Sun Movement
Content
Rowlands
Understanding the Sun’s movement
Developing understanding of the Sun’s movement across the sky
Mark Rowlands
This article discusses the nature of the Sun’s movement across the sky, as viewed from the Earth’s surface, as well as changes over the seasons and differences between different places
On primary initial teacher training courses, my colleagues and I regularly teach a short topic on ‘The Earth and space’, going through ideas at key stages 1 and 2 and also discussing relevant aspects of students’ background knowledge at key stage 3 and beyond. From these sessions, I often have the impression that many students are particularly keen to ‘know the facts’ (since they might, after all, soon be teaching the topic themselves) but that what they understand by ‘fact’ is the scientific model of the Earth as a globe, spinning once a day on a tilted axis, and orbiting the Sun once a year. It almost seems that they are not interested in, or want to move quickly on from, what can actually be observed of the skies from the Earth’s surface. In this article, I want briefly to try to redress the balance and to present some of the things that can be observed about how the Sun moves across the sky, as well as discussing some of the teaching and learning issues associated with this.
ABSTRACT The details of how the Sun moves across the sky are not immediately apparent, particularly its three-dimensional nature. Ways of developing an understanding of this are discussed, including the use of planetaria, three-dimensional models, drawings and computer software. Drawings are presented of the Sun’s path as seen from this country, including seasonal changes, and from other places on the globe. The article sets out to redress the balance between observations of the Sun’s path and the explanation of these (apparent) movements in terms of the scientific model of the Earth in space.
Seeing the pattern of the Sun’s (apparent) movement
What, then, can be seen of the Sun in the sky? Obvious starting points are that the Sun rises in the east and sets in the west, and that during the day it is at various intermediate points in the sky. Between its places of rising and setting the Sun moves across the sky. (With our deeper understanding, we would say that it apparently moves, but this does not take away from what we see!) Making systematic observations of this literally everyday phenomenon is a challenging but rewarding task; see, for example, Moeschl (1993) for practical suggestions for how to go about this. Measuring the angle between the horizontal and the line from the observer to the Sun is a useful aspect to include, and Clish (1983) describes a way of using a clinometer to do this without having to look directly at the Sun. However, the investigator also has to overcome a range of practical difficulties. First, the Sun’s brightness is a potential hazard to the eyes: it is very important that as a teacher one ensures that pupils know not to gaze directly at the Sun, and that optical aids such as telescopes must never be used. Then there is the all-too-common opposite difficulty – not seeing it at all because of cloud cover! Also, most of us live in an urban environment where it may well be difficult to obtain a clear view of the sky – buildings, trees and so on get in the way and are particularly limiting in a flattish area. Add to this the slowness of the daily movement, which is a real test of patience, and seasonal changes happening over many months. These are not reasons for giving up on direct observation –
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overcoming them can be very satisfying. Nevertheless, knitting observations into a coherent pattern is difficult and there is a need to use other means to support and extend the process of thinking this through. An example of one way of bringing together information is given in Figure 1, which is taken from the Learn website linked to the key stage 3 unit ‘The solar system and beyond’ from the QCA exemplar scheme of work. Most of the information of the original is included but it lacks the computer animation: this shows, on the press of a key, the Sun actually moving.
Apparent height of the Sun Summer Autumn and spring equinoxes Winter
East sunrise
midday
West sunset
set in the hemisphere of the sky above and around us. Probably the best aid to realising this is to see a simulation in a planetarium. Both the London Planetarium and the Planetarium at Liverpool Museum, for example, have programmes that include the diurnal movement of the Sun across the sky. Smaller planetaria are also available, including ones that can be inflated inside a classroom (Stockdale, 1997). Further details of local and travelling planetaria can be obtained from the British Association of Planetaria (see Websites). On an even smaller scale, one can use a threedimensional model of the sky. Homemade ones are of course entirely possible but a commercially available one is the Lenart Sphere (details under Apparatus). This is intended as an aid to mathematics teaching to introduce geometry on a curved surface, but it is very suited to demonstrating the Sun’s path as well. The kit consists of a transparent plastic sphere about 40 cm in diameter but also comes with hemispherical ‘transparencies’, made out of transparent, reasonably thick plastic; they are flexible but firm enough to stand without collapsing. They are made to fit over the sphere but can be used (and purchased) separately. A transparency is a very good model of the sky, and felt-tip pens can be used to draw on it various positions of the Sun’s path.
Figure 1 Sun’s movement across the sky (Learn website).
