If we put the financial resources behind it, we (meaning: a very few of us) could leave the solar system right now. It's just that we lack the technology to do it right, with minimal risk and a lot of comfort. This is an engineering problem which we could solve, but choose not to. Putting together a generation ship to leave the system would probably succeed, but it would also utterly consume all our resources. The reason for this is that we choose to suck at space. For all our achievements in other areas, our space program is basically still in the sixties.

The main thing that is missing which would allow for us to even colonize the solar system, and potentially other star systems, is a good way to get lots of energy, such as nuclear fusion. There is nothing physically preventing us from developing a fusion reactor, we just haven't done it yet. Leaving the solar system will get even easier once we master the process of changing the substrate our minds run on from biological matter to something more appropriate, but again, this is not strictly required.

FTL travel is not really needed for us to colonize the galaxy either. It would be nice to have, but at this point it's just beyond our means to think about it. The other stuff isn't, though.

Energy is possibly the biggest barrier towards future space colonization. It is entirely possible that we discover some new source of energy that allows us to:

1. Send a sustainable human population out of the solar system;

2. Travel to an inhabitable planet which may be millions of light-years away;

3. Geo-engineer that planet to the extent that it can self-sustain a moderate human population.

None of these steps is trivial. The pessimistic side of me thinks that we may actually never overcome any of these challenges.

Yes, the Wikipedia lists a couple of technologically feasible options of leaving our solar system [1], some of which date back to the fifties. Using for example nuclear pulse propulsion we could reach Alpha Centauri in about 150 years.

[1] https://en.wikipedia.org/wiki/Interstellar_travel#Proposed_m...

Hmm, interesting.

I was going to go with our hard-deadline for life on earth, 800 million to 1 billion years in the future the sun will have baked us so hot there's no liquid water left.

But you're probably more accurate. It's entirely conceivable that by then the increased solar output and our own tech advances will have made it possible to take up residence in other places in the solar system, which may even have become slightly more habitable by then due to the increased solar radiation. Hmmm.

That's possible too. But eventually, even the universe will succumb to entropy. I guess it's just a question of whether we die out in the solar system, or in some other star system.

My view: we will leave our solar system, but not as lumps of meat.

e.g. Greg Egan's Diaspora or Accelerando by Charlie Stross.

>>but it turns out that the laws of physics means there's no practical way to leave our solar system.

Note that at one point of time, laws of physics said lighter than air flying machines were impossible.

Yet here we are, we have the airplane.

The problem is we don't know physics completely to say if something is impossible.