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THE PROBLEM OF TEACHING THE ORIGIN OF THE SEASONSRoland Szostak
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THE PROBLEM OF TEACHING THE ORIGIN OF THE SEASONSRoland Szostak
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The strategy of transforming the frame of reference breaks down in the case of explaining the seasons in school. There is another strategy for teaching the seasons which is very successful even for children down an age of ten. This is achieved by a thermocoloric model sphere which changes colour at elevated temperatures. The colour pattern on this sphere presents a belt like hot zone when being irradiated during rotation. This hot zone shifts towards north respectively towards south by inclining the axis. One recognizes visually that the seasons are due to the inclination of the axis against the orbital plane.
The seasons are one of the most familiar experiences in daily life. So in our schools they should be explained in a way that everybody understands it. But everybody knows, that the success in this field is very poor: If one asks people, one finds some good knowledge of the Earth being a planet, which orbits around the Sun once a year and rotates around its axis once a day. But asking for explaining the seasons, you will find in most cases no or very vague ideas.
It is obvious to everybody, that the seasons are due to the insolation of the Sun. But a widespread opinion supposes a varying distance between Sun and Earth. Especially well educated people are inclined to prefer this hypothesis. They remember vaguely some elements of the elliptical character of Kepler's orbits. Nevertheless, these people are honest. It is our fault, that they have not been taught the right way.
The problem is: The concept of reference frames runs into serious difficulties in the case of the seasons. The reason for this failure is the fact that one needs a superposition of several transformations in this case: By a first transformation the roles of the Sun and the Earth are exchanged with regard to the orbit. One does not yet take into account the rotation of the Earth. This is done in a second transformation step. But usually the rotational axis is simply imagined to be perpendicular to the orbital plane.
These two transformation steps may be sufficient for treating several phenomena.
But essentially they are not sufficient in the case of the seasons. Then some additional transformations are necessary: Next, one has to transform the rotation around the mentioned perpendicular axis to a rotation whose axis is inclined against the orbital plane. Equivalently then the equatorial plane is inclined against the orbital plane. Finally one has to make a transformation from this geocentric frame to the local frame of the terrestrial observer due to his geographical latitude.
Just these transformations are rather sophisticated. When these frames are in motion, it is very difficult to imagine the details, which are observed in the local frame. To overcome this difficulty, the usual teaching procedure selects two special positions, which can be depicted in one plane (fig. 1).
These are the two solstice positions with the observer being at noon. There one can see, that the angle of the incident light is steeper in summer than in winter. But what about this angle of incidence in the local frame, different position when the Earth is rotating or when the Earth is in a different position on the orbit? For example at equinox? It is obvious, that the superposition of all these transformations is an unreasonable demand in didactics. So the usual teaching procedure stops at this point, meanwhile the depicted two situations in the drawing stay isolated.
But even these four transformations would not give an adequate description of the seasons, because summer and winter are a matter of temperatures. These are not only equivalent to the momentarily irradiated heat but also essentially a result of the stored heat. So one has to combine these cinematic transformations with another type of transformation, which makes a balance of the stored heat. Here the strategy of transforming the frames of reference definitely breaks down. As this classical approach has been prove to be didactically unreasonable, we developed a different approach, which is very successful in practical school teaching down to an age of 10 years. This strategy starts from the common experience that summer and winter are characterized by temperatures.
We covered a sphere of styrofoam with a thermocoloric paint which changes reversibly colour at a certain temperature. In our case it turns from yellow to red when exceeding 400C. We expose this sphere to the irradiation of a heater. When keeping it simply in the hand without special motion, it gets a red spot on that part, which is most directly exposed to the heat irradiation. Rotating then the sphere stepwise by hand, one can produce a sequence of those spots, which finally results in a belt like zone around the sphere. For easier rotation the sphere may be mounted on an axis. This may be simply a needle as well as a motor driven device (fig. 2).
All this can be done easily with children even in primary school. This is direct experience in concrete terms. You need no analytical geometry, no angles, no mathematics.
It is normal to start with a vertical axis. Then one gets a hot tropical zone along the equator, meanwhile the poles stay cold. This result is reasonable to every child. But what about the seasons? In order to find this out, one may put this little globe closer to the heater or more far apart from it. But this changes the red zone only to be more or less intense (fig 3).
For obtaining the right result one has to take into consideration that the seasons are reverse to each other on both of the hemispheres. This means that the red zone must be shifted towards north or south respectively. The question is now, how this may be achieved.
An obvious idea for this is to place the heater somewhat lifted and inclined, so that it irradiates the globe from a position above the equatorial plane. This produces a temperature pattern on the globe corresponding to summer in our hemisphere. For the same result one may leave as well the heater in its central position and place the globe in a somewhat lower position. (The heater needs only be inclined towards the globe).
For producing the winter pattern in the position half an orbit later, one has to place the globe lifted on the other side of the heater (fig. 4). Then the heater will irradiate the globe from a position below the equatorial plane. Fig 4 shows already the essential features for the origin of the seasons, although the presentation of the inclined orbital plane appears somewhat unusual.
But we need only tilt the drawing or the head sideways for changing the frame of reference and seeing the orbital plan horizontally (fig 5). This is rather trivial, because the physical world will stay the same whether you tilt your head or not.
One may find the seasonally shifted temperature pattern also in a different way: We had started by exposing the rotating sphere to the heater with a vertical axis and gained the red zone symmetrically along the equator. But if one exposes the rotating sphere accidentally in a way, that the axis is inclined against the heater, then the red zone appears shifted. By analysing this accidentally produced temperature pattern, it becomes evident that the asymmetric pattern is due to this inclination. So one may start the experiment this way with the globe in the left position of figure 6.
When trying to produce the pattern for winter half an orbit later, one obviously can check it in the position right of the globe in figure 6. In doing so there is usually a peculiar surprise: One of the children takes the sphere with its mechanical frame and carries it to the new position. But unwillingly it often happens, that the sphere is placed there with a reversed orientation which again gives the summer pattern. This happens because the body of the child makes half a turn when carrying the device around. It is very encouraging that the children find out themselves that the unexpected summer pattern is caused by the wrong orientation of the axis. By changing it to its correct orientation they are successful.
So they find out, that the axis of the Earth stays stable in space! Then you need only tell them: "Look at the polar star. You see it all the year in the same position".
An additional prove of the result, that the seasons are caused by the inclination of the equatorial plane against the orbital plane can be made by the model in the following way: If the termocoloric sphere is carried around the heater, while rotating with a vertical axis, there is no shift of the hot zone, evidently (fig. 7). So in the case of a vertical axis we would have no seasons. This is an aspect, by which children feel being touched. So they will learn it.
One more remark about the better quality of knowledge: This seasonal shift of the temperature pattern must obviously be synchronous with the orbital period. So it becomes evident that one orbit of the Earth leads us just through on whole cycle of the seasons. In a certain way one can feel the orbit by the phenomenon of the seasons. I think this gives more sense than the usual unexplained statement in many textbooks that the Earth orbits around the Sun just in one year.
One may finally object to the fact that the hottest and coldest periods of the year do not occur at the solstices but somewhat delayed. But even this peculiar feature can be correctly demonstrated by the thermocoloric technique: When being irradiated the sphere needs some time for getting warm and for changing colour. Similarly it needs some time for cooling. This behaviour corresponds to everybody's experience in daily life. If one now carries the rotating sphere with a suitable speed on its orbit around the heater, the position of the red zone will show a time lag. So the hot zone will reach its highest and lowest positions correspondingly delayed in the right way.
