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Monday, 29 May 2017 02:17

Roland Szostak

"EAAE Summerschools" Working Group

University of Münster, Germany

One of most elementary experiences of nature is the knowledge that a day begins when the Sun rises at the horizon and ends with sunset. It is also one of the earliest observations that a place which is sunny in the rnorning, may be in the shadow at aftemoon. Similarly it is not sophisticated to be aware that the burning sun in summer is rather high in the sky at noon.

Induced by these general experiences it is attractive for children to put a stick vertically on the ground in order to observe how its shadow changes with time. This first sun-dial gives an idea of the path of the sun but still in a rather qualitative way. The length of the shadow is much less noticed than its direction. And a backward extrapolation from the tip of the shadow via the top of the gnomon to the sun is a matter of only very approximate imagination. On this level of observation it does not become evident, that the daily path of the sun is very close to an ideal circle with a very constant speed.

But this path of the sun can be obtained as a real and precise measurement by very simple means, which can be performed by children easily. You have the best conditions, if there is a classroom with its windows towards East and if the sunshine floods the room in the morning hours, may be even to the wall on the opposite side. Put a little marking dot on this wall, using it as a fixed point of reference. Then take a cardboard of normal letter size with a hole in it of about I cm in diameter to be used as a bean mask. Hold this beam mask against the window pane and try to find which beam, passing this hole, is hitting the point of reference. You will see this beam forming an image of the sun at the wall. When you have centred this image of the sun well symmetrically on the point of reference, make a dot at the window pane in order to document the position where the beam has passed.

lf you repeat this measurement five minutes later, you can see at the window pane, how the sun has moved. Continuing this way you obtain a nice chain of dots, which represent the path of the sun. In order to make it better visible, you may fix circular yellow selfadhesive labels on these dots. Then the path of the sun is displayed at the window pane in a very impressive way.

If you take the intervals of time very accurately and if you do the adjustments of the solar image to the point of reference very carefully, you may obtain a surprising precision. In a case, where the wall had a distance of about 4 m from the window, I obtained distances of about 10 cm from dot to dot at the window pane for intervals of 5 min each. The measured scattering of these dots was about 1 mm which is equivalent to a sundial with 3 sec precision. Taking even a scatter of 3 mm when made by children, one gets a precision of 10 sec anyway.

But also without this level of evaluation, the visual impression of the very regular motion of the sun gives a deep first experience, how strictly and reliably nature runs due to its laws. This inevitable path of the sun is different from any experiment in physics, which is technically arranged on the table and which is removed, when being finished. The children know, that the sun keeps running this uninfluenced path all the time. And they may leave this documentation at the window pane ail the year, because it looks nice.

When repeating this measurement a few days later, there is a first Surprise. The sun moves in the same direction, but somewhat displaced parallel. It becomes evident that this is a matter of seasonal change. In springtime, for instance, the solar path occurs higher every following day so that in summer the sun will be higher and will have a longer route above horizon. The advantage of this type of observation is that this behaviour is documented so precisely at the window pane. An interval of three days is well sufficient in order to show this seasonal effect clearly.

The children see that the sun does not rise perpendicularly from the horizon but with a certain angle against it. If you hold a globe in a way that the place where you live is on top, then you can show that this path coincides with the orientation of the equatorial plane. So the dots at the window become a part a circle in the sky, parallel to the equator. This gives an easy access to the insight that the daily path of the sun is caused by the rotation of the earth. It is worthwhile mentioning then, that its axis points to the polar star, which is just in the right position. This may be shown by a long time exposure photograph of the circumpolar sky at night. By discussing these relations it becomes evident that the sunrise is more or less steep, depending on the place where we live on the globe, and that by measuring this angle of sunrise one can determine the local latitude.

All this can easily be done with children of ten years. But the same type of measurement can be performed again with pupils of 18 years without being silly. When the measurements are made accurately in time for an interval of a few days, given by a reliable clock, there is a next surprise. The sun is somewhat early, for instance, as seen in fig. 2. A measurement of this shift reveals that the sun is early by about 40 sec in this case. This observation may trigger a discussion about the mean solar time, which we use in our daily life, and about the equation of time. Then one may analyse these deviations and we will find that they are caused by the elliptical orbit of the earth and by the inclination of the equatorial plane against the orbital plane. It is interesting that these sophisticated effects can be treated with this simple experiment.

There is also another presentation of the solar path, which is more complete and more convincing in three dimensions. The window pane is replaced by a hemispherical transparent dome, say, of 50 cm in diameter.

The measurements are made with a beam mask, which is simply a sheet of paper containing a hole punched by a needle. The point of reference in the centre of the sphere should be inclined towards to the equatorial plane, in order to avoid that the solar image is displayed too much oblique on the referential surface.

This hemisphere is placed outside and measurements can be made throughout the whole day. When measurements are made during the whole year, the paths of the sun cover a broad band between the limits of the solstices. So the seasonal influence is displayed with all details, the declination of the sun ranging up to 23,50°. Similarly the influence of the time equation can be followed throughout the whole year. The discussion can be extended to the type of solar path, seen from a different local latitude, for instance being on the equator or on the pole. As the spiralling character of this path is evident now, it is easy to discuss the polar night and the midnight-sun.