Using two-dimensional drawings
Two-dimensional drawings that attempt to depict three dimensions are also possible – and are used in this article for obvious reasons. My impression is that some people find these diagrams very easy to interpret (and probably find easy grasping the threedimensional nature of the Sun’s path, anyway). Others – like me! – may not find it easy; if you are one of the latter, you may need a model to start with. However, I will also provide an explanation of how these are drawn and what they are intended to show. As a suitable starting point, I have shown in Figure 2 the Sun’s path in the sky, at a place on the latitude of Manchester, at about the time of either of the equinoxes. First imagine that you are on a flat plain, with no trees, buildings or hills obscuring the view – or it could be out at sea somewhere – and it is a very clear day. Because of the curvature of the Earth, even if the atmosphere were very, very clear, the distance you could see would be limited. You would see the horizon all around you, forming a circle, at a distance
Such an impression is probably sufficient for learning at a basic level. But it does lack the third dimension and may be misleading in terms of how someone might use it to visualise how the Sun moves. (It is also misleading in implying that the Sun rises and sets in the same directions on each day of the year.) Grasping for oneself the three-dimensional nature of the Sun’s path seems to me of real value for teaching at key stage 3 (lower secondary school in the UK, pupils aged 11–14 years) and possibly for key stage 2 (upper primary in the UK, pupils aged 7– 11 years) as well. It is valuable for clarifying one’s own and pupils’ understanding; for answering questions that they may ask; for extending the thinking of some; or perhaps just for enabling us as teachers to be more confident in our knowledge of how the Sun moves, particularly if we want to guide pupils in making firsthand observations. The central point about this is that the Sun’s path is along an arc that is (in terms of our direct perception)
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Understanding the Sun’s movement
Zenith
sky
East
North
P
South
West
horizon
Figure 2 Diagram showing the three-dimensional nature of the Sun’s path.
of about 2/3 miles. On the other hand, the curvature would be so slight (relative to how big people are) that you would not be aware of it: the ground would seem perfectly flat. So the simplified diagram shows such an area, seen from somewhere above it, with the circular horizon drawn as an ellipse because of perspective. Above you is the sky – one can imagine it is a good day with a bright blue sky extending all around. The sky looks rather like a beautiful blue surface that is the underside of a hemispherical bowl under which we live: and so it is drawn like that in the diagram. (The other half of the hemisphere is below us, and the whole is called the celestial sphere.) Of course there is no real surface and it is misleading in certain respects to think that the sky extends to the same distance all around us. But this is a good enough approximation. The directions of east, west, north and south are shown, as is the zenith – the point vertically above in the sky. Now, at last, we have some reference points for drawing on the path of the Sun’s (apparent) movement. In this country, around March 21 and September 21 – the spring and autumn equinoxes – the Sun rises due east of where you stand and sets due west. Over the day it moves across the sky between those places of rising and setting, and on these days this movement
takes 12 hours to accomplish. Because the sky appears to be hemispherical, the Sun appears to be ‘on’ the sky and this is a reasonable way of depicting it in the diagram. The Sun’s path therefore follows the line of a semicircular arc. The path does not take it through the zenith directly above you and at its high point – at midday/noon, halfway in time between sunrise and sunset – it is still at an angle in the sky. In other words, the plane of the disc the edge of which is the Sun’s path is at an angle to the ground. (At the latitude of Manchester this angle is about 60 degrees.) Once the Sun has set it is of course no longer visible but because it rises in the east 12 hours after it has set in the west, it is a good assumption that it keeps on moving after it has set, moves at the same speed as it did during the day and along the same-shaped path. In other words, the complete path of the Sun over the 24 hours is in the shape of a circle, half above the horizon and half below. The latter is shown as a dotted line in the diagram. And now the explanation of what the diagram shows is complete! This is the basic pattern of the Sun’s path but there are interesting changes in this path during the course of the year. The obvious one is that between September and March the time during a day of 24 hours that the Sun spends above the horizon is shorter
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longest day shortest day
East North South
West
Figure 3 Sun’s path at the equinoxes and solstices.
than the time it spends below (long nights, short days). The shortest day is on or near December 21. On the other hand, between March and September, there are longer days than nights, with the longest day on or near June 21. How are these changes in day length reflected in the Sun’s path across the sky? This is depicted in Figure 3, which again depicts the situation in Manchester or a place at the same latitude. In comparison to Figure 2, Figure 3 now includes the Sun’s paths on the shortest and longest days. On the longest day, the Sun’s path is in a position shifted northwards. It rises in a position north of due east and sets in a position north of due west. But the plane of the circular path is still inclined at the same angle to the horizontal. Hopefully it can be seen from Figure 3 that the northward shift of the Sun’s path means that more of its path is above the horizon than is below, that is, the day is longer than the night. Hopefully, too, the diagram’s depiction of the Sun’s path at the shortest day will be clear to the reader without further explanation. The reader may well be struck by several features shown by Figure 3 about the Sun’s path. One is that the Sun is never directly overhead, even on the longest day – though it does become progressively higher from the shortest day to the longest day. Another is the large extent of the shift: on the longest day the Sun is rising as far north as about NE and is setting as far as NW. There is a correspondingly large shift south by the time of the shortest day. The differences between the Sun’s paths are shown even more strikingly when presented as shown in Figure 4.
Shortest day
Equinoxes
Longest day
Figure 4 Differences between the Sun’s path between shortest and longest days.
