Asteroid Solar Power Absorption Area · CAP 2011 #20
Physics · thermodynamics
Problem
A spherical asteroid with a radius of 1 km is illuminated by sunlight. In order to calculate the solar power absorbed by the asteroid, what area should be used? a) 1 km². b) 3.14 km². c) 12.6 km². d) Answer cannot be determined from the available data.Intuitive explanation
The key insight is that only the side of the asteroid facing the sun receives direct sunlight—not the entire surface. When parallel rays (sunlight) hit a sphere, they illuminate a circular disk, not the full spherical surface. The cross-sectional area of that disk is what intercepts the solar power, so you need the area of a circle with radius 1 km, not the surface area of the sphere. This is why we use rather than .
Intuitive explanation
The key insight is that only the side of the asteroid facing the sun receives direct sunlight—not the entire surface. When parallel rays (sunlight) hit a sphere, they illuminate a circular disk, not the full spherical surface. The cross-sectional area of that disk is what intercepts the solar power, so you need the area of a circle with radius 1 km, not the surface area of the sphere. This is why we use rather than .