing the development of models solicit a list of possible technologies from students. Whilst most students will identify the telescope many actually neglect the human eye. Few however are likely to identify some of the others in the list below as technologies: · · · · · · · · Human eye Telescope Gnomon or upright stick in the ground. In various forms this is the basis for sundials. Astrolabe, quadrant and cross-staff Water-clock Pendulum (and the pendulum clock) Writing and recording, including clay tablets, papyrus, parchment, printing and books Mathematics. There are a few branches key to the development of cosmological models including: o Numbers systems and notation (including zero) o Geometry o Irrational numbers o Algebra o Logarithms o Calculus (or theories of fluxions and inverse fluxions as Newton originally named it)

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Science Teachers' Workshop 2006 Of course technologies are not separate from the cultures and societies that use or develop them so there is a wealth of possible topics for discussion in this section. One or two examples can be used to illustrate the application of these technologies in earlier times. These could include Eratosthenes' measurement of the Earth's circumference using a gnomon, well and camel caravan. Students can link up with another school to perform Eratosthenes' experiment as part of a 2006 competition for National Science Week organised by RMIT, http://www.rmit.edu.au/scienceweek. Newton's deduction of the inverse-square law for gravity of Kepler's empirical laws of planetary motion and the use of calculus to determine the gravitational force between the Earth and Moon. Central to models prior to Kepler was a philosophical reliance on the circle and sphere as the basis for all celestial motions. This mind-set dominated for a few thousand years and influenced models as disparate as Aristotle and Copernicus. Even Kepler spent many years fixated on trying to establish a mathematical model based on regular solids and circular paths to fit observations of the planets. Only through tedious and painstaking calculations did he eventually realise that planetary orbits are elliptical, not circular, with the Sun at one focus (Figure 3).

Figure 3: Kepler's First and Second Laws of planetary motion. Credit: R. Hollow, CSIRO Students can gain an appreciation of the skill of early observers by trying to measure positions of stars or planets using simple inclinometers or cross-staffs. Crude refracting telescopes can be purchased from stores such as Australian Geographic and issued to students to see if they can detect the Galilean moons of Jupiter. The science supplier Cider House, www.ciderhouse.com.au now imports and distributes the Project STAR material developed by the Science Education Department at the Harvard-Smithsonian Center for Astrophysics. This includes a simple refractor kit and a model celestial sphere that students can construct. Visualisation tools including planetarium-type programs and online applets allow students to examine and explore different models and view phenomena such as retrograde motion in a timely manner. Examples are provided in the references at the end of the paper, with even more listed on our website.

Cosmology, the Big Bang and the Expansion of Space
The discovery of the expansion of space was a defining step in our understanding of the Universe. The discovery by Edwin Hubble was the culmination of work conducted by many people over a few decades applying the then limits of technology. The story is an interesting one as it illustrates how developments in several fields including theory and technology when linked together can lead to major breakthroughs.

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Science Teachers' Workshop 2006 Hubble's work relied upon the use of the world's then largest telescope, the 100 inch Hooker telescope on Mt Wilson, in itself the relatively new technology of a large reflecting telescope as compared with traditional large refractors. He required long photographic exposures on glass plates of faint light from distant galaxies that had been passed through a spectrograph.

