I think the cargo starship will come in around $100/ton to orbit. Pad it a few multiples once you add in life support and everything else a person needs, but just hauling my ass to orbit would be $10,000. I know SpaceX thinks that when the system is mature that amount will be on the lower end of between $1000-10,000, including life support. The additional energy to a Mars insertion isn't really that much. Hopefully by that time there will be an Aldrin cycler (maybe made out of an assembly of Starships socked together) that would have all the power generation, food production, light manufacturing, rooms, and entertainment needed for a comfortable trip. The same starship that's carrying 100+ people packed in tight for $5000 a seat would be able to dock with the cycler for the trip to Mars, and then you'd get back on the passenger ship for Mars EDL. Actual cost to ship a person to Mars at scale could be under $10k. You could literally take a few years or decades and "work from home" on Mars and earn enough money to live comfortably importing supplies from Earth at $100-300/kg for shipping (that's not far off from how much it costs to ship internationally with UPS) (not really, but it feels like it).
First of all, I think you mean $100/kg, but let's take $100/ton.
This is very far-future wishful thinking. Generally, if we go by my favorite source of information on this kind of stuff, namely scifi spacefaring forums, you can theoretically go down to about high thousands of dollars on chemical rockets. The reasoning is roughly like so:
LEO is the lowest you HAVE to go to get something into space and keep it there for a reasonable amount of time. All the rest you can do with non-rocket propulsion. The rough upper limit of rocket mass is thousands of tons, maybe low tens of thousands (10X starship). Starship is already in the order of magnitude of the largest thing you want to launch for dozens of reasons. A 2/3/4-stage rocket weighing 10 000 tons can put about 250 tons into LEO and is close to optimum efficiency in that regard. Rounding up, that's 10 000 tons of fuel and the cheapest you can go right now is CH4+LOX which has never been lower than about $200/MT (at nearly free methane prices and LOX at energy input prices). Barring massive changes in the economy and fueling economics, that's $2M in just fuel and oxidizer. Even if you design a perfect rocket (cigar rocket, i.e. an infinite-stage rocket that perfectly adheres to the integral rocket equation) you don't get lower than about ~5000 tons of fuel for 250 tons of payload. So fuel, no other costs at all, that's $2M/250~$8000/ton.
This assumes the rocket and operations are free, which they aren't. SpaceX is still a tens-of-billions-per-year-operation even if they build zero rockets. All that needs to be paid, and they don't launch that many tons into orbit. Just ops adds tens of thousands of dollars per ton, not even mentioning the rocket itself. So as long as we use chemical rockets anywhere in the chain, anything below like $100-150k/ton is basically impossible. And the absolute floor is at around $10k/ton in a world where only fuel is considered (the only truly non-reusable part)
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Before we get into cheap spaceflight, what is the true bottom of the market right now?
SpaceX has carried about 8000 tons to orbit and let's say invested about $40B to get there (we don't know for sure, but it's at least in the ballpark). That implies they have at least charged on average $50M/ton to survive so far. Without hard evidence it's hard to verify, but given the awarded contracts they surely must be cheaper by this point, maybe as low as $20M/ton on average.
The cheapest recent launches have been well below that, but that's... like, I get how you can sort of say you can launch a Falcon for $20M (implied <$1M/ton), but if all SpaceX did was launch $20M Falcon missions, they'd go bankrupt. That doesn't actually cover the costs. That's more like a marginal cost estimate, but they are clearly subsidizing this with specialty missions, military launches, etc.
But it's clear that marginal launch costs are going to inch below $1M/ton. If we assume no big space infrastructure projects are going to happen anytime soon, that's about the end of it. To do it cheaper requires more scale-up that doesn't have a market right now.
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How can we get cheaper? Well, space infrastructure! 10k tons to orbit sounds like a lot to you? What about 100k tons
just in fuel? That's the kind of launch quota you need to even start about thinking to put a robot-operated moon base in place. Another 100k tons just in materials per year to service it. And that's, also, roughly the limit of chemical rockets. At that point, you're able to put so much stuff into space that cheaper launch methods start becoming viable. For instance, mountain-based mass drivers are totally doable for ~$10-100B and have a 'fuel' cost of about 30kWh/kg - even with expensive electricity that's maybe $10/kg in fuel and at 100k tons per year, that's something you can pay off with hundreds of dollars per ton in repayments - orders of magnitude cheaper than chemical rockets. You still need some additional launch tech to insert something into orbit and do transfers, but that's something rockets can do very cheaply if they're stationed in orbit and don't need to get out of the gravity well to begin with. Altogether, maybe $20k/ton is possible that way.
Want to get to $10/kg? One of the first problems is that you need more than $10/kg in energy to begin with. This requires some kind of significant breakthrough in energy technology, something like nuclear fusion (the scifi kind, not the real kind) or megastructure renewables (orbital solar, etc.). Then you also need to be able to construct something that efficiently puts you into orbit but doesn't cost much, which is impossible as even the amount of concrete and steel you need for a launch loop or skyhook or space elevator is humongous. This is 100+ years out, if we ever get there.