In 2014 the European Space Agency's Rosetta spacecraft was 5000 km from the comet 67 P / Churyu

step 1 In this problem, we are going to calculate the temperature of the surface of the comet 67pcg. So

In 2014 the European Space Agency's Rosetta spacecraft was...

In 2014 the European Space Agency's Rosetta spacecraft was $5000 \mathrm{~km}$ from the comet $67 \mathrm{P} /$ Churyumov-Gerasimenko. Rosetta turned its infrared sensors toward the comet and measured a flux of $96.3 \mathrm{~W}$ per square meter of cometary surface. Assuming the dark, dusty comet radiated like a blackbody, what was its temperature?

In 2014 the European Space Agency's Rosetta spacecraft was $5000 \mathrm{~km}$ from the comet $67 \mathrm{P} /$ Churyumov-Gerasimenko. Rosetta turned its infrared sensors toward the comet and measured a flux of
$96.3 \mathrm{~W}$ per square meter of cometary surface. Assuming the dark, dusty comet radiated like a blackbody, what was its temperature?

Key Concepts

Blackbody Radiation

Blackbody radiation refers to the idealized emission of electromagnetic radiation by a body that absorbs all incident radiation, irrespective of frequency or angle of incidence. It is a fundamental concept in thermodynamics and quantum mechanics, serving as a baseline model for the thermal emission spectrum of objects, including celestial bodies. In many physics and astronomy problems, objects are approximated as blackbodies to simplify calculations of their temperature based on the radiation they emit.

Stefan-Boltzmann Law

The Stefan-Boltzmann Law relates the total energy radiated per unit surface area of a blackbody in unit time to the fourth power of its temperature. Mathematically, it is expressed as F = ?T^4, where F is the radiant flux, T is the absolute temperature in kelvins, and ? is the Stefan-Boltzmann constant. This law is crucial in determining the temperature of an object when the energy flux emitted by it is known.

Radiative Flux

Radiative flux refers to the amount of energy emitted, transferred, or received per unit area per unit time. In the context of astrophysics and thermal radiation, it represents the measured power per unit area from a radiating body. Understanding radiative flux is important when using the Stefan-Boltzmann Law to connect the observed energy with the intrinsic temperature of celestial objects.

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