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.

我们基于简易宇宙学与天体物理模型，通过几何论证手段，介绍了奥伯斯佯谬（Olbers' paradox）及其若干求解方案。一项鲜为人知的夜空光度计算结果显示，宇宙膨胀对夜空黑暗效应的贡献仅略超半数；剩余部分则来自恒星（与星系）仅在宇宙有限时段内发光的稀疏分布。高中或本科阶段的教师可通过富有启发性、跨学科且兼具历史视角的方式，对该主题开展教学探索。