Why is the sky dark at night? Geometric considerations with a historical and pedagogical look at the Olbers paradox

We present the Olbers paradox and some proposals for its solutions with geometric arguments based on simple cosmological and astrophysical models. A little-known sky splendor calculation shows that the Universe expansion to the night darkness is responsible for little more than half of the effect; the remainder comes from the low distribution of stars (and galaxies) that shine during a finite time in the Universe. High school or undergraduate teachers can explore this subject in an instigating, interdisciplinary, and historical way.

我们将介绍奥伯斯佯谬（Olbers paradox），并基于简单宇宙学与天体物理模型，结合几何论证方法，阐述该佯谬的若干解决方案设想。一项鲜为人知的夜空亮度计算结果表明，宇宙膨胀对夜空黑暗效应的贡献仅略超一半；剩余贡献则源于恒星（及星系）仅在宇宙有限时段内发光，且其空间分布密度偏低。高中或本科阶段的教师可以通过兼具启发性、跨学科性与历史脉络的方式，开展该主题的教学探索。