FYKOS Year 38 Series 4 Problem 3 — a sphere in a shadow · FYKOS 38 #38.4.3
Physics · thermodynamics · optics
Problem
A small sphere is positioned at the furthest possible distance from Earth such
that that it remains completely within the planet's shadow. At what temperature
will the sphere reach equilibrium, assuming Earth behaves as a black body with
a homogeneous temperature of TE=20∘\mathupC? Neglect all light sources
other than the Sun and assume that light rays propagate in straight lines,
ignoring refraction in the atmosphere or relativistic effects.