Student handout: Grey space capsule

Contemporary Challenges 2021
In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.

A grey space capsule is sent on a trip to the Moon. The surface is designed to reflect 50% of the incident sunlight (i.e. it is “grey” for wavelengths less than about 3 or 4 \(\mu\text{m}\)). The total intensity of radiation emitted by the surface (wavelengths longer than about 3 or 4 \(\mu\text{m}\)) are still described by \(\sigma T^4\).

The capsule is spherical and has a radius of 3 meters.

The space capsule reaches thermal equilibrium after being bathed in sunlight for a few hours. The capsule is rotating and is made of thermally conducting metal, so that all sides have the same temperature. Find the temperature.

Hint: The energy of the sunlight absorbed by a sphere can be calculated by finding the area of the shadow, which is also known as its cross-sectional area.

blackbody Stefan-Boltzmann Law
Learning Outcomes