In terms of the literature, the two-dimensional depiction of the hemispherical sky is commonly used in many popular astronomy books to show the stars of the night skies, but rarely used for the Sun’s path. Notable exceptions are the works of Norman Davidson (1987, 1993), although these are not easy to obtain. As one might expect, there are a range of relevant websites (see Useful websites), although most of the ones I have found do not go beyond the kind of drawing given in Figure 3. The wonderful CD-ROM Starry Night (Sienna Software) simulates what you
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can see in the sky from an astonishing and seemingly unlimited range of times and places (including daytimes, despite its title); however, it shows at any one time only what can be seen of the sky in a particular direction rather than the whole of the sky. (See Beare, 2004, for a useful discussion of Starry Night and how best to obtain it.) Hopefully at this stage, you have gained a reasonably clear, three-dimensional picture in your mind of the Sun’s path. If you have come to the article with little prior specialist knowledge, I hope that you have discovered things you had not previously known; you may even have shed a few misconceptions. And the above has focused only on what can be seen and has included hardly a mention of theory! The task of using theory to explain observation is of course central to science teaching – I have wanted to focus on observation in this article only because there seems to be a lack of emphasis on it in literature and a corresponding emphasis on the theory. Even so, it is useful to bear in mind how challenging it can be for pupils and students actively to use the ‘tilted Earth’ explanation of seasonal changes in day length (Parker and Heywood, 1998, and also noted in the QCA unit for year 7, ‘The solar system and beyond’). An example of such seasonal change is, of course, depicted in Figure 3 above. But this refers only to what happens in a place at about the same latitude as Manchester. If someone understands the theory well enough to explain these observations (or the corresponding observations in his
or her own place of residence), can they use the theory to make predictions about the Sun’s path in other places on Earth and the seasonal changes at those places? I for one have to own up to being unable to do this initially, and can therefore point out how useful this investigation can be for deepening one’s grasp of the theory!
Helpful software: SunPath
As well as in this article, drawings of the Sun’s path in various places on Earth can be found in Davidson (1987, 1993), but a more easily accessible and probably more useful source in this context is SunPath, software which can be found within the Australia National University’s website (www.anu.edu.au/) at: http://solar.anu.edu.au/Sun/SunPath/index.html If you like the look of it, you can download it on to your hard disc from: http://solar.anu.edu.au/Sun/help/download.html and run it as a stand-alone program. The basic format of the program is shown in Figure 5. You can put in information about the time and place, and it will calculate and show the corresponding path of the Sun. Although it has limitations, such as not including different longitudes, it is a wonderfully flexible tool to have at your disposal. However, I think that it is worth considering carefully about how it
Figure 5 SunPath.
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might be used – either when exploring your own understanding or when pupils and students explore theirs. Typing in a few places and times at random, and perhaps being surprised by the shapes that are produced, might be interesting but might not do much to extend understanding. A more systematic approach is likely to be more useful, disciplining oneself to think through one’s theory to make predictions from it, using SunPath to check those predictions and rethinking one’s theory as necessary. One possible imaginary journey is described below: I hope that the patterns of the Sun’s path depicted at various places will convince you that the activity is worth doing and the patterns worth explaining.
The Sun’s path across northerly skies
Going to places east or west of somewhere in Britain, the main thing that changes is that sunrise and sunset times on a particular day are both later for places to the west and earlier for places to the east – relative, that is, to the place where you are. However, there are no differences in the actual periods of daylight and of darkness, and the patterns of change in these periods over the year are the same. This is not the case for places to the north and south. Even travelling about in Britain there are noticeable differences in day length during summer and winter between, say,
South of England longest day Orkney longest day Z
the south of England and Orkney. On midsummer’s day, Orkney has almost two hours more daylight – although it has correspondingly shorter days in the winter. Figure 6 shows diagrammatically the differences in the paths of the Sun in the two places. First, the plane of the Sun’s path in Orkney is always more towards the horizontal than in the south of England (by about eight degrees). On the equinoxes sunrise and sunset are to the east and west in both places; during summer, the directions of sunrise and sunset also move northwards on successive days in both places. But because of the differing tilts in the Sun’s plane of movement, by midsummer’s day sunrise and sunset have shifted further north in Orkney than they have in England: sunrise and sunset are even north of NE and NW respectively while in England they are a bit south of NE and NW. The overall effect is that the Sun at Orkney is above the horizon for even more of the day. A perhaps unexpected detail is that on midsummer’s day, the Sun at noon is further south of the zenith in Orkney than it is in England. Going even further north, it is well known that within the Arctic Circle there are days of 24 hours’ daylight. But even if you know that, can you describe how the Sun moves in the sky? The diagram for this is presented in Figure 7. This diagram could show what happens on a summer’s day at a place inside the Arctic Circle. The angle of the plane of the Sun’s path is even nearer the horizontal than it is in Scotland and at midnight the
South of England equinox Orkney equinox
North
South
Figure 6 Sun’s path compared for South of England and Orkney.
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noon
midnight North South
Figure 7 Sun’s path during a summer’s day at a place north of the Arctic Circle.
Sun is still above the horizon. Pictures and books often give the impression that this light at midnight is somewhat eerie, but it is a light that matches how far above the horizon the Sun is. For example, well within the Arctic Circle, the Sun is well above the horizon at midnight; the quality of light changes from midafternoon leading up to midnight to mid-morning after midnight. There is nothing at all like twilight at any stage. Incidentally there is a very beautiful popular poster titled ‘Norway – Land of the Midnight Sun’ (HusmoFoto, Box 231, Skoyen, 0212 Oslo 2, Norway). It is composed of a series of photographs taken in Norway north of the Arctic Circle, from the same spot. As the day progressed, the photographer turned to point the camera at the Sun. The tall, thin photographs were then pasted together in a long line so that one can see the successive positions of the Sun. The overall effect is shown in simplified form in Figure 8. It is another
way of showing the same thing as Figure 7 (although I remember that it took me a long time to see this!) It is a good further test of one’s understanding of the patterns involved to predict what the situation is at the North Pole. Yes, there are 24 hours of daylight each day in the summer and 24 hours of darkness each day in the winter. But what is the path of the Sun like? Astonishingly, the Sun circles in the sky above! (Figure 9). The plane of the Sun’s path remains horizontal to the ground but between midsummer’s day and the autumnal equinox this plane comes down closer and closer to the horizon. Davidson describes this in the following memorable way: At the poles another extreme is reached in that the year consists of only one day. . . dawn and dusk last for over seven weeks each. . . dark night as such lasts for about two and a half months . . . (Davidson, 1987: 54–55)
horizon 1800 hrs 2000 hrs 2200 hrs mid night 0200 hrs 0400 hrs 0600 hrs 0800 hrs 1000 hrs noon 1400 hrs 1600 hrs
Figure 8 Sun’s positions in the sky during a summer day at a place north of the Arctic Circle.
