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Earth, Moon, and the Sun - Lunar eclipse

Grade 7CBSE

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

🔑Concepts

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A Lunar Eclipse occurs when the Earth moves between the Sun and the Moon, blocking the sunlight that usually reflects off the Moon. This happens only on a Full Moon night.

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For a lunar eclipse to occur, the three celestial bodies must be in a straight line, a state known as syzygy. The order is Sun→Earth→MoonSun \rightarrow Earth \rightarrow Moon.

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The Earth's shadow consists of two distinct parts: the Umbra (the innermost and darkest part where the Sun is completely hidden) and the Penumbra (the outer part where the light is only partially blocked).

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Types of Lunar Eclipses: 1. Total Lunar Eclipse: The entire Moon passes through the Earth's Umbra. 2. Partial Lunar Eclipse: Only a part of the Moon enters the Umbra. 3. Penumbral Lunar Eclipse: The Moon passes through only the Penumbra.

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The 'Blood Moon' phenomenon occurs during a total lunar eclipse. This is due to Rayleigh Scattering, where the Earth's atmosphere filters out blue light and bends (refracts) red light into the Umbra, casting a reddish glow on the Moon.

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Lunar eclipses do not occur every month because the Moon's orbit is tilted at an angle of approximately 5∘5^{\circ} relative to the Earth's orbit around the Sun (the ecliptic plane).

📐Formulae

Alignment Order: Sun−Earth−Moon\text{Alignment Order: } Sun - Earth - Moon

Orbital Tilt: θ≈5∘\text{Orbital Tilt: } \theta \approx 5^{\circ}

Condition for Total Eclipse: Moon⊂Umbra\text{Condition for Total Eclipse: } Moon \subset Umbra

Condition for Partial Eclipse: Moon∩Umbra≠∅ and Moon⊄Umbra\text{Condition for Partial Eclipse: } Moon \cap Umbra \neq \emptyset \text{ and } Moon \not\subset Umbra

💡Examples

Problem 1:

Explain why a Lunar Eclipse does not occur on every Full Moon day if the tilt of the Moon's orbit is 5∘5^{\circ}.

Solution:

The Moon's orbital plane is tilted at an angle of 5∘5^{\circ} to the Earth's orbital plane (the ecliptic).

Explanation:

Because of this 5∘5^{\circ} tilt, the Moon usually passes above or below the Earth's shadow during a Full Moon. An eclipse only occurs when the Full Moon happens at the points where the two orbits intersect, known as nodes.

Problem 2:

During a particular eclipse, only 40%40\% of the Moon's surface enters the Earth's Umbra. Identify the type of eclipse.

Solution:

Areaeclipse=0.4×AreaMoonArea_{eclipse} = 0.4 \times Area_{Moon}

Explanation:

Since only a portion (40%40\%) of the Moon is covered by the darkest part of the shadow (Umbra) and not the entire Moon, it is classified as a Partial Lunar Eclipse.

Problem 3:

Calculate the approximate angular alignment required for a perfect syzygy in degrees.

Solution:

180∘180^{\circ}

Explanation:

In a perfect lunar eclipse alignment, the Sun, Earth, and Moon form a straight line, which mathematically represents an angle of 180∘180^{\circ}.