The OP said the sun just quit shining. It just went dark, its mass didn’t disappear. Earth will continue happily, yet cooly, along its regular orbit. Gravity-related cataclysms won’t occur.
Grow lights don’t maintain a useful spectral output for very long. I think after six months to a year, the plants would start suffering and crapping out. Could Iceland make more bulbs?
I wonder how many people we could actually keep alive living entirely under artificial light?
The sun won’t stop shining in 5 billion years, that’s just when it stops being the sun we know today.
In around 5 billion years the sun will start to puff up becoming huge. Around 200 times bigger than today! So big it’ll totally engulf Mercury, Venus and possibly even the Earth. It won’t stop shining at this point, in fact it’ll be brighter and hotter than today!
Eventually it’ll blow away it’s outer layers, leaving a super dense extremely hot core, called a white dwarf.
This white dwarf will still shine for a very, very long time. Eventually it’ll cool and become a black dwarf. But this process takes so long that black dwarfs are purely theoretical. The universe isn’t old enough for any black dwarfs to have formed yet. White dwarfs last a very long time. Trillions of years!
So anyway, to cut a long story short, the sun won’t stop shining in 5 billion years.
You’ve got that mixed up. There are two different kinds of black dwarf: Those formed from a cooled-off white dwarf, and those formed from cooled-off red dwarfs. Red dwarfs can last for trillions of years, so the Universe isn’t yet old enough for that kind of black dwarf to exist yet. White dwarfs, though, last for a much shorter time, depending on how cool is cool enough to be considered “cooled off”, and the Universe is old enough for that kind of black dwarf.
Funny, I just wrote an article about this a few weeks ago.
http://scienceblogs.com/startswithabang/2010/07/q_a_how_long_would_we_have_if.php
If you mean “what if the nuclear reactions powering the Sun suddenly and permanently stopped”, it turns out that we’d have about 100,000 years before things got really bad here on Earth, which might even be plenty of time to figure it out.
It turns out that even in the case of a cooling white dwarf, it would still take many billions of years more for it to go black than the Universe has been around for.
The Sun, for instance, has about 5-7 billion years before it finishes its life cycle and becomes a white dwarf. But, barring any “interesting” things happening to it, it’s estimated to take much longer than the 13.7 billion years our Universe has been around for it to fade out of the visible.
While we don’t need to wait the quadrillion (10^15) years necessary for it to get down to CMB-level temperatures (a few Kelvin), for it to lower to temperatures that would render it invisible even in visible light (although it would still be clearly visible in IR) takes at least 10^11 years (100 billion years).
However, if the proton is eventually unstable, white dwarf stars would have a much different fate than even becoming a black dwarf. See this paper (warning, pdf file) by Adams and Laughlin: System Unavailable