Figure 4: The conceptual challenges for students came in trying to make sense of Hubble's observations and interpretation. To simplify and paraphrase the findings, Whilst many practising cosmologists and astronomers may prefer to use the term model a scientific theory is one supported by significant observational or experimental evidence. As a model, the Big Bang has several free parameters, some of which are now fairly well constrained. Whilst the Big Bang model is currently the most widely accepted and successful model it has limitations and some problems yet to be resolved. The Big Bang model rests on several key pieces of evidence: · The Universe is expanding. This expansion was first detected by Edwin Hubble in the 1920s by measuring the redshift of galaxies. His results showed that the further a galaxy is from us, the faster it is receding from us. This is not due to the motion of the galaxy itself which may be in any direction relative to us. Instead it is due to the expansion of space itself. The relationship between recession velocity and distance is a linear one and is now known as Hubble's Law. A major goal of astronomers since its discovery has been to accurately measure Hubble's Constant, H0, the current expansion rate of the Universe. The two best current value for Hubble's Constant, are: WMAP: H0 = 71 ± 4 km s-1 (5% margin) HST Key Project: H0 = 71 ± 6 km s-1 which in turn suggest that the Universe is 13.7 ± 0.2 billion years old. Evidence for an expanding Universe now comes from a variety of independent observations. · Cosmic Microwave Background Radiation (CMBR). This is the remnant radiation from the Big Bang, and dates to the "decoupling era" 380,000 years after the Big Bang. As the Universe has expanded the energy density has dropped so the initial temperature of 1019 K at the end of the Inflationary era has cooled to an

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Science Teachers' Workshop 2006 average background temperature of 2.725 K. This corresponds to a peak wavelength that corresponds to microwave frequencies. The CMBR was first detected in 1963 by Penzias and Wilson for which they were awarded the 1978 Nobel Prize for Physics. · The ratio of primordial elements. The Big Bang model makes predictions about the relative primordial ratios of the light nuclei; hydrogen, deuterium, helium-3, helium-4 and lithium. Observational results fit the model. This baryonic matter is ~75% H and ~25% He by mass. The formation and distribution of large-scale structure in the Universe. The minute irregularities present in the early Universe have grown due to a slight increase in gravitational attraction over surrounding material. Eventually matter would clump together and continue to grow, forming large gravitationally bound clusters of galaxies. This large-scale structure has been a particularly active field of research over the last decade. Large scale surveys such as the Australian 2dF Galaxy Redshift Survey on the Anglo-Australian Telescope have proved invaluable in helping test and extend our understanding of this field. Observed evolution. Recent improvements in telescopes and instrumentation now allow us to observe distant (hence normally interpreted as old young) galaxies. They do not look the same as nearby galaxies thus suggesting that they have changed over time. The fact that the Universe has changed over time became evident in the late 1950s and early 1960s via radio surveys of the sky. Bright, extragalactic sources are not randomly distributed Quasars. These extremely luminous, high-redshift objects are thought to be supermassive black holes in the centre of early galaxies. The absence of any nearby quasars again supports the idea that the Universe has evolved. Recent observations show that quasars with supermassive black holes with a mass of 109 solar masses in their cores had formed within a billion years of the Big Bang.

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Concepts to Emphasise
1. The Big Bang was not an explosion. Most books and portrayals of the big bang incorrectly depict it as some form of explosion. This is a mistake. If it was an explosion it must explode from somewhere to somewhere else. This leads to point 2. The centre of the Universe. This is always a conceptually challenging idea for students. It is natural to think that the Universe must have a centre. In fact, going back to point 1 above, the centre of the Universe is all around us. Actually the big bang occurred all around us and the remnant of this can be seen in every direction. The Universe does not have a centre in much the same way as the surface of a sphere has no centre. Not a Doppler shift: The redshift as measured by Hubble and others since is not actually an example of the Doppler effect arising due to proper motion of galaxies through space. It is instead a cosmological redshift due to the expansion of space itself. Actually there are several types of redshift including gravitational redshift and expansion redshift. Galaxies are not moving through space. To clarify this, what we are really talking about are galaxies moving through space on a cosmological scale. In fact all galaxies show relative motion through space, typically 300 km s-1. Some nearby galaxies are actually moving towards us. Once this is accounted for, the so-called Hubble expansion is due to the fact that space between galaxies is expanding rather than galaxies all moving through space away from us. It is important to emphasise that galaxies themselves do not expand, local gravitational influence is string enough to overcome any expansion effect. The issue of formation of structure of galaxies, clusters of galaxies and large-scale structure is one still being resolved. In general "top-down" scenarios have fallen out of favour compared with bottom-up or hierarchical scenarios with cold dark matter (CDM). In these, very high-mass stars form first then form structures equal in mass to globular clusters that then form the protogalaxies. These smaller galaxies, typically of 106 Mì then produce the larger 1011 Mì galaxies seen today through collapse and mergers. The initial process leading to structure formation comes from gravitational instabilities in the distribution of matter produced in the big bang. By matter we include the baryonic matter such as protons and neutrons and non-baryonic matter that comprises sold dark matter. As yet we still do not know what this CDM is comprised of but currently the neutralino, a supersymmetric particle, is the best candidate. Cold means that it is slow moving or has non-thermal energies; dark means it does not emit or radiate light and matter because it interacts gravitationally. The Big Bang model is currently the most widely accepted and successful model. There are still several key questions that remain unanswered but work continues on them. It serves as a useful example of science in action. The big bang paradigm has replaced steady state alternatives. There are other models that some researchers discuss (plus a wealth of fringe or crackpot theories, most of which set out to prove Einstein wrong) but they are not widely accepted.

