> Presume there are only 1 billion people left on Earth when we decide it's time to go
The scenario that leads to have only 1B left from where we're at would entail such a catastrophic meltdown of society that even building a rocket would likely not be feasible, let alone anything significant for a human exode.
Think about it, you're fighting against something that killed 7B people, be it the end of fossil fuels, climate change, a massive and deadly pandemic, a war or another type of catastrophe. There are probably global food shortage, areas that can't be lived in anymore. The global supply chain doesn't exist anymore, and government is much more localized, very different. Being down to 1B is probably not the bottom line of your decline, 1B people is still a lot. Your priorities are based on survival, you're trying to figure out how to grow enough food, gather enough water. You don't have enough reserve capacity that you can spare it on projects like building a lot of rockets and colonizing another planet.
Rockets are a thing of complex societies with abondant energy ; not a last minute effort to preserve the human race.
The GP was just setting a lower bound of 1B to establish a basis for calculating the cost to move humanity offworld. The cost for 5B people or 7B people would be even more cost prohibitive.
But also the shrinkage would not have to happen abruptly. In theory you might be able to get to a population of 1B over the course of 200 years without the kind of catastrophic meltdown you're describing.
I completely agree this would happen over a long time, barring a disaster like nukes or asteroids, which does not seem like the most credible scenario (I dont think I said anything to the contrary)- and I'll confess to a pessimistic vision of the future, when our demise is self inflicted.
But look at Covid for a reference point. I mean all things considered this was still too mild to reduce humanity to 1B. This almost immediately (in the span of a year) led to big issues with the supply chain. Products removed from the shelves, years long backlogs on cars. People getting sick all around you and hospitalized, and yet there were societal debates on whether the disease actually existed, whether we should wear masks, or take the vaccine. Climate change is in the same line, people denying change with snarky remarks every time we receive a snowflake, and any step forward being accompanied by two steps backwards (look at the Paris accords). What I mean there is that there is no change witnessed without actual pain, and the change required for something truly threatening for humankind (e.g climate) won't see any actual action till we're already greatly suffering, and probably beyond the point of repair.
Now imagine a large chunk of the population disappearing, even over the course of decades, and whether that would leave society in a state where it can afford a significant "gtfo of here" space program. My personal opinion, and that is only an opinion, is that this is not systemically possible ; and therefore I don't believe in GP's base assumption, even if that's departing from the motivation of simplifying that they made :)
In any case, beyond cost, short of inventing completely new physics, I doubt earth even has enough resources to catapult us all into and then out of orbit.
The most likely scenario to me is a handful of elites (which fortunately for them are fewer and fewer) embarking on rockets, accompanied with scientists and engineers to give them a fighting chance, plus a bunch of slaves to do the grunt work and die, because surviving ain't worth it if you can't enjoy life.
(once again, I confess is a pessimistic vision, and is also departing a bit from the initial statement from GP)
The scenario that leads to have only 1B left from where we're at would entail such a catastrophic meltdown of society that even building a rocket would likely not be feasible, let alone anything significant for a human exode.
Think about it, you're fighting against something that killed 7B people, be it the end of fossil fuels, climate change, a massive and deadly pandemic, a war or another type of catastrophe. There are probably global food shortage, areas that can't be lived in anymore. The global supply chain doesn't exist anymore, and government is much more localized, very different. Being down to 1B is probably not the bottom line of your decline, 1B people is still a lot. Your priorities are based on survival, you're trying to figure out how to grow enough food, gather enough water. You don't have enough reserve capacity that you can spare it on projects like building a lot of rockets and colonizing another planet.
Rockets are a thing of complex societies with abondant energy ; not a last minute effort to preserve the human race.