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

[jau]

Homework Statement

How does the temperature of the Earth change when the sun suddenly stop radiating?
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

 

[Irid]

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.

 

[rootX]

but, I guess you also need to consider the time, it takes EMs to reach the earth