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Wednesday, 23 August 2017 09:47

Leonarda Fucili

"EAAE Summerschools" Working Group

SMS "V. Mordini", 3rd University Rome (Italy)

Every phenomenon can be experienced in two ways.

These two ways are not arbitrary, but are bound up with the phenomenon

- developing out of its nature and characteristic - :

externally or inwardly

Kandinsky

Abstract

I propose an active workshop about the Sun's path above and below the local horizon. The focus is the sun's position at midnight.

By a systematic organisation of observations and strategies of reasoning and by using significant questions, discussions and models, participants are guided to imagine what usually they can't see in the sky, the position of the midnight sun, and define a general law for any latitude and season. Being in Lapland in summer, where the midnight sun can be seen and not only thought, helps to achieve a deeper understanding of the topic.

The workshop supports an earth-centred view, founded on the direct, personal experience and the senses of space and movement natural to the human being in his normal earth based environment. It may look simple-minded, but the aim is high: to connect the earth-centred view and the sun-centred, the direct human experience of the celestial motions and the abstract thinking.

An active personal involvement is required to participants: they will produce actions, imaginations, thoughts and useful materials for their didactic practice.

Some proposals for didactical activities

Everybody knows midday is when the sun is due south and at its highest above the horizon for that day, but it is a surprise to become aware of the sweep upwards and downwards which the noon positions of the sun make in the south as well as of the swing along the horizon which risings and settings make through the seasons.

Thinking the midnight positions of the sun is much more unusual and surprising. This workshop will guide participants just understand where the sun is at midnight in relation to its noon position above (or below) the local horizon at any latitude and season. From this approach, an astronomic course on the Sun-Earth system and motions can be developed.

Phases of the workshop:

  1. Investigation of common sense experience and knowledge about the topic
  2. Construction of models
  3. Discovering a general law

1. Investigation of common sense experience about the topic, making explicit the implicit concepts, by some questions and actions and a general discussion.

ACTION 1: "WHERE IS THE MIDNIGHT SUN?" a question and a gesture

"Knowing the direction south-north of the local meridian, point your arms in the directions of the sun at midday and midnight."

People act all together: as we are working in Lapland, beyond the polar circle, and it is summer, the midnight sun is visible due north above the horizon and the action seems very simple. But we can foresee different gestures (fig. 1a, 1b, 1c).

a. Arms are symmetrical in relation to the axis of the body.

b. Arms point to different altitudes in the sky.

c. Arms are in opposite directions.

Which of them is right, in Lapland, in summer?

Investigating the implicit motivations of every gesture, a lot of questions arise:

What is the correct angle between the arms (or between the noon and midnight positions of the sun?

Is it the same for all the latitudes?

Is it the same in different seasons?

"Repeat the gesture imagining you are today in your country"

Figure 1 - Which of these gestures, pointing to the midday and midnight sun, are correct, in Lapland, in summer.
Figure 1 - Which of these gestures, pointing to the midday and midnight sun, are correct, in Lapland, in summer.

ACTION 2: a drawing

"Draw a picture concerning the position of the midnight sun in relation to the local horizon and to the Earth"

Everybody presents his drawing by a sheet, but usually some difficulties emerge.

Firstly, it's difficult to represent in two dimensions what in reality is three-dimensional and spherical: the difference between what is seen in the sky and what can be represented in the plane is considerable. It is important to focus that geometrically there is no way of reproducing on a plane a picture exactly as it appears on the celestial sphere. Every sky and earth map, based on one of many methods of projection onto a flat plane, necessarily distorts the reality. 

Secondly, a struggle between the earth-centred view and the sun-centred often appears. One cause may be one is familiar with pictures or photographs in books on astronomy that do not explain the differences and connections between the two points of view. Another reason may be the lack of observations while learning Astronomy at school.

ACTION 3: discussion

We discuss the different gestures, drawings and hypothesis concerning the midnight sun.

Consideration of the "extreme situations" about time (equinoxes and solstices) and geographical places (tropics, equator and poles) may be useful to our discussion.

Attention will be focused on some points that can cause difficulties in understanding space and celestial motions. Some misconceptions and mistakes are:

Often people believe that the midnight sun is at 180° in relation to the midday sun. This is a partially correct answer, because it is true only at the equinoxes (the arm's inclination depends on the latitude) (Fig. 2a, 2b, 2c).

