Propositional knowledge statements

The following section presents propositional knowledge statements associated with the Earth, the Sun and the Moon.

4.3.1 The Earth-Moon-Sun system

The Sun is at the centre of the solar system, surrounded by planets and their satellites. The Sun radiates light and other forms of energy in all directions. A small fraction of the Sun‘s rays shines on the planets and their satellites. These rays appear to be parallel by the time they reach the planets (because the planets are so small as compared to the Sun, and because the rays will have travelled long distances).

The Earth, being one of the planets, orbits the Sun once in 365¼ days. In addition, the Earth spins on its axis once in 24 hours. The Sun and the Moon appear to rise in the east and set in the west as a result of this spin. The Moon changes position relative to the Earth, the Sun and the stars in the course of a month. That is, if we imagine the Moon located in a certain position relative to the Earth and the Sun, and among the stars; the Moon takes 27.3 days to orbit the Earth and get back to the same position relative to the stars (the duration known as the sidereal month). However the Moon needs to take a longer journey to get back to its original position relative the Earth and the Sun because the Earth changes position relative to the Sun in the course of a month. The period of the Moon‘s orbit around the Earth to get back to the same position relative to the Earth and Sun, known as the synodic month, takes 29.5 days. The Moon rises about 50-to-60 minutes later as a result of its orbit around the Earth.

The Moon‘s orbital path around the Earth is tilted at 5o

to the ecliptic (the plane of the Earth‘s orbital path around the Sun). That is, if the Earth-Sun system is drawn on a horizontal plane so that the Earth orbits the Sun in this plane, the plane of the Moon‘s orbital path around the Earth has to be drawn at 5o from the horizontal plane. This implies that the Moon is not precisely in line with the Earth-Sun system. This, in turn, suggests that the Earth only rarely casts a shadow on the Moon (which explains why eclipses occur only rarely).

The direction of the Moon‘s orbit depends on the location of viewers on the Earth. For viewers in the southern hemisphere, the Moon appears to orbit the Earth in a clockwise direction (see Figure 4.1).

Figure 4.1 Direction of the Moon's orbit as seen from the southern hemisphere

For viewers in the northern hemisphere, the Moon appears to orbit the Earth in a counter clockwise direction (see Figure 4.2).

Figure 4.2 Direction of the Moon's orbit as viewed from the northern hemisphere

The Moon‘s orbital path around the Earth appears to be almost circular when seen from one of the poles (as illustrated in Figures 4.1 and 4.2). However, this orbital path appears to be an oval if viewed at some angle from the poles.

4.3.2 Phases of the Moon

Figures 4.1 and 4.2 show that the Sun illuminates half of the Moon‘s surface at any given point and time. The Moon can be seen from Earth if part of its illuminated surface reflects sunlight towards the Earth. Sun’s rays Sun’s rays Earth 8 7 6 5 4 3 1 2 South Pole Moon’s orbit Earth Sun’s rays Sun’s rays 2 3 4 5 6 7 1 8 North Pole Moon’s orbit

Figure 4.3 illustrates the Moon in 8 positions on its orbital path around the Earth, and shows corresponding phases of the Moon. Figure 4.3a illustrates phases of the Moon as seen from the southern hemisphere while Figure 4.3b illustrates these phases as seen from the northern hemisphere.

Figure 4.3 Moon phases as seen from (a) the southern hemisphere and (b) the northern hemisphere

The following discussion describes phases of the Moon as seen from Earth when the Moon is in each of the eight positions in its orbital path around the Earth.

 New Moon: This phase occurs when the Moon is in Position 1. The illuminated surface of the Moon faces away from the Earth and therefore reflects sunlight away from the Earth. As a result, the Moon is not visible from the Earth during this phase. This phase marks the beginning of the lunar cycle (hence the name New Moon).

 Waxing Crescent: This phase occurs when the Moon is between Positions 1 and 3, and it lasts for about 7 days and 9 hours. During this phase, less than half of the illuminated surface of the Moon faces Earth and therefore reflects sunlight towards the Earth. As a result, the Moon appears to be crescent-shaped as seen from the Earth. The crescent appears to be on the left- hand side of the Moon (facing the right-hand side) as seen from the southern hemisphere (see Figure 4.3a). On the other hand, the crescent appears to be on the right-hand side of the Moon (facing the left-hand side) as seen from the northern hemisphere (see Figure 4.3b).

 First Quarter: This phase occurs when the Moon is in Position 3. Half of the illuminated surface of the Moon faces the Earth and therefore reflects sunlight towards the Earth. As a result, viewers on Earth see half of the Moon. This half appears to be on the left-hand side of the Moon (facing the right-hand side) when seen from the southern hemisphere. However, the half appears to be on the right-hand side of the Moon (facing the left-hand side) when seen from

Sun’s rays Sun’s rays Earth 8 7 6 5 4 3 1 2 South Pole 1 2 3 4 5 6 7 8 Earth 2 3 4 5 6 7 1 8 North Pole 1 2 3 4 5 6 7 8

the northern hemisphere. The phase is called First Quarter because the Moon has travelled the first quarter of its orbital path.

 Waxing Gibbous: This phase occurs when the Moon is between Positions 3 and 5, and it lasts for about 7 days and 9 hours. During this phase, more than half of the illuminated surface of the Moon faces Earth and therefore reflects sunlight towards the Earth. The Moon appears to be gibbous-shaped as seen from the Earth. The gibbous shape appears to be on the left-hand side of the Moon (facing the right-hand side) as seen from the southern hemisphere, and to be on the right-hand side of the Moon (facing the left-hand side) as seen from the northern hemisphere.

 Full Moon: This phase occurs when the Moon is in Position 5. The entire surface of the Moon illuminated by the Sun‘s rays faces the Earth and therefore reflects sunlight towards the Earth. The Moon appears to be a complete circle as seen by viewers on Earth (hence the name Full

Moon).

 Waning Gibbous: This phase occurs when the Moon is between Positions 5 and 7, and it lasts for about 7 days and 9 hours. During this phase, part of the illuminated surface of the Moon is now facing away from the Earth, and therefore reflects sunlight away from the Earth. Like in Position 4, the Moon appears to be gibbous-shaped as seen by viewers on Earth. However, the gibbous appears to be on the right-hand side of the Moon (facing the left-hand side) as seen from the southern hemisphere, and on the left-hand side of the Moon (facing the right-hand side) as seen from the northern hemisphere.

 Last Quarter: This phase occurs when the Moon is in Position 7. Half of the illuminated surface of the Moon faces away from Earth and therefore reflects sunlight away from the Earth. Viewers on Earth see only half of the Moon. This half appears to be on the right-hand side of the Moon (facing the left-hand side) as seen from the southern hemisphere and to be on the left- hand side of the Moon (facing the right-hand side) as seen from the northern hemisphere. The phase is called Last Quarter because the Moon has travelled three quarters of its orbital path (and has to travel one quarter to complete its orbit).

 Waning Crescent: This phase occurs when the Moon is between Positions 7 and 1, and it lasts for about 7 days and 9 hours. During this phase, less than half of the illuminated surface of the Moon faces the Earth and therefore reflects sunlight towards the Earth. Like in Position 2, the Moon appears to be crescent-shaped as seen from the Earth. However, the crescent appears to be on the right-hand side of the Moon (facing the left-hand side) as seen from the southern hemisphere and on the left-hand side of the Moon (facing the right-hand side) as seen from the northern hemisphere.

Figure 4.4 Time lapse between phases of the Moon

These propositional knowledge statements were used during the design of the diagnostic test presented in Appendix B.