What Happens to Earth's Temperature If the Sun Stops Radiating?

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If the sun were to suddenly stop radiating, Earth's temperature would begin to drop significantly over time. The discussion highlights the use of Newton's law of heat transfer to model this temperature change, indicating that the rate of temperature decline is proportional to the difference between Earth's temperature and the cosmic background temperature of approximately 4 K. The equation provided suggests that various heat properties of the Earth, represented by a constant k, would influence the rate of cooling. Additionally, the time it takes for electromagnetic radiation to reach Earth is a factor that needs consideration in this scenario. Understanding these principles is essential for predicting how Earth's climate would respond to such an extreme event.
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Homework Statement


How does the temperature of the Earth change when the sun suddenly stop radiating?:confused:
how will the temperature vary with time? Please help me solve this one. can we answer this one using models or simply through theories? can you explain how?

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The Attempt at a Solution

 
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I think one useful equation is Newton's law for heat transfer, or it may be called Fourier's law for uniform temperature distribution or smth. similar. Anyway, it says that the rate of change of temperature of proportional to the difference between the object and its surroundings, mathematically

\frac{dT}{dt} = -k (T-T_0)

where T_0=4 K is the background temperature of the cosmos and k is a constant, depending on various heat properties of the Earth.
 
but, I guess you also need to consider the time, it takes EMs to reach the earth
 

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