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Classroom Activities for Cosmology
There are many simple activities, analogies and ideas to help convey cosmological concepts in the classroom. How best to model or convey the idea that a universe can expand yet not have a centre? Several methods can be employed. 1. Balloons. Students can mark a balloon with several dots, each with a number or letter. Blow the balloon up slightly then using string, measure the distance from, eg A to B, A to C and so on and record. Blow the balloon up a bit more and repeat measurements. Do this a third time then study the data. Students should see that the greater the distance initially between two dots, the greater they move apart over time relative to nearby dots. If you use the simple relationship that velocity (speed) = distance/time and take each additional inflation as one time unit they can calculate that more distant dots actually move apart faster than nearby dots. This is the essence of Hubble's Law. One problem with the balloon analogy is that the dots students draw (which are supposed to represent clusters of galaxies) actually expand when they blow up the balloon. In reality galaxies themselves do not expand as the Universe ages. It is not the galaxies that are even moving at all; rather it is the space between them that is expanding. Balloons can also be used to try and convince students that the concept of the centre of the universe is meaningless. Ask them where is the centre of the surface of the balloon (or of the Earth)? Obviously the balloon's surface is only two-dimensional whereas the universe has extra dimensions but the analogy is sound. To show there are no preferential locations ask them to repeat the initial activity measuring all distances from point B or C. Again, they should see that from B's perspective, all the points move away over time. Of course, having balloons in the classroom may also lead to real "big bangs" in cases of over-inflation. Students may also experience deflationary universes! 2. 3. Balloons 2 ­ the CMBR. Draw a transverse wave on a balloon. As you blow the balloon up the wave stretches out to longer wavelengths just as radiation is redshifted in an expanding universe. Dough & sultana models. Dough mixed with sultanas and yeast prepared before a class can be left to naturally expand. An advantage of this approach is that the sultanas do not expand though it is harder to perform quantitative measurements. Overlays of expanding space. The Astronomical Society of the Pacific's http://www.astrosociety.org/index.html, Universe at Your Fingertips resource manual contains an excellent activity by David Chandler Visualizing the Expansion of Space. It uses two seemingly identical images of the Universe where one is photocopied onto a transparency and overlaid on the other. Using both images as transparencies allows you to show it on an OHP for quite dramatic effect. (Copies of this handed out during the workshop). The manual also contains other relevant activities for classroom use. Physiotherapy in Space. Many ageing educators (including me) have a Theraband for physiotherapy. These are really useful for demonstrating the expansion of space. Get two students, each holding one end to stand at the front of the room. Other students stand behind the band and each put a large, different coloured peg onto it. The pegs represent galaxy clusters. As the band is stretched, each student can see the distance to the other pegs or students increase but the ones further away move even more than the nearby ones. Another option with a theraband is to lay it flat and draw a transverse wave on it. This represents the background radiation or indeed radiation emitted from a source. As you stretch the band, the wave is also stretched out to a longer wavelength or lower frequency. Computer simulation of formation of large-scale structure. There are several sites that allow you to view supercomputer simulations of the formation of galaxies, star clusters and large-scale structure. These are useful in conveying the role of simulation and mathematical modelling in modern cosmology and astrophysics. Computer-based activities. Software-based activities such as those provided by Project CLEA (see resources at end) provide an interesting and effective way of engaging students and demonstrating some of the principles and technologies involved. The CLEA activities are free and come with detailed manuals as well as pre and post-tests. Of particular use are the CLEA modules The Hubble Redshift Distance Relation and Large Scale Structure of the Universe. The CMBR on TV. About 1% of the noise or "snow" seen on a TV screen is actually due to the CMBR. Turn on a TV and turn to a channel between normal stations. Part of the noise truly comes from the Big Bang. This is a handy introduction to a lesson.