Figure 2 - Equinoctial situation.
Figure 2 - Equinoctial situation.

Somebody points to the direction of his own feet, the nadir, opposite to the zenith where the sun at midday is supposed to be. But the sentence "the sun at midday is at its highest above the horizon for that day" doesn't mean the sun is at the zenith. It happens only at the latitudes between the tropics and only at the equator, at the equinoxes, midnight sun is at the nadir. (Fig. 3)

Figure 3 - Equinox: midday sun and midnight sun at equator.
Figure 3 - Equinox: midday sun and midnight sun at equator.

Often people say: "The midnight Sun is on the other side of the earth", but this sentence can have different implicit meanings that refer to different symmetries of the earth sphere. In fact "the other side of the earth" can be in relation to: (Fig. 4ª, 4b, 4c)

a. the centre of the earth

b. the equator

c. the earth axis

"The other side of the earth" can be in relation to:

Figure 4 - Which is the correct meaning concerning our topic?
Figure 4 - Which is the correct meaning concerning our topic?

We focus our attention also on the main graphic and linguistic ambiguities often emerging from participant's drawings and explanations.

The axis of the earth can be drawn oblique (a) or vertical (b) in relation to the graphic plane, but we have to know that this situation is connected with putting as horizontal:

a. the ecliptic (Fig. 5a)

b. the equator (Fig. 5b)

In some drawings the terminator, the edge between light and darkness, may be confused with a meridian, crossing the poles like the axis of the earth, but it is true only at the equinoxes.

Sometimes there is a misunderstanding with regard to:

a. the wall maps - where, by mistake, the North is considered on the top and the East on the right - and the orientation in the local horizon where, pointing to the South, the East is on the left.

b. the celestial north pole, the earth north pole and the northern direction on the local horizon

2. The models

We'll construct and use several models to reflect about the topic and understand the daily and yearly path of the sun for any latitude. They facilitate mental images and explanations, improve, construct and transfer knowledge and enable participants understand reality better and predict phenomena.

1. Celestial sphere: it shows the path and the height of the sun in relation to the horizon at midday and midnight, for any season and latitude.

2. Sun marksman: it points to the positions of the midday and midnight sun on the local horizon at the equinoxes and at the solstices.

3. Some paper dynamic models (Solar quadrant, sunrays disk…) help to consider the same topic from different points of view.

Materials and instructions about models will be given to participants during the workshop.

3. Discovering a general law

By using observations, discussions and models, participants will be guided to connect theoretical knowledge and their earth-centred view, concerning:

Position of the observer on the earth

Local horizon and its directions

Sun's altitude at midday and midnight in different seasons

Relation between solstices and tropics

Relation between ecliptic, equator and their axes

Motions of the celestial sphere in relation to the observer's position on the earth

Step by step, a general law can be found as solution of the problem "where is the midnight sun". The key is a special "butterfly" we can see in the Figure 6: it shows the position of the sun at midday and midnight in the northern hemisphere (observer's latitude 45°).

Figure 6 - The position of the sun at midday and midnight for an observer of the northern hemisphere (latitude 45°N ).
Figure 6 - The position of the sun at midday and midnight for an observer of the northern hemisphere (latitude 45°N ).

In one day, apparently, the sun rounds the axis of the earth but not the observer's axis. Only exactly at the poles the two axes coincide and the positions of the noon and midnight sun are symmetrical in relation to the observer.

At the poles the sun stands the same height at midday and midnight:

At the other latitudes the midnight sun is due north as lowest below the horizon when it stands at the winter solstice as the midday sun is due south highest above the horizon when it stands at the summer solstice: these angles are the same - as absolute value - and depend on the latitude.

The general law is:

References

L. Fucili "Thinking about a round world", 4th EAAE Summer School Proceedings, 2000

N. Lanciano "Dentro il cielo" Materiali Laboratorio Didattica delle Scienze nº 6. University.La Sapienza Rome, 1992

Astronomical Society of the Pacific "The Universe at your fingertips" Project Astro 1995

N. Davidson, "Astronomy and the Immagination", Routledge& Kegan Paul, Usa, 1985

"The astronomer" by Camille Flammarion.