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Figure 9 Sun’s path at the North Pole.
The Sun’s path across southerly skies
I have discussed so far what happens at places to the north of Britain. What about places to the south? As one travels southwards, the angle of the plane of the Sun’s path becomes closer to the vertical. Places along the Tropic of Cancer are a good first stopping place. Here the angle is 23.5° from the vertical, so at midday, no matter what the time of year, the Sun is always very high in the sky. As in Britain, there is still the ‘migration’ of the Sun’s path northwards and southwards during the course of the year. A particular point of interest is that the Sun is vertically overhead at noon only on one day of the year: midsummer’s day (Figure 10). Finally, we reach the equator (Figure 11). This has the particular interest that the Sun’s path is vertical to the Earth’s surface. However, the Sun is directly overhead only on two days of the year: the equinoxes. On midsummer’s day, sunrise has moved to a position north of east and sunset north of west, and by midwinter’s day there has been a corresponding movement of sunrise to south of east, and sunset to south of west.
Continuing with our imaginary journey southwards, the situation in the southern hemisphere can be summed up as the mirror image of that in the northern hemisphere. As an example to illustrate the principle, Figure 12 compares the Sun’s path at the time of the equinoxes as it is in Manchester (53 degrees north of the equator) with the Sun’s path in the Falkland Islands (about 52 degrees south of the equator). Following the principles discussed so far, the reader who has followed the making of the diagrams so far will be able to construct similar ones for other places in the southern hemisphere – remembering, of course, that summer is from September to March and winter from March to September. There is one final and fascinating twist to the tale: by the time one has journeyed to the South Pole, one has got to a situation where the Sun circles in the sky during the summer period (Figure 13). So, just like at the North Pole, one cannot tell from the Sun’s path what is east or west. But in contrast to the North Pole, the Sun now circles in an anticlockwise direction – that is, as one looks up at it in the sky. This at least informs the observer that he or she is at the South rather than the North Pole!
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Z
Understanding the Sun’s movement
Figure 10 Sun’s path at a place on the Tropic of Cancer.
21 June Z 21 December
E North South
W
Figure 11 Sun’s path at a place on the Equator.
E North South
Figure 12 Sun’s path compared for places 53° S and N.
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W
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Figure 13 Sun’s path at the South Pole.
References
Beare, R. (2004) Resources to enliven the teaching of astronomy to upper secondary students. School Science Review, 85(313), 115–125. Clish, D. V. (1983) Exploring the heavens with pupils aged 9 to 11 years. Devon: Glenmore Publications. Davidson, N. (1987) Astronomy and the imagination, a new approach to man’s experience of the stars. London: Routledge and Kegan Paul Davidson, N. (1993) Sky phenomena: a guide to naked-eye observation of the heavens. Edinburgh: Floris Books. Moeschl, R. (1993) Exploring the sky, projects for beginning astronomers. Chicago: Chicago Review Press. Parker, J. and Heywood, D. (1998) The earth and beyond: developing primary teachers’ understanding of basic astronomical events. International Journal of Science Education, 20(5), 503–520. QCA/DfES (1997–2003) Schemes of Work, science at key stage 3, Unit 7l: The solar system and beyond. www.standards.dfes.gov.uk/schemes2/secondary_science/ Sienna Software CD-ROM Starry Night. Details on: www.starrynight.com Stockdale, D. L. (1997) Portable planetarium. The Science Teacher, 64, 42–45.