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Luminosity, Colour and Temperature of Stars
The third section of the syllabus for The Cosmic Engine examines the relationship between effective (surface) temperature for a body and the radiation it emits and relates this to the colour of stars. Whilst not explicitly stating that stars can be approximated as black body radiators this is the key to this section. One immediate problem that some students have in linking colour to temperature is that in their everyday experience they normally equate red with hot or warm and blue with cold or icy. Often temperature dials on air conditioners and heaters reinforce this notion. With a black body radiator the opposite is the case, that is red hot is cooler than blue hot. The simplest analogy to use is to ask students which type of Bunsen flame is hotter ­ the orange safety flame or the blue heating flame? A black body radiator is a theoretical object that is totally absorbent to all thermal energy that falls on it, thus it does not reflect any light so appears black. As it absorbs energy it heats up and re-radiates the energy as electromagnetic radiation. In the real world some objects approximate the behaviour of blackbodies. These must be sources of thermal energy and must be sufficiently opaque that light interacts with the material inside the source. Examples of such objects include the tungsten filaments of incandescent lamps and the cores of stars. The continuous spectrum produced by a black body is distinctive and can be shown as an intensity plot of intensity against emitted wavelength. This plot is called the blackbody curve or the Planck curve, after the German physicist Max Planck who first postulated that electromagnetic radiation was quantised. The plot below (Figure 5) shows a Planck curve for an object with a 6,000 K effective temperature, the same temperature as the Sun.

Figure 5: Planck curve for a black body at 6,000 K Credit: M. Horrell http://staff.imsa.edu/science/astro/blackbody/ If you look closely at the curve you will notice that the object emits some radiation at every wavelength including in the ultraviolet and infrared wavebands. You should also notice that the amount of energy emitted is not the same for all wavelengths and that in this case, the peak wavelength falls within the region of visible light. Now what happens if the temperature of the black body source is different? Figure 6 on the next page shows Planck curves for an object at four different temperatures from 6,000 K to 4,000 K. Note the wavelength here is expressed in units of ångstroms. 1 ångstrom = 0.1 nanometers.

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Figure 6: Planck curves for black bodies of different temperatures. Plot generated from an applet (http://csep10.phys.utk.edu/guidry/java/planck/planck.html) courtesy of Mike Guidry How do the curves compare? Two key points should be apparent. Firstly, a hotter object emits more energy at every wavelength than a cooler one. Secondly, the hotter the object, the shorter the wavelength of the peak of the curve. The 6,000 K object clearly peaks in the visible part of the spectrum whereas the peak of the 4,000 K object borders the visible and the infrared regions. As already mentioned, stars approximate black body objects and can vary in their effective temperatures from around 2,000 K to about 30,000 K. If you tried to plot the intensity of two stars with these extremes on a plot like the one above it would be extremely difficult to show them on the same linear scale.

