Practical Exercise 3: APPARENT SIZE OF THE SUN AND MOON IN THE SKY – TYPES OF SOLAR ECLIPSES

When viewed from Earth, the disk of the Sun is approximately the same size as the disk of the Moon. Therefore, there may be a total solar eclipse, during which the Moon will completely cover the Sun. There may also be an annular eclipse of the Sun, in which the apparent size of the Moon is smaller than the Sun, and therefore a ring of the radiant Sun can be seen around the Moon's shadow. If the apparent size of both bodies is exactly the same and the lunar disk covers the solar disk exactly, a hybrid solar eclipse will occur. If the Moon disk shades only a part of the Sun, a partial solar eclipse occurs.

The Moon also does not orbit the Earth in the same plane as the Earth around the Sun (= in the ecliptic plane). Therefore, a solar eclipse will occur only if all three bodies exceptionally reach the same plane. If they orbited in the same plane constantly, the Sun would be eclipsed with each new moon.

Let's try to consider which types of solar eclipses could or could not occur if the size or distances of the bodies were significantly different. (We consider parameter changes so big that fluctuations in distance during the circulation of bodies have no effect.)

a) Both the Sun and the Moon are as big as they really are, but the Moon orbits closer to the Earth. What types of eclipses could occur (total, annular, hybrid, partial)? Would solar eclipses be more frequent or rarer than they actually are?

b) Both the Sun and the Moon are as big as they really are, but the Moon orbits further from the Earth. What types of eclipses could occur (total, annular, hybrid, partial)? Would solar eclipses be more frequent or rarer than they actually are?

c) Both the Sun and the Moon are as big as they really are, but the Earth orbits closer to the Sun. What types of eclipses could occur (total, annular, hybrid, partial)? Would solar eclipses be more frequent or rarer than they actually are?

d) Both the Sun and the Moon are as big as they really are, but the Earth orbits further from the Sun. What types of eclipses could occur (total, annular, hybrid, partial)? Would solar eclipses be more frequent or rarer than they actually are?

e) In fact, the Moon is slowly moving away from the Earth. Which of the situations a) to d) describes this? What will be the gradual development of the occurrence of individual types of eclipses?

Objective of Practical Exercise

The aim of this activity is to explain to pupils the differences between different types of solar eclipses – total, annular, hybrid and partial. Furthermore, thanks to this activity, pupils will consolidate the idea of the mutual position of the bodies during the eclipse. In connection with the correct answers to questions c) and d), they will clarify the effect of the inclination of the plane of the Moon's orbit around the Earth relative to the ecliptic plane on the frequency of solar eclipses.

Methodical notes for the teacher

• If the changes in distances in the individual points a) to d) were small, there could be a situation where the fluctuation of the distance during circulation on the elliptical trajectory would have a greater effect than the change considered in the exercise. Then, of course, all considerations would be much more complicated, all eclipses could occur, only the frequency of their occurrences would change. Therefore, it is generally said in the assignment that the changes in distances are large enough. In the case of a pupil's question, it is possible to specify: The distance of the Moon from the Earth fluctuates in orbit on an elliptical trajectory by 11%, the distance of the Earth from the Sun by less than 3.5%. Sufficiently large changes in distance are therefore changes greater than this natural fluctuation.

• It is possible to prepare other sets of questions that will vary the actual size of the bodies instead of the distance. The possibility of combining changes in the size and distance of both bodies, the Sun and the Moon, is interesting. Alternatively, it is also possible to discuss the effect of the size of the Earth on the number of eclipses.

• It is possible to mention that the passage of a planet through the Sun, which also sometimes occurs, is actually a partial eclipse of the Sun by this planet.

Sample answer

a) The Moon orbits closer, its shadow has a larger angular size than the Sun. A total eclipse may occur, but an annular or hybrid eclipse cannot occur. Because the shadow is larger, eclipses will occur more often. (The inclination of the plane of the Moon's orbit around the Earth relative to the ecliptic plane remains the same, the angular size of the Sun remains the same, the angular size of the Moon is larger.)

b) The Moon orbits further away, its shadow has a smaller angular size than the Sun. There can be no total or hybrid eclipse, only annular one. Because the shadow is smaller, eclipses will occur less often. (The inclination of the plane of the Moon's orbit around the Earth relative to the ecliptic plane remains the same, the angular size of the Sun remains the same, the angular size of the Moon is smaller.)

c) The Sun is closer to the Earth, its angular size in the sky is larger than that of the Moon. There can be no total or hybrid eclipse, only annular one. Because the Sun has a larger angular size and the Moon is still moving in the same belt defined by the inclination of its plane of orbit to the ecliptic plane, the Moon is more likely to get in front of the Sun and eclipses would be more frequent. In that regard, the reasoning is fundamentally different from point b), although the first impression leads to the conclusion that situations b) and c) are, in the end, identical.

d) The Sun is further from the Earth, its angular size in the sky is smaller than that of the Moon. A total eclipse may occur, but an annular or hybrid eclipse cannot occur. Eclipses will be less frequent. Because the Sun has a smaller angular size and the Moon is still moving in the same belt defined by the inclination of its plane of orbit to the ecliptic plane, the Moon is less likely to get in front of the Sun and eclipses would be less frequent. In that regard, the reasoning is fundamentally different from point a), although the first impression leads to the conclusion that situations a) and d) are, in the end, identical.

e) In the future, the situation described in point b) will gradually occur. Gradually, in particular, total eclipses will decrease until they cease to exist completely. Hybrid eclipses will be rarer, in the limited case they can only occur if the bodies are exactly in one line. Annular eclipses will occur continuously, but the shape of the ring may gradually become more asymmetric.

Adaptation guidelines for pupils with SEN