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Earth and Space - Phases of the Moon

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Moon does not produce its own light; it is a non-luminous body that reflects light from the Sun (Solar RadiationSolar\ Radiation).

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At any point in time, exactly 50%50\% of the Moon's surface is illuminated by the Sun, while the other 50%50\% is in shadow.

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Lunar phases are caused by the Moon's orbit around the Earth, which changes the angle from which we view the illuminated half. One complete cycle of phases (New Moon to New Moon) is called a synodic month and takes approximately 29.529.5 days.

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The 'Waxing' phase refers to the period when the visible illuminated part of the Moon is increasing (from New Moon to Full Moon).

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The 'Waning' phase refers to the period when the visible illuminated part of the Moon is decreasing (from Full Moon back to New Moon).

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The sequence of phases is: New Moon →\rightarrow Waxing Crescent →\rightarrow First Quarter →\rightarrow Waxing Gibbous →\rightarrow Full Moon →\rightarrow Waning Gibbous →\rightarrow Third Quarter →\rightarrow Waning Crescent →\rightarrow New Moon.

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The Moon orbits the Earth at an average distance of approximately 3.84×105 km3.84 \times 10^5 \text{ km}.

📐Formulae

Tsynodic≈29.5 daysT_{synodic} \approx 29.5 \text{ days}

Tsidereal≈27.3 daysT_{sidereal} \approx 27.3 \text{ days}

Phase Interval≈29.58≈3.7 days per sub-phase\text{Phase Interval} \approx \frac{29.5}{8} \approx 3.7 \text{ days per sub-phase}

💡Examples

Problem 1:

If a New Moon occurs on the 1st1^{st} of a month, approximately on what date will the Full Moon occur?

Solution:

Approximately the 15th15^{th} or 16th16^{th} of the month.

Explanation:

A full lunar cycle is 29.529.5 days. The Full Moon occurs halfway through the cycle. Therefore, 29.52≈14.75\frac{29.5}{2} \approx 14.75 days. Adding 14.7514.75 to the 1st1^{st} gives roughly the 15th15^{th} or 16th16^{th} day.

Problem 2:

Identify the phase: The Moon is positioned between the Earth and the Sun, so the side facing Earth is in complete shadow.

Solution:

New Moon

Explanation:

During a New Moon, the Moon's elongation is 0∘0^{\circ}, meaning it is aligned between the Earth and Sun, making the side facing us dark.

Problem 3:

How many days does it take for the Moon to transition from the First Quarter phase to the Third (Last) Quarter phase?

Solution:

≈14.75 days\approx 14.75 \text{ days}

Explanation:

The transition from First Quarter to Full Moon is 14\frac{1}{4} of a cycle, and from Full Moon to Third Quarter is another 14\frac{1}{4}. Total distance is 12\frac{1}{2} of the 29.529.5 day cycle, which is 14.7514.75 days.

Phases of the Moon - Revision Notes & Key Formulas | IGCSE Grade 6 Science