There are at least two approaches to colonizing a planet or a moon:
- you can send a relatively small number of people there and assume the population will grow in the way small populations sometimes do;
- you can send a relatively large number of people there.
Effects of lifting a large number of people
So, considering the case where we plan to send a fairly large number of people, an interesting thing then is to consider whether, with rockets driven by fossil fuels, you can lift a large number of people without doing enormous damage to the remaining population. One particular enormous damage you might do is to cause enough warming that bad things happen in due course. We're already doing this in other ways of course, but it's worth looking at the $\mathrm{CO_2}$ emissions of lifting people off Earth in really large numbers.
To do this properly is quite hard: you need to work out the $\Delta V$ properly, know the $I_\mathrm{sp}$ of your launch system, consider how much fuel gets burnt in the atmosphere (obviously the fuel you burn out of the atmosphere does not count, at all), consider other impacts of burning the fuel (aerosols, which may cause some cooling, other pollutants which may do either), consider the cost of producing launch vehicle, the oxidiser, any fuel which does not dirctly produce $\mathrm{CO_2}$ and so on: it's a big engineering calculation.
So, as an annoying theoretical physics person, I'm going to do a horrible spherical-cow estimation in the hipe that the answer is right to a factor of a few. I'll make the following assumptions:
- we're lifting people with something like an S-IC, burning RP-1;
- that system can lift enough to put one person and their required support equipment on Mars (so they need something like 3 times more support equipment to live on Mars indefinitely than the Apollo astronauts did to live, briefly, on the Moon, and I assume that the Apollo stack could have put someone on Mars) (note also it does not matter whether you send the support equipment separately: it still costs you to lift it);
- There is a production-cost fudge factor, $k$ which accounts for emissions from anything but the first-stage (the S-II should not have emitted anything directly, but probably making its fuel did) and emissions in production. I'll assume $k = 2$ initially.
So, OK, let's do the maths.
- The S-IC contained $770\,\mathrm{m^3}$ of RP-1, or $770\times 10^3\,\mathrm{l}$;
- RP-1 has a density of about $0.82\,\mathrm{kg/l}$, so the mass of fuel in the S-IC was about $630\times 10^3\,\mathrm{kg}$;
- Burning $1\,\mathrm{kg}$ of RP-1 emits about $3\,\mathrm{kg}$ of $\mathrm{CO_2}$.
So the direct amount of $\mathrm{CO_2}$ emitted by an S-IC is about $1.9\times 10^6\,\mathrm{kg}$ (the additional mass comes from the oxidizer!). And with our fudge factor to account for other emissions associated with a launch this comes to $3.8\times 10^6\,\mathrm{kg}$.
So the $\mathrm{CO_2}$ cost per person to Mars is about $3.8\times 10^6\,\mathrm{kg}$.
So the question is: is this a problem? Well, let's assume you're not going to do the small-colony-and-breed thing: let's say you're going to lift a million people this way. The cost of doing that is is $3.8\times 10^{12}\,\mathrm{kg}$ or $3.8\times 10^9\,\mathrm{t}$.
Human emissions at present are somewhere around $10^{10}\,\mathrm{t/y}$, which is extremely non-sustainable, to say the least.
So how bad is the cost of lifting a million people? Well, if you did it in a year it would be very bad indeed. If you did it over a century not so bad. Note also that these costs are borne by the people you don't lift, which, if you lift a million people, is 'almost everyone'. Of course, this is the result of some kind of Fermi estimation process: it may be wrong by a factor of ten or something. But it's good enough to tell you two things:
- someone should do a real engineering calculation to get real numbers as the results are clearly in the significant-to-catastrophic range;
- we're definitely not going to be living in some world where a million people a year (a little over one person in ten thousand) go on holiday to Mars or the Moon, until we've solved the emissions problem, and we're probably not going to be lifting a million people at all, unless we're happy to kill very large numbers of the remaining population, where that remaining population is almost everyone.
How many people could we lift?
Another question is: given the known fossil fuel reserves, how many people could we lift, if we don't care about the consequences for the people left on Earth? Again I will use the Apollo stack as my source of information:
- each S-IC contains $770\,\mathrm{m^3}$ of RP-1;
- there is a fudge factor, $k = 2$ to account for other fossil fuels used in the production of the system;
- each rocket puts a single person on Mars.
I will base my information on fossil fuel reserves on BP's Statistical review of world energy, and I'll just focus on oil reserves. They say that there are about $1.7\times 10^{12}$ barrels of crude oil left in proved reserves (I am not sure what 'proved' means but I suspect it means there is more we don't know about). A barrel is $159\,\mathrm{l}$ or $0.159\,\mathrm{m^3}$, so there are about $2.8\times 10^{11}\,\mathrm{m^3}$ of crude oil left.
I'll assume that all of that oil is RP-1. This is absurdly optimistic, but on the other hand I haven't taken any account of the coal-fired rockets. So the number of launches we can do – the number of people we can lift – if we burn all our oil, is
$$
\begin{aligned}
N &= \frac{2.8\times 10^{11}}{770\times 2}\\
&= 1.8\times 10^8
\end{aligned}
$$
the current world population is about $7\times 10^9$: if we burn all the oil we can lift about 1 person in every 40. Or, in other words, we could lift more than half of the population of the US.
If we did this we would emit $6.8\times 10^{14}\,\mathrm{kgCO_2}$: about $68$ times current annual emissions. The consequences of that would be catastrophic for the people left on Earth.
I am not going to try and work out how much coal it takes to drive a rocket, but presumably you could in theory lift some more people with coal-fired rockets: there is quite a lot of coal I think.
Note that I am not arguing that the $\mathrm{CO_2}$ emissions from Apollo, or from space exploration in general, were or are a problem: they are not, and I am very strongly in favour of space exploration. The emissions from lifting people in large numbers, on the other hand, would be a big problem.