Apparatus
The Lenart Sphere kit is made by Key Curriculum Press, California, and can be purchased in this country from QED Books (Pentagon Place, 195B Berkhamsted Road, Chesham, Bucks HP5 3AP)
Useful websites
Association for Astronomy Education: www.aae.org.uk British Association of Planetaria: www.planetarium.org.uk Learn.co.uk (‘The apparent movement of the Sun across the sky’): www.learn.co.uk/default.asp?WCI=Unit&WCU=2435 Lakota Star Knowledge: www.kstrom.net/isk/stars/starkno3.html Cornell University: http://astrosun.tn.cornell.edu/courses/astro201/ sun_ithaca.htm Madison Planetarium and Observatory: www.madison.k12.wi.us/planetarium/ftdg2.htm Montana State University – Solar Physics Group: http://solar.physics.montana.edu/YPOP/Classroom/Lessons/ Sundials/sunpath.html
Mark Rowlands is senior lecturer in science education at the Institute of Education, Manchester Metropolitan University. E-mail: [email protected]
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School Science Review, March 2005, 86(316)
Understanding the Sun’s movement
Developing understanding of the Sun’s movement across the sky
Mark Rowlands
This article discusses the nature of the Sun’s movement across the sky, as viewed from the Earth’s surface, as well as changes over the seasons and differences between different places
On primary initial teacher training courses, my colleagues and I regularly teach a short topic on ‘The Earth and space’, going through ideas at key stages 1 and 2 and also discussing relevant aspects of students’ background knowledge at key stage 3 and beyond. From these sessions, I often have the impression that many students are particularly keen to ‘know the facts’ (since they might, after all, soon be teaching the topic themselves) but that what they understand by ‘fact’ is the scientific model of the Earth as a globe, spinning once a day on a tilted axis, and orbiting the Sun once a year. It almost seems that they are not interested in, or want to move quickly on from, what can actually be observed of the skies from the Earth’s surface. In this article, I want briefly to try to redress the balance and to present some of the things that can be observed about how the Sun moves across the sky, as well as discussing some of the teaching and learning issues associated with this.
ABSTRACT The details of how the Sun moves across the sky are not immediately apparent, particularly its three-dimensional nature. Ways of developing an understanding of this are discussed, including the use of planetaria, three-dimensional models, drawings and computer software. Drawings are presented of the Sun’s path as seen from this country, including seasonal changes, and from other places on the globe. The article sets out to redress the balance between observations of the Sun’s path and the explanation of these (apparent) movements in terms of the scientific model of the Earth in space.
Seeing the pattern of the Sun’s (apparent) movement
What, then, can be seen of the Sun in the sky? Obvious starting points are that the Sun rises in the east and sets in the west, and that during the day it is at various intermediate points in the sky. Between its places of rising and setting the Sun moves across the sky. (With our deeper understanding, we would say that it apparently moves, but this does not take away from what we see!) Making systematic observations of this literally everyday phenomenon is a challenging but rewarding task; see, for example, Moeschl (1993) for practical suggestions for how to go about this. Measuring the angle between the horizontal and the line from the observer to the Sun is a useful aspect to include, and Clish (1983) describes a way of using a clinometer to do this without having to look directly at the Sun. However, the investigator also has to overcome a range of practical difficulties. First, the Sun’s brightness is a potential hazard to the eyes: it is very important that as a teacher one ensures that pupils know not to gaze directly at the Sun, and that optical aids such as telescopes must never be used. Then there is the all-too-common opposite difficulty – not seeing it at all because of cloud cover! Also, most of us live in an urban environment where it may well be difficult to obtain a clear view of the sky – buildings, trees and so on get in the way and are particularly limiting in a flattish area. Add to this the slowness of the daily movement, which is a real test of patience, and seasonal changes happening over many months. These are not reasons for giving up on direct observation –
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overcoming them can be very satisfying. Nevertheless, knitting observations into a coherent pattern is difficult and there is a need to use other means to support and extend the process of thinking this through. An example of one way of bringing together information is given in Figure 1, which is taken from the Learn website linked to the key stage 3 unit ‘The solar system and beyond’ from the QCA exemplar scheme of work. Most of the information of the original is included but it lacks the computer animation: this shows, on the press of a key, the Sun actually moving.
Apparent height of the Sun Summer Autumn and spring equinoxes Winter
East sunrise
midday
West sunset
set in the hemisphere of the sky above and around us. Probably the best aid to realising this is to see a simulation in a planetarium. Both the London Planetarium and the Planetarium at Liverpool Museum, for example, have programmes that include the diurnal movement of the Sun across the sky. Smaller planetaria are also available, including ones that can be inflated inside a classroom (Stockdale, 1997). Further details of local and travelling planetaria can be obtained from the British Association of Planetaria (see Websites). On an even smaller scale, one can use a threedimensional model of the sky. Homemade ones are of course entirely possible but a commercially available one is the Lenart Sphere (details under Apparatus). This is intended as an aid to mathematics teaching to introduce geometry on a curved surface, but it is very suited to demonstrating the Sun’s path as well. The kit consists of a transparent plastic sphere about 40 cm in diameter but also comes with hemispherical ‘transparencies’, made out of transparent, reasonably thick plastic; they are flexible but firm enough to stand without collapsing. They are made to fit over the sphere but can be used (and purchased) separately. A transparency is a very good model of the sky, and felt-tip pens can be used to draw on it various positions of the Sun’s path.
Figure 1 Sun’s movement across the sky (Learn website).
