Timeline of Manned Interstellar Travel, Based on Simple Economics: No Humans on Alpha Centauri Planets Until 2613

It has been estimated that a manned Mars mission would cost $100 billion. Compare this to the most recent unmanned lander, Insight, at $830 million; putting people on Mars then comes with a cost multiplier of 120.

The Initiative for Interstellar Studies estimates that an unmanned interstellar mission would cost at least "in the trillions"; Centauri Dreams cites Odenwald at $174 trillion. Assuming the same scaling, the lower and upper bounds on that then suggest that a manned mission would cost from $240 trillion to $21 quadrillion.

If on the other hand we take the projected cost of a manned mission to Mars, and assume it scales linearly with distance, a manned Mission to Alpha Centauri would cost $55 quadrillion.

It's worth pointing out here that world GDP is $80 trillion. Let's assume an annual economic growth rate over time of 2%. Let's also assume that starting tomorrow we put ALL of GDP toward such a mission - that is, every last human is working this mission and just barely otherwise just barely surviving as peasants eating crumbs.

Assuming an annual economic growth rate over time of 2%, then at earliest, we can launch a manned interstellar mission at the earliest by 2227; at latest, by 2501.

But forget about that. Because neither you, nor any other human on this planet will sign up tomorrow for their descendants being reduced to slavery for centuries for a space mission, which is what those numbers assume. So let's assume we continue to spend money on space exploration at the same rate that we in the US currently are - about 0.11% of GDP. This is already quite a generous assumption, given that most countries can't afford to dedicate such a fraction of wealth to endeavors that don't quickly return on investment. If you're more optimistic and want to set the relative rate of expenditure (over centuries) to the highest it has ever been (in a democracy - you said you were optimistic right?) that's 1966 USA, which is about twice what it is today, and only makes it happen 35 years earlier. (This is more dependent on economic growth than space program expenditure.) So let's stick with current NASA budget fraction, and assume that the future space program is ONLY working on this one mission.

By these assumptions, we can launch the mission at earliest by 2570; for the upper bound estimate, by 2845.

Our fastest spacecraft so far would take another 30,000 years after launch to get there. Let's be more optimistic and assume that the light sail technology we're talking about for unmanned probes also applies to manned craft, and can get the ship up to 10% of the speed of light. Therefore, taking into account travel time and speed-of-light delays, we wiill get the interstellar "Eagle has landed message" at an absolute cheapest earliest date of 2618.

Of course this is still unrealistic, because we're still assuming mission development starts in earnest tomorrow, assuming every government on Earth will let us use a NASA-sized fraction of their GDP for this, and that they will continue to cooperate for at least 550 years building the mission. Think of this in reverse: it's as if in 1470, the middle of the War of the Roses, and the Russians and Poles and Lithuanians still throwing off the Mongol yolk, everyone started spending money and cooperating on a project and continued to cooperate on it until this year.

I think it is unlikely, barring unforeseeable scientific revolutions, that human beings will leave the Solar System this millennium. I think it is likely that there will be civilization or species-threatening or destroying events in this millennium. This discussion of colonizing other planets to mitigate existential risks has a scatter plot listing a probability of event happening within 200 years/risk of civilizational collapse for nuclear war, coronal mass event, rogue AI, and nuclear war as 90%/20%, 70%/90%, and 95%/70%.

Using those same numbers, in the time period until launch there's a greater than a 96.6% chance of a rogue AI, and a greater than 99% chance of coronal mass event or nuclear war.

But fully automated probes could get out more quickly, particularly if we design self-reproducing von Neumann probes. We should start terraforming Mars now, as practice for remotely terraforming planets with von Neumann probes for when we eventually get there. We have time to terraform them, because if physical human bodies ever do get there, it will be in the distant future. But we do not have that much time to get the launch the hardware, which suggests we should at least colonize the Moon as insurance. Cryonics and hibernation technology at this point is still basically science fiction. These numbers are depressing given our previous dreams, but we calibrated on going from powered flight to standing on the moon in 2/3 of a century.