With this understanding of how the Sun will evolve, we can follow its evolution on the HR diagram.
If the Sun became a red giant will the Earth still be able to support life here?
Jagadheep: No, the Earth will not be able to support life if the Sun becomes a giant star. Giant stars have large radii as their name implies. When the Sun becomes a giant star, it may become so large as to engulf Earth, in which case the planet will be destroyed. Even if this does not happen, the sun will expand so far out that the temperatures on Earth will become extremely high so that all oceans will evaporate away, and there will be no water left on Earth. So, no life which depends on water will be able to survive.
When the sun starts expanding in about 5 billion years, what will be the first signs of this process?
Karen: The Sun is a relatively low mass star and as such its death will be relatively mundane (at least by Astronomical standards). The Sun's luminosity and radius have been increasing since it started life and will continue to gradually increase in this manner for another 4.5 billion years or so. When the hydrogen in the core is all used up energy generation will stop there, however it will continue in a thin shell around the core. It is this which makes the Sun expand since it heats up the outer layers more. Funnilly enough this makes the very outer layer cooler so that sun will actually redden as well as becoming brighter and expanding. I suspect that this reddening might be the first signs the the Sun has left the Main Sequence.
How long will it take from the process starts til the earth is engulfed, or at least uninhabitable?
Timescales are difficult in evolutionary models of stars. It's not clear quite what'll happen to the Earth either. It could be engulfed by the Sun, or it might get pushed out into a larger orbit and freeze as the Sun expands. The Sun will be a Red Giant for a few million years. By then I think it's safe to say that the Earth will be uninhabitable.
Will the earth catch fire while humans still live here or will the planet simply dry out?
I think that the temperature would kill life before anything caught on fire. It would only need to be 100F or so all the time for humans to be wiped out (we don't survive long in the desert, right).
Is it probable that life on earth will survive that long, or will asteroids wipe us out before then?
Probability wise, it's likely that the Human Race will have been killed off by the time the Sun leaves the Main Sequence. I don't think that any species in history has dominated the Earth for that long. Of course we could be the first....
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