Question

for the earth (looking down from above), and the moon in different positions, as seen from above (you should be looking from above the sun-earth-moon system). which object (earth or the moon) or the light of the sun could the earth be completely dark in any of these diagrams? are these diagrams to scale? a) no, the moon is always lit by the sun. b) yes, always in diagrams 2 and 3, but never in diagram 1. c) yes, always in diagram 2, but never in diagrams 1 or 3. d) yes, always in diagram 2 and sometimes in diagram 3.

Explanation:

Step1: Analyze Moon's Illumination

The Moon is always illuminated by the Sun (half - lit, but from Earth's view, phases change). In the diagrams, the "dark side" (not visible from Earth) is always lit by the Sun, but the question is about the side facing Earth being completely dark. For a full dark (new moon - like), Earth, Moon, Sun alignment: Earth - Moon - Sun (Moon between Earth and Sun) makes Moon's face to Earth dark. Diagram 2: Moon is between Earth (blue) and Sun? Wait, no—wait, the blue is Earth? Wait, the diagrams: in Diagram 2, Moon is between Earth and Sun? Wait, no, let's re - think. The side of the Moon facing Earth is dark when Moon is between Earth and Sun (so Earth sees the dark side). In Diagram 2, if Moon is between Earth (blue) and Sun, then Earth's view of Moon is dark. In Diagram 1: Moon is behind Earth relative to Sun? No, Diagram 1: Earth, Moon, Sun? Wait, no, the key is: the Moon's dark side (to Earth) occurs when Moon is between Earth and Sun (so Earth sees the unlit side). Now, check the options:

Option A: No, the Moon is always lit by the sun (correct, but the question is about the side facing Earth being dark). Wait, the question is "Are there any positions (or times) when the side of the Moon that faces Earth is completely dark in any of these diagrams?".

Wait, let's parse the options:

Option A: "No, the Moon is always lit by the sun." But the Moon's side facing Earth can be dark (new moon) when Moon is between Earth and Sun (so the lit side is away from Earth). So A is wrong.

Option B: "Yes, always in Diagrams 2 and 3, but never in Diagram 1." No, Diagram 2: if Moon is between Earth and Sun, then Earth - facing side is dark. Diagram 3: Moon is on the other side? Wait, maybe the diagrams: Diagram 1: Moon is behind Earth (Earth between Moon and Sun), so Moon's Earth - facing side is lit (full moon). Diagram 2: Moon between Earth and Sun (new moon, Earth - facing side dark). Diagram 3: Moon is on the side, so Earth - facing side has some light? Wait, no, the option D: "Yes, always in Diagram 2 and sometimes in Diagram 3." Wait, no, let's re - evaluate.

Wait, the correct logic: The Moon's Earth - facing side is completely dark only when Moon is between Earth and Sun (new moon). So in Diagram 2 (if Moon is between Earth and Sun), it's dark. In Diagram 3, if Moon is in a position where it's between Earth and Sun (sometimes), but Diagram 1: Moon is behind Earth (Earth between Moon and Sun), so Moon's Earth - facing side is lit (full moon, so never dark). So the correct option is D? Wait, no, the options:

Wait the options are:

A) No, the Moon is always lit by the sun.

B) Yes, always in Diagrams 2 and 3, but never in Diagram 1.

C) Yes, always in Diagram 2, but never in Diagrams 1 or 3.

D) Yes, always in Diagram 2 and sometimes in Diagram 3.

Wait, the Moon's Earth - facing side is dark when Moon is between Earth and Sun (Diagram 2: Moon between Earth and Sun → Earth - facing side dark). In Diagram 3, if Moon is moving towards the between - Earth - and - Sun position, sometimes it can be dark? No, actually, the new moon (dark side to Earth) is only when Moon is exactly between Earth and Sun. But maybe the diagrams: Diagram 2 is Moon between Earth and Sun (always dark), Diagram 3: sometimes (when Moon is in the new - moon - like position). Diagram 1: Moon is behind Earth (Earth between Moon and Sun), so Moon's Earth - facing side is lit (full moon), so never dark. So the correct option is D? Wait, no, let's check again.

Wait, the key is: The side of the Moon facing Earth is completely dark only during new moon, which is when Moon is between Earth and Sun. So in Diagram 2 (Moon between Earth and Sun) → always dark. In Diagram 3, if Moon is in a position where it's approaching or in new moon, sometimes dark. Diagram 1: Moon is on the opposite side of Earth from Sun (Earth between Moon and Sun) → Moon's Earth - facing side is lit (full moon), so never dark. So the correct option is D: "Yes, always in Diagram 2 and sometimes in Diagram 3."

Step2: Evaluate Options

- Option A: Wrong, because even though Moon is always lit by Sun, the side facing Earth can be dark (new moon).
- Option B: Wrong, Diagram 3 doesn't always have the dark side facing Earth.
- Option C: Wrong, Diagram 3 can sometimes have the dark side facing Earth (when Moon is in new - moon - like position).
- Option D: Correct, as Diagram 2 (Moon between Earth and Sun) always has Earth - facing side dark, and Diagram 3 can sometimes (when Moon is between Earth and Sun) have it dark.

Answer:

D. Yes, always in Diagram 2 and sometimes in Diagram 3.