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TWO STEPS TOWARDS THE MOVEMENTS OF THE STARS :
A DEMONSTRATOR AND
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TWO STEPS TOWARDS THE MOVEMENTS OF THE STARS :
A DEMONSTRATOR AND
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This workshop is in two parts. In the first one the participants will build a demonstrator of the stars' movements in the celestial sphere. It is only necessary to enter the place's latitude in the device to give simple answers to these questions:
When we teach students about stars and constellations, we start by giving them a list of names. After that, we want them to learn the shape and configuration of every constellation and sometimes we explain some mythologies and geometrical rules to find one constellation near another one, or one star on a straight line from another. This process can be more or less attractive to students depending on the kind of presentation used by the teacher. However, this presentation does not have special difficulties. Problems may appear when we consider the movement of the celestial sphere around the terrestrial axes. The student can understand very well that if the observer lives at the North Pole he/she can see all the stars of the Northern Hemisphere and if he/she lives at the South Pole it will be possible to see all the stars of the Southern Hemisphere. (We only below consider different observation locations in the Northern Hemisphere to simplify the presentation and of course, all European countries are in this situation).
But the problems appear, for our students, when the observer lives somewhere that is not one of the poles, which is the situation of most observers. In this case, they put the stars into three different categories (for every latitude): circumpolar, stars that rise and set, and invisible stars. All us have the experience of students being very surprised when they discover that they live in the Northern Hemisphere and they can observe some stars from the Southern Hemisphere.
Depending on the students' ages, they can understand with more or less difficulty what stars are circumpolar in their city, but it is much more difficult to discover which of them are circumpolar in other cities. If we ask about if one specific star, e.g. Sirius, rises and sets in Bonn, they cannot answer us. We will use the star demonstrator for studying the different types of stars depending on the latitude of the place of observation.
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The main objective is to discover which constellations are circumpolar, which rise and set and which are invisible at specific latitudes. Of course, if we change the latitude of the observer, some constellations that were circumpolar may rise and set, or the opposite may be true. If we observe from latitude of around 45º N, it is clear that we can see stars from the Southern Hemisphere rise and set every night (Fig. 1). |
In our case, the demonstrator some constellations have been drawn with different declinations (without considering their right ascensions because in this case it is not our objective). It is a very good idea to use constellations that are well known to students and with different right ascensions, in order to have constellations visible in different months of the year.
To select the constellation for drawing, only the bright stars were considered to recognise the shape of each constellation, and we do only not use constellations in the same meridian, because we decided to choose constellations that would be well known to students who sometimes observed the sky (Table 1).
(If you are interested in doing this study for each season, you can make four different demonstrators, one for each season. For example, you can use constellations which have different declinations, but always with right ascension between 21h and 3h for the autumn, the same idea with right ascension from 3h to 9h for the winter, the same between 9h and 14h for spring and finally until 14h to 21h for the summer.
If we decide to consider only one season, it can be difficult to select one constellation between +90º and +60º, another between +60º +40º, another between +40º and +20º, and another between +20º to -20º and so on, without overlapping and reaching -60º to -90º. If we also want to select constellations well known to students, with bright stars, and which are big enough to cover the entire meridian with a small number of them, it can be difficult to achieve our objective. As the sky does not have the same kind of constellation (big, well known and bright) distributed during all the year, it may be better to make only one demonstrator to consider all the different right ascensions at the same time.
There is also another argument for building only one demonstrator. The difference between the sky between the four seasons really exists at latitudes around the middle of the hemisphere. If you live in latitudes near the polar circle where your sky is more or less the same all year round, then this concept is relative and introducing more demonstrators is not necessary.)
To obtain a sturdy demonstrator, it is a good idea to glue both pieces on cardboard before cutting. It is a good idea to construct one of them twice as big for use by the teacher.
The instructions to build it appear below.
To start to use the demonstrator you have to enter the latitude that you selected. We will travel on the Earth's surface on an imaginary trip using the demonstrator.
You should hold the main piece of the demonstrator (fig. 2a) by the blank area (below the latitude quadrant) with your left hand. Select the latitude and move the horizon disc until it shows the latitude chosen. With your right hand, move the disc with the constellations drawn from right to left several times. You can observe what constellations are always on the horizon (circumpolar), what constellations rise and set, and which of them are always below the horizon (invisible). Using the demonstrator in this way, the students solve the different activities below easily.
1) If we introduce a latitude equal to +90º, the observer is at the north pole, and we can see that all the constellations in the Northern Hemisphere are circumpolar. All of them in the Southern Hemisphere are invisible and there are no constellations which rise and set. 2) If the latitude is 0º, the observer is on the equator, and we can see that all the constellations rise and set (perpendicular to the horizon). None are circumpolar or invisible. 3) If the latitude is +20º, there are less circumpolar constellations than if the latitude is +40º. But there are a lot more stars that rise and set if the latitude is +20º in front of +40º. 4) If the latitude is +60º, there are a lot of circumpolar and invisible constellations, but the number of constellations that rise and set is reduced compared to the latitude +40º. 5) Finally, using the demonstrator we can suggest that students complete a table like Table 2.
