How will the temperature of the earth change through time if the sun stops radiating?

Answer 1

The heat radiated away from the Earth would be:
Heat loss = Area * sigma * T^4

- Area = 4*pi*R_earth^2
- sigma = Stefan-Boltzmann constant
- T = absolute temperature of the earth

If you model the earth as an object with a single temperature and total heat capacity C, you get:
C*dT/dt = - 4*pi*R^2*sigma*T^4
dT/dt = - (4*pi*sigma*R^2/C)*T^4
= - k*T^4
dT/T^4 = -k*dt

(1/T(t)^3 - 1/T(0)^3) = 3*k*t

1/T(t)^3 = 1/T(0)^3 + 3*k*t
T(t)^3 = T(0)^3/(1 + 3*k*t*T(0)^3)

or
T(t) = [T(0)^3/(1 + 3*k*t*T(0)^3)]^(1/3)
where
k = 4*pi*sigma*R_earth^2/C
C = heat capacity of earth.

This solution pretends that you can model the earth as having a single temperature. Not a great assumption, but if you want to do something better, you need to calculate the heat-diffusion equation. That would be real work.

Answer 2

I suppose all the evironmentalist wackos will claim that the earth will get to cold, "and we'll all die". I can see it now, "solar extinction global cooling" ... right.

They'll all be wrong, of course. Take doug_donaghue's claim, for example, that the earth's temperature will drop to "a few tenths of a Kelvin". The cosmic background radiation temperature is 4.3 K. Can he explain how the earth's temperature can drop below that? I didn't think, so. That means he doesn't know what he's talking about, and everything will be just fine if the sun goes out :-)

Answer 3

It would depend quite a bit on why the sun stopped radiating. Has every thing stopped radiating including the earth? Does radioactive decay still take place? Is there such a thing as an electrical conductor?

Answer 4

If the Sun stops radiating it will do nothing except get colder until it's a few tenths of a Kelvin away from absolute zero.

Doug

Answer 5

its gonna get pretty damn cold, considering tht most of the heat we feel is from the sun. of course, if that doesn't kill us off, then all the crops and therefore animals dying will.