Correct Option
The correct option is (a).
Explanation
The Moon is Earth's only natural satellite. Its physical dimensions and orbital mechanics are distinct, characterized by its size relative to Earth and the phenomenon of synchronous rotation, which locks its rotational period to its orbital period.
Statement-wise Analysis
- Statement 1 is Correct: The diameter of the Moon is approximately 3,475 km, while the diameter of the Earth is approximately 12,742 km. The Moon's diameter is roughly 27% of Earth's, which corresponds to about one-quarter.
- Statement 2 is Incorrect: The Moon moves around the Earth in about 27 days (specifically 27.3 days for a sidereal month). It does not take 45 days.
- Statement 3 is Incorrect: The Moon does not take longer to spin on its axis than to orbit the Earth. Instead, the time taken to complete one spin on its axis is exactly the same as the time taken to complete one orbit around the Earth (about 27 days). This phenomenon is known as synchronous rotation, which results in the same side of the Moon always facing the Earth.
Key Takeaway
Synchronous Rotation: The Moon's period of rotation on its axis and its period of revolution around the Earth are identical (approximately 27 days), causing only one side of the Moon to be visible from Earth.