Using two-dimensional drawings
Two-dimensional drawings that attempt to depict three dimensions are also possible – and are used in this article for obvious reasons. My impression is that some people find these diagrams very easy to interpret (and probably find easy grasping the threedimensional nature of the Sun’s path, anyway). Others – like me! – may not find it easy; if you are one of the latter, you may need a model to start with. However, I will also provide an explanation of how these are drawn and what they are intended to show. As a suitable starting point, I have shown in Figure 2 the Sun’s path in the sky, at a place on the latitude of Manchester, at about the time of either of the equinoxes. First imagine that you are on a flat plain, with no trees, buildings or hills obscuring the view – or it could be out at sea somewhere – and it is a very clear day. Because of the curvature of the Earth, even if the atmosphere were very, very clear, the distance you could see would be limited. You would see the horizon all around you, forming a circle, at a distance
Such an impression is probably sufficient for learning at a basic level. But it does lack the third dimension and may be misleading in terms of how someone might use it to visualise how the Sun moves. (It is also misleading in implying that the Sun rises and sets in the same directions on each day of the year.) Grasping for oneself the three-dimensional nature of the Sun’s path seems to me of real value for teaching at key stage 3 (lower secondary school in the UK, pupils aged 11–14 years) and possibly for key stage 2 (upper primary in the UK, pupils aged 7– 11 years) as well. It is valuable for clarifying one’s own and pupils’ understanding; for answering questions that they may ask; for extending the thinking of some; or perhaps just for enabling us as teachers to be more confident in our knowledge of how the Sun moves, particularly if we want to guide pupils in making firsthand observations. The central point about this is that the Sun’s path is along an arc that is (in terms of our direct perception)
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Understanding the Sun’s movement
Zenith
sky
East
North
P
South
West
horizon
Figure 2 Diagram showing the three-dimensional nature of the Sun’s path.
of about 2/3 miles. On the other hand, the curvature would be so slight (relative to how big people are) that you would not be aware of it: the ground would seem perfectly flat. So the simplified diagram shows such an area, seen from somewhere above it, with the circular horizon drawn as an ellipse because of perspective. Above you is the sky – one can imagine it is a good day with a bright blue sky extending all around. The sky looks rather like a beautiful blue surface that is the underside of a hemispherical bowl under which we live: and so it is drawn like that in the diagram. (The other half of the hemisphere is below us, and the whole is called the celestial sphere.) Of course there is no real surface and it is misleading in certain respects to think that the sky extends to the same distance all around us. But this is a good enough approximation. The directions of east, west, north and south are shown, as is the zenith – the point vertically above in the sky. Now, at last, we have some reference points for drawing on the path of the Sun’s (apparent) movement. In this country, around March 21 and September 21 – the spring and autumn equinoxes – the Sun rises due east of where you stand and sets due west. Over the day it moves across the sky between those places of rising and setting, and on these days this movement
takes 12 hours to accomplish. Because the sky appears to be hemispherical, the Sun appears to be ‘on’ the sky and this is a reasonable way of depicting it in the diagram. The Sun’s path therefore follows the line of a semicircular arc. The path does not take it through the zenith directly above you and at its high point – at midday/noon, halfway in time between sunrise and sunset – it is still at an angle in the sky. In other words, the plane of the disc the edge of which is the Sun’s path is at an angle to the ground. (At the latitude of Manchester this angle is about 60 degrees.) Once the Sun has set it is of course no longer visible but because it rises in the east 12 hours after it has set in the west, it is a good assumption that it keeps on moving after it has set, moves at the same speed as it did during the day and along the same-shaped path. In other words, the complete path of the Sun over the 24 hours is in the shape of a circle, half above the horizon and half below. The latter is shown as a dotted line in the diagram. And now the explanation of what the diagram shows is complete! This is the basic pattern of the Sun’s path but there are interesting changes in this path during the course of the year. The obvious one is that between September and March the time during a day of 24 hours that the Sun spends above the horizon is shorter
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longest day shortest day
East North South
West
Figure 3 Sun’s path at the equinoxes and solstices.
than the time it spends below (long nights, short days). The shortest day is on or near December 21. On the other hand, between March and September, there are longer days than nights, with the longest day on or near June 21. How are these changes in day length reflected in the Sun’s path across the sky? This is depicted in Figure 3, which again depicts the situation in Manchester or a place at the same latitude. In comparison to Figure 2, Figure 3 now includes the Sun’s paths on the shortest and longest days. On the longest day, the Sun’s path is in a position shifted northwards. It rises in a position north of due east and sets in a position north of due west. But the plane of the circular path is still inclined at the same angle to the horizontal. Hopefully it can be seen from Figure 3 that the northward shift of the Sun’s path means that more of its path is above the horizon than is below, that is, the day is longer than the night. Hopefully, too, the diagram’s depiction of the Sun’s path at the shortest day will be clear to the reader without further explanation. The reader may well be struck by several features shown by Figure 3 about the Sun’s path. One is that the Sun is never directly overhead, even on the longest day – though it does become progressively higher from the shortest day to the longest day. Another is the large extent of the shift: on the longest day the Sun is rising as far north as about NE and is setting as far as NW. There is a correspondingly large shift south by the time of the shortest day. The differences between the Sun’s paths are shown even more strikingly when presented as shown in Figure 4.
Shortest day
Equinoxes
Longest day
Figure 4 Differences between the Sun’s path between shortest and longest days.
