Astronomy – Size comparison of Moon and Earth Approximately what fraction of Earth’s volume is the Moon’s volume?

Introduction / Context:Understanding basic size ratios in the Earth–Moon system helps with scale intuition in astronomy. The Moon is much smaller than Earth, and a commonly cited approximation is its volume relative to Earth’s.

Given Data / Assumptions:

• Earth radius R_E, Moon radius R_M ≈ 0.273 * R_E.
• Volume of a sphere V ∝ r^3, so volume ratio depends on the cube of the radius ratio.
• We want the nearest simple fraction from the options.

Concept / Approach:Use the proportionality of volumes to the cube of radius: V_M / V_E = (R_M / R_E)^3. With a radius ratio near 0.273, the cube is close to 0.020, i.e., about 1/50. This provides a quick mental-math method for such comparisons.

Step-by-Step Solution:Take R_M / R_E ≈ 0.273.Compute cube: 0.273^3 ≈ 0.0204.Interpret 0.0204 as about 2.04% of Earth’s volume.Convert to reciprocal: 1 / 0.0204 ≈ 49.0 → about one-fiftieth.Choose the closest option: 1/50 th.

Verification / Alternative check:Remember that 1/50 = 0.02; this aligns well with the 2% estimate from the radius-ratio method.

Why Other Options Are Wrong:

• 1/40 th (2.5%) and 1/60 th (1.67%) are farther from the accepted ~2% value.
• 1/20 th (5%) is much too large.

Common Pitfalls:Comparing diameters or surface areas instead of volumes; volume scales with the cube, not the square or first power.

Final Answer:1/50 th