A small cube-shaped satellite

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A small cube-shaped satellite,

0.50\,\text{m}

on a side, orbits Earth while slowly tumbling so that each face receives equal time facing the Sun. The satellite’s surface coating has the same visible absorptivity and infrared emissivity, denoted by the symbol

\epsilon

. Internal electronics dissipate

120\,\text{W}

of waste heat, which is transferred uniformly to the satellite’s surfaces. Additional information: • The average solar radiant flux incident on the satellite’s orbit is

1.36\,\text{kW}\,m^{-2}

. • Because of the tumbling motion, the time-averaged projected area that intercepts sunlight equals one-quarter of the satellite’s total surface area. • No other heat sources or sinks are significant. The mission requirement is that the satellite’s surface temperature must not exceed

320\,\text{K}

. (1) Part 1: Calculate the average solar power absorbed by the satellite in orbit in terms of

\epsilon

. (2) Part 2: Write an energy-balance expression for the satellite at the maximum allowable temperature of

320\,\text{K}

, including both absorbed solar power and internal waste heat. (3) Part 3: Using your expression from part (b), determine the minimum emissivity

\epsilon_{\text{min}}

that will satisfy the temperature requirement. (4) Part 4: Discuss qualitatively how raising the satellite’s orbital altitude (thus reducing incident solar flux) would influence the required value of

\epsilon_{\text{min}}

, and explain why.

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