In terms of the literature, the two-dimensional depiction of the hemispherical sky is commonly used in many popular astronomy books to show the stars of the night skies, but rarely used for the Sun’s path. Notable exceptions are the works of Norman Davidson (1987, 1993), although these are not easy to obtain. As one might expect, there are a range of relevant websites (see Useful websites), although most of the ones I have found do not go beyond the kind of drawing given in Figure 3. The wonderful CD-ROM Starry Night (Sienna Software) simulates what you
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can see in the sky from an astonishing and seemingly unlimited range of times and places (including daytimes, despite its title); however, it shows at any one time only what can be seen of the sky in a particular direction rather than the whole of the sky. (See Beare, 2004, for a useful discussion of Starry Night and how best to obtain it.) Hopefully at this stage, you have gained a reasonably clear, three-dimensional picture in your mind of the Sun’s path. If you have come to the article with little prior specialist knowledge, I hope that you have discovered things you had not previously known; you may even have shed a few misconceptions. And the above has focused only on what can be seen and has included hardly a mention of theory! The task of using theory to explain observation is of course central to science teaching – I have wanted to focus on observation in this article only because there seems to be a lack of emphasis on it in literature and a corresponding emphasis on the theory. Even so, it is useful to bear in mind how challenging it can be for pupils and students actively to use the ‘tilted Earth’ explanation of seasonal changes in day length (Parker and Heywood, 1998, and also noted in the QCA unit for year 7, ‘The solar system and beyond’). An example of such seasonal change is, of course, depicted in Figure 3 above. But this refers only to what happens in a place at about the same latitude as Manchester. If someone understands the theory well enough to explain these observations (or the corresponding observations in his
or her own place of residence), can they use the theory to make predictions about the Sun’s path in other places on Earth and the seasonal changes at those places? I for one have to own up to being unable to do this initially, and can therefore point out how useful this investigation can be for deepening one’s grasp of the theory!
Helpful software: SunPath
As well as in this article, drawings of the Sun’s path in various places on Earth can be found in Davidson (1987, 1993), but a more easily accessible and probably more useful source in this context is SunPath, software which can be found within the Australia National University’s website (www.anu.edu.au/) at: http://solar.anu.edu.au/Sun/SunPath/index.html If you like the look of it, you can download it on to your hard disc from: http://solar.anu.edu.au/Sun/help/download.html and run it as a stand-alone program. The basic format of the program is shown in Figure 5. You can put in information about the time and place, and it will calculate and show the corresponding path of the Sun. Although it has limitations, such as not including different longitudes, it is a wonderfully flexible tool to have at your disposal. However, I think that it is worth considering carefully about how it
Figure 5 SunPath.
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might be used – either when exploring your own understanding or when pupils and students explore theirs. Typing in a few places and times at random, and perhaps being surprised by the shapes that are produced, might be interesting but might not do much to extend understanding. A more systematic approach is likely to be more useful, disciplining oneself to think through one’s theory to make predictions from it, using SunPath to check those predictions and rethinking one’s theory as necessary. One possible imaginary journey is described below: I hope that the patterns of the Sun’s path depicted at various places will convince you that the activity is worth doing and the patterns worth explaining.
The Sun’s path across northerly skies
Going to places east or west of somewhere in Britain, the main thing that changes is that sunrise and sunset times on a particular day are both later for places to the west and earlier for places to the east – relative, that is, to the place where you are. However, there are no differences in the actual periods of daylight and of darkness, and the patterns of change in these periods over the year are the same. This is not the case for places to the north and south. Even travelling about in Britain there are noticeable differences in day length during summer and winter between, say,
South of England longest day Orkney longest day Z
the south of England and Orkney. On midsummer’s day, Orkney has almost two hours more daylight – although it has correspondingly shorter days in the winter. Figure 6 shows diagrammatically the differences in the paths of the Sun in the two places. First, the plane of the Sun’s path in Orkney is always more towards the horizontal than in the south of England (by about eight degrees). On the equinoxes sunrise and sunset are to the east and west in both places; during summer, the directions of sunrise and sunset also move northwards on successive days in both places. But because of the differing tilts in the Sun’s plane of movement, by midsummer’s day sunrise and sunset have shifted further north in Orkney than they have in England: sunrise and sunset are even north of NE and NW respectively while in England they are a bit south of NE and NW. The overall effect is that the Sun at Orkney is above the horizon for even more of the day. A perhaps unexpected detail is that on midsummer’s day, the Sun at noon is further south of the zenith in Orkney than it is in England. Going even further north, it is well known that within the Arctic Circle there are days of 24 hours’ daylight. But even if you know that, can you describe how the Sun moves in the sky? The diagram for this is presented in Figure 7. This diagram could show what happens on a summer’s day at a place inside the Arctic Circle. The angle of the plane of the Sun’s path is even nearer the horizontal than it is in Scotland and at midnight the
South of England equinox Orkney equinox
North
South
Figure 6 Sun’s path compared for South of England and Orkney.
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noon
midnight North South
Figure 7 Sun’s path during a summer’s day at a place north of the Arctic Circle.
Sun is still above the horizon. Pictures and books often give the impression that this light at midnight is somewhat eerie, but it is a light that matches how far above the horizon the Sun is. For example, well within the Arctic Circle, the Sun is well above the horizon at midnight; the quality of light changes from midafternoon leading up to midnight to mid-morning after midnight. There is nothing at all like twilight at any stage. Incidentally there is a very beautiful popular poster titled ‘Norway – Land of the Midnight Sun’ (HusmoFoto, Box 231, Skoyen, 0212 Oslo 2, Norway). It is composed of a series of photographs taken in Norway north of the Arctic Circle, from the same spot. As the day progressed, the photographer turned to point the camera at the Sun. The tall, thin photographs were then pasted together in a long line so that one can see the successive positions of the Sun. The overall effect is shown in simplified form in Figure 8. It is another
way of showing the same thing as Figure 7 (although I remember that it took me a long time to see this!) It is a good further test of one’s understanding of the patterns involved to predict what the situation is at the North Pole. Yes, there are 24 hours of daylight each day in the summer and 24 hours of darkness each day in the winter. But what is the path of the Sun like? Astonishingly, the Sun circles in the sky above! (Figure 9). The plane of the Sun’s path remains horizontal to the ground but between midsummer’s day and the autumnal equinox this plane comes down closer and closer to the horizon. Davidson describes this in the following memorable way: At the poles another extreme is reached in that the year consists of only one day. . . dawn and dusk last for over seven weeks each. . . dark night as such lasts for about two and a half months . . . (Davidson, 1987: 54–55)
horizon 1800 hrs 2000 hrs 2200 hrs mid night 0200 hrs 0400 hrs 0600 hrs 0800 hrs 1000 hrs noon 1400 hrs 1600 hrs
Figure 8 Sun’s positions in the sky during a summer day at a place north of the Arctic Circle.