In Table 3 we present the solution to Table 2 obtained using the demonstrator.
If we consider the Sun as a star with variable declination between -23.5º and +23.5º, it appears as a circular star at Arctic latitudes and we can see the Sun at midnight during the summer, and the Sun appears as an invisible star during the winter.
For other observers who live at intermediate latitudes, the Sun appears as a star which rises and sets.
The previous presentation offers a simple process for presenting the stars' movement from different points of observation. It is not enough to give only the previous universal presentation of this phenomenum to the students. It is of course very important to teach them a local presentation of the same movement and to connect with orientation concepts. It is disappointing to discover that a student cannot discuss the position of the Ursa Minor on the local horizon when his/her course of Basic Astronomy is finishing. If he/she tries to find this constellation on the southern horizon, we have proof that the universal presentation of this topic is necessary but is not sufficient. We propose the following simple local model of the horizon.
We start by taking a collection of photos of the horizon. It is only necessary to use the camera on the tripod with a cable release and spend some seconds of exposure time (depending on the light pollution we can spend 5-10 seconds). It is a good idea to take the photos of the horizon from the school where the students observe during every practical activity. Of course, photos taken from outside the city are better than from inside it, but it is important that they recognise the horizon very clearly and can compare the photographic horizon with the real horizon. It is very important to mark the place where we take the photos because we will put the model in the same place.
It is necessary to take every photo with a common overlap area with the next one. When we have the photos on paper, we want to glue one photo to another to obtain a "photographic belt" of the horizon (like a small cylinder). After that we fix the photo-cylinder on a piece of wood according to the orientation of the real horizon (fig. 3).
 | The first step is to introduce the axes of the Earth's rotation in the model. This is very simple. We only have to measure the altitude of the Pole star using a simple instrument that the students themselves can make with a protractor, a ruler and a lead weight. This angle is the local latitude f. Using this value, it is possible to fix the wire representing the Earth's axis. If the model is oriented, this wire marks the position of the Pole star (depending on the students' age we can compare it with the compass direction and it is possible to introduce the idea of magnetic declination). Then we can introduce the north-south and the east-west lines. |
The second step is to include the local meridian. This meridian is very easy to define, but it is more difficult to see. It is possible to fix a circular wire from the north cardinal point on the horizon, attached to the Earth's axis, to the south cardinal point. Students can imagine this line in the sky above their heads through constellations. At this point when making the model it is a good idea to take a collection of photos of the local meridian. Obviously, these photos cannot be taken in the city. It is necessary to take them outside the city, very far away from small villages to avoid light pollution and it is also interesting to take the photos on a day with no Moon. It is always possible to find a place which fulfils these criteria and at similar latitude to that of the school. If take a collection of photos, then the students understand that really the meridian is not exactly the same, but the images are very similar. They know that the stars on the local meridian change continuously. To obtain these photos we need the camera on a tripod with a cable release and to spend some minutes of exposure time (depending on light pollution we can spend 10-20 minutes). We start by taking a photo of the Pole star zone, then another of the area of the sky above our heads, another on the same meridian towards the south cardinal point, and we continue in this way until the last one containing the south cardinal point is taken. It is a good idea to take the photos with a overlap area with the next photo.
| When we have the copies on paper we glue all of them together to obtain a "photo band". If we made a hole where the Pole star is and we introduce the stick representing the Earth's axis and put the "photo band" on the meridian wire we can see the celestial sphere crossing the local meridian (fig. 4).
 fig.4 Of course it is also possible to hold the "photo band" over our head to visualise the different parallels. In particular, we can see the equator as a straight line (Fig. 5). The parallels in the Northern Hemisphere are concave, similar to a cup, and the parallels in the Southern Hemisphere are convex, like an umbrella. If we want to introduce some parallels in the model, it is necessary to include some more wires.
For considering correct inclination we again use photographs. We can take photos of the east and west cardinal points. In this case, it is very important to put the camera on the tripod using a spirit level. The position of the camera is thus correct. The angle between the horizon or the bottom negative and the star trace is the same as the angle between the horizon and the parallel in the model, i.e. the co-latitude, 90º- f . |
 Star's traces photo of the west cardinal point.
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With this model, students can see the celestial sphere from outside (like the usual presentation on drawings by the majority of authors) and from inside (according to the experience of observation). This is an excellent opportunity for clarifying concepts that are sometimes difficult to explain.
After these activities the students have a better understanding of:
