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

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SUMMARY

The discussion focuses on the implications of the Sun ceasing to radiate energy on Earth's temperature. It highlights the application of Newton's law of heat transfer, specifically the equation \(\frac{dT}{dt} = -k (T-T_0)\), where \(T_0\) is the cosmic background temperature of 4 K. The conversation emphasizes the need to consider the time it takes for electromagnetic radiation to reach Earth, which is crucial for understanding the temperature variation over time. Theoretical models and equations are essential for accurately predicting these temperature changes.

PREREQUISITES
  • Understanding of Newton's law of heat transfer
  • Familiarity with Fourier's law for uniform temperature distribution
  • Basic knowledge of thermodynamics and heat transfer principles
  • Awareness of cosmic background radiation and its effects
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  • Research the implications of Newton's law of cooling in astrophysical contexts
  • Study the effects of electromagnetic radiation delay on temperature changes
  • Explore advanced thermodynamic models for planetary temperature variations
  • Investigate the role of cosmic background radiation in planetary science
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Students in physics and environmental science, astrophysicists, and anyone interested in the effects of solar radiation on planetary temperatures.

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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?

Homework Equations





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

[tex]\frac{dT}{dt} = -k (T-T_0)[/tex]

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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