1. The problem is to understand how heat flow from a body in space is mathematically modeled. 2. Heat transfer in space primarily occurs through radiation because there is no medium for conduction or convection. 3. The fundamental formula used is the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature: $$P = \sigma A T^4$$ where: - $P$ is the total power radiated (heat flow rate) in watts, - $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \text{W/m}^2\text{K}^4$), - $A$ is the surface area of the body in square meters, - $T$ is the absolute temperature of the body in kelvin. 4. For real bodies, emissivity $\epsilon$ (between 0 and 1) modifies the formula to: $$P = \epsilon \sigma A T^4$$ 5. This means the heat flow depends strongly on temperature (to the fourth power) and the body's surface properties. 6. In space, since there is no conduction or convection, this radiative heat loss is the dominant mechanism for a body to lose heat. 7. To model heat flow from a body in space, you calculate $P$ using the body's temperature, surface area, and emissivity. 8. This model helps in spacecraft thermal design to ensure components maintain safe temperatures. Final answer: Heat flow from a body in space is modeled by the Stefan-Boltzmann law $$P = \epsilon \sigma A T^4$$ describing radiative heat loss.