Summary

The brightness of a star dims in proportion to the square of the distance. This is called the Inverse Square Law. The Inverse Square Law can be explained using the concept of similarity ratios.

When a star is placed at the vertex of similar cones, the base at height 1 and the base at height h are similar. Since the heights of the two cones correspond as proportional sides, the similarity ratio can be determined by the ratio of their heights. In this case, the area of the base is the square of the similarity ratio. Since the same amount of light spreads over an area that increases by the square of the distance, the brightness becomes 1/h²​.

Implication

Stars shining with different brightnesses can be explained using the Inverse Square Law. The Inverse Square Law can be explained using the concept of similarity.

Underlying context – Background behind

Knowledge on middle school geometry might be useful.

Notions – Key ideas

• Similarity: A shape that becomes congruent to another shape when scaled by a certain factor
• Corresponding sides: Sides that correspond to each other in similar figures
• Similarity ratio: The ratio of the lengths of corresponding sides in two similar figures

Index – Source(s)

How to Think Like Mathematicians / 피타고라스 생각 수업
11 How Bright Does a Star Shine? | Inverse Square Law / 별은 얼마나 밝게 빛날까 | 역제곱의 법칙

Trajectory – Where I’m headed now

None