Demonstrations and ideas for luminosity, brightness and colour
There are many simple ideas you can use in the classroom or elsewhere to reinforce the concepts of luminosity, brightness and colour.. 1. Standard candles. In discussing how to determine stellar and extragalactic distances students should be introduced to the concept of "standard candles". Tea candles at different distances in a room can simulate stars at different distances. In asking students to identify which "star" is furthest away, challenge them to state the assumptions on which their answer is based. Are they assuming that stars have the same "brightness"? Probe them to explain what they mean by "brightness" than try and lead them to linking this with the energy given of by a star or candle then the energy per unit time, that is the power output or luminosity of a star. Variations on the candle theme could use low power bulbs or LEDs at different distances. Of course, if using bulbs you can then complicate matters by running them at different voltages to produce "stars" of differing intrinsic luminosities and even colour. Intrinsic and extrinsic luminosity & brightness. Differences in the brightness of a star may arise due to internal processes or characteristics of a star (intrinsic) or be due to some external factor such as an intervening cloud or nebula between the star and the observer (extrinsic). Once students are comfortable with brightness and luminosity use different size candles or bulbs connected to a variable power pack to produce "stars" with different intrinsic luminosities. The concept of extrinsic luminosity can be shown using sheets of Perspex or stiff transparent plastic. If you have more than one sheet, coat one with soot from a candle flame. It represents a dark nebula, a cold cloud of dust and gas blocking out light from stars behind it. Perhaps the best example is the Coalsack Nebula adjacent to Crux, the Southern Cross. 3. Star field images and photos. One of the most versatile resources for teaching is the magnificent poster The Southern Cross and the "Pointers" produced by CSIRO Parkes Observatory using a photo by the renowned astrophotographer, Akira Fujii. It shows Crux and the Pointers in colour plus the region around Eta Carina. If possible, have a laminated copy in your classroom when teaching astrophysics. A view similar to the poster is shown in Figure 3 that also has some of the key objects labelled. The unlabelled original of this photo by Professor Mike Bessell can be found online at http://www.mso.anu.edu.au/~bessell/thumbnails/. Ask students to identify the brightest star in the photo then ask them to justify their choice. Challenge them to think why it is brightest. Most should soon see the relationship between the width of the star image and its brightness. Using a laminated copy of the poster students could actually measure the width of various stars and try and determine a relationship between image size and magnitude. If really keen here you can go into the photochemistry of photons interacting with the film material. It is important to point out that all the stars on the image are so far away that they should still be point sources. (The poster is available from Parkes Observatory Visitors Centre, phone 02 6861 1777, or email parkes-vdc@csiro.au).

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Figure 7: Crux Region with key features labelled (Credit: Adapted from an image by M. Bessell) 4. Colour and Colour Index. Using either the online photo or the poster of the Crux region, students are easily able to detect the variations in colours of stars. This provides an effective way of introducing colour, blackbody curves, Wien's Law, and the value of observing through different filters. Provide students with red, yellow and blue cellophane filters. Many ray box kits used to come with colour transparency filters and these are excellent as they are robust and easily held. When students view a coloured star field through different filters they will see that different stars are brighter through different filters; red stars are brighter through red filters and blue stars brighter through blue filters. If you have a Polaroid instant camera or a digital camera and a darkened room you may like to try and photograph different coloured "stars" through different coloured filters. To create the stars simply use a ray box with different coloured transparency slides in the outlet slit or use a fibre optic torch with red, clear, yellow and blue cellophane over different fibres. Use coloured cellophane or ray box transparencies as the filters in front of the camera. Using different filters compare the relative image size of the stars. A ray box or large 12 V bulb connected to a rheostat is also a quick and effective way to reinforce the relationship between temperature and colour. When low voltage is used, the filament glows dimly and appears red or orange. As the voltage is increased the filament becomes hotter and goes yellowish then white. There