I haven’t seen the movie, but from a scientific point of view…
- Could a sunspot be that big, and what would it mean to the sun? To the earth?
A single sunspot covering 25% of the sun? I’d say it’s very, very unlikely. Now, lots of normal-sized sunspots adding up to 25% is somewhat more believable, but we don’t know if that would actually reduce the energy output of the sun. That is, a lot of sunspots means a lot of magnetic activity, so the rest of the sun can get brighter. Also, remember that sunspots aren’t completely dark. It’s just darker than the rest of the sun.
2)How much would the sun need to change (+/-) to make life difficult for us?
The temperature of the earth is where the incoming energy from sunlight balances the energy radiated away as infrared. Radiation is prportional to T[sup]4[/sup]. So if the sun became 1/16 as bright, the temperature of the earth will drop till the earth radiates 1/16 of the amount. That happens at half the present temperature, or about 150K (-120C).
So what temperature is “difficult for us”? Maybe 30 degrees C difference? That’s 0.9 times the current temperature, so energy output (=input) will decrease to 0.9[sup]4[/sup]=0.65 of the present value. That’s a 35% decrease. A 15-degree difference will still require a 20% drop in the sun’s brightness.
3)If there is a significant change in the sun, how long before we feel the effect here on earth?
8 minutes is the obvious answer, but it probably takes several months for the temperature to drop by the amount calculated above. That’s how long seasonal temperature changes seem to take. (Hottest days of summer comes a months or two after summer solstice)
4)How long would earth have if the sun went dark suddenly?
How long would it have what? Ability to support life? What kind of life?
Of course, there is some speculation that during the Middle Ages the sun’s output was slightly decreased, resulting in worldwide famine. There were fewer sunspots during that time, called the Maunder Minimum. Fewer sunspots indicates reduced activity in the sun.