Angular scale on the Moon — distance corresponding to 1° of latitude If two points on Earth that differ by 1° of latitude are about 110 km apart, what is the approximate linear distance for 1° of latitude between two astronomical positions on the Moon?

Introduction / Context:
The linear distance represented by 1° of arc on a planetary body depends on the body’s radius. Comparing Earth and Moon provides quick order-of-magnitude checks useful in selenography and interplanetary cartography.

Given Data / Assumptions:

• Earth: 1° of latitude ≈ 111 km (commonly rounded to 110 km).
• Moon mean radius R_m ≈ 1,737 km.
• Circumference = 2 * π * R; distance per degree = circumference / 360.

Concept / Approach:

The Moon’s circumference is much smaller than Earth’s, so the distance per degree is correspondingly smaller. Compute the Moon’s circumference and divide by 360 to find the approximate kilometers per degree on the lunar surface.

Step-by-Step Solution:

Verification / Alternative check:

Using a more precise radius (1,737.4 km) yields 30.34 km per degree, confirming the 30 km approximation.

Why Other Options Are Wrong:

• 10 km and 25 km underestimate the lunar degree length.
• 50 km overestimates it substantially.
• 5 km is off by an order of magnitude.

Common Pitfalls:

• Confusing arc on a great circle with arc along an arbitrary curve.
• Using Earth’s value directly without scaling by body size.

Final Answer:

30 km.