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Figure 9 Sun’s path at the North Pole.
The Sun’s path across southerly skies
I have discussed so far what happens at places to the north of Britain. What about places to the south? As one travels southwards, the angle of the plane of the Sun’s path becomes closer to the vertical. Places along the Tropic of Cancer are a good first stopping place. Here the angle is 23.5° from the vertical, so at midday, no matter what the time of year, the Sun is always very high in the sky. As in Britain, there is still the ‘migration’ of the Sun’s path northwards and southwards during the course of the year. A particular point of interest is that the Sun is vertically overhead at noon only on one day of the year: midsummer’s day (Figure 10). Finally, we reach the equator (Figure 11). This has the particular interest that the Sun’s path is vertical to the Earth’s surface. However, the Sun is directly overhead only on two days of the year: the equinoxes. On midsummer’s day, sunrise has moved to a position north of east and sunset north of west, and by midwinter’s day there has been a corresponding movement of sunrise to south of east, and sunset to south of west.
Continuing with our imaginary journey southwards, the situation in the southern hemisphere can be summed up as the mirror image of that in the northern hemisphere. As an example to illustrate the principle, Figure 12 compares the Sun’s path at the time of the equinoxes as it is in Manchester (53 degrees north of the equator) with the Sun’s path in the Falkland Islands (about 52 degrees south of the equator). Following the principles discussed so far, the reader who has followed the making of the diagrams so far will be able to construct similar ones for other places in the southern hemisphere – remembering, of course, that summer is from September to March and winter from March to September. There is one final and fascinating twist to the tale: by the time one has journeyed to the South Pole, one has got to a situation where the Sun circles in the sky during the summer period (Figure 13). So, just like at the North Pole, one cannot tell from the Sun’s path what is east or west. But in contrast to the North Pole, the Sun now circles in an anticlockwise direction – that is, as one looks up at it in the sky. This at least informs the observer that he or she is at the South rather than the North Pole!
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Figure 10 Sun’s path at a place on the Tropic of Cancer.
21 June Z 21 December
E North South
W
Figure 11 Sun’s path at a place on the Equator.
E North South
Figure 12 Sun’s path compared for places 53° S and N.
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Figure 13 Sun’s path at the South Pole.
References
Beare, R. (2004) Resources to enliven the teaching of astronomy to upper secondary students. School Science Review, 85(313), 115–125. Clish, D. V. (1983) Exploring the heavens with pupils aged 9 to 11 years. Devon: Glenmore Publications. Davidson, N. (1987) Astronomy and the imagination, a new approach to man’s experience of the stars. London: Routledge and Kegan Paul Davidson, N. (1993) Sky phenomena: a guide to naked-eye observation of the heavens. Edinburgh: Floris Books. Moeschl, R. (1993) Exploring the sky, projects for beginning astronomers. Chicago: Chicago Review Press. Parker, J. and Heywood, D. (1998) The earth and beyond: developing primary teachers’ understanding of basic astronomical events. International Journal of Science Education, 20(5), 503–520. QCA/DfES (1997–2003) Schemes of Work, science at key stage 3, Unit 7l: The solar system and beyond. www.standards.dfes.gov.uk/schemes2/secondary_science/ Sienna Software CD-ROM Starry Night. Details on: www.starrynight.com Stockdale, D. L. (1997) Portable planetarium. The Science Teacher, 64, 42–45.
Apparatus
The Lenart Sphere kit is made by Key Curriculum Press, California, and can be purchased in this country from QED Books (Pentagon Place, 195B Berkhamsted Road, Chesham, Bucks HP5 3AP)
Useful websites
Association for Astronomy Education: www.aae.org.uk British Association of Planetaria: www.planetarium.org.uk Learn.co.uk (‘The apparent movement of the Sun across the sky’): www.learn.co.uk/default.asp?WCI=Unit&WCU=2435 Lakota Star Knowledge: www.kstrom.net/isk/stars/starkno3.html Cornell University: http://astrosun.tn.cornell.edu/courses/astro201/ sun_ithaca.htm Madison Planetarium and Observatory: www.madison.k12.wi.us/planetarium/ftdg2.htm Montana State University – Solar Physics Group: http://solar.physics.montana.edu/YPOP/Classroom/Lessons/ Sundials/sunpath.html
Mark Rowlands is senior lecturer in science education at the Institute of Education, Manchester Metropolitan University. E-mail: [email protected]
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