Elon Musk has unveiled SpaceX's latest plan to colonize Mars. Despite its insanely optimistic schedule, this year's plan seems more plausible than last year's. SpaceX's long-range plan to pay for the Mars program is particularly outlandish. They want to fly commercial passengers intercontinentally: New York to Shangai in 30 minutes, for example.

Skeptical of this zany idea's cost effectiveness, I ran the numbers to determine cost per passenger. Surprisingly, the best-case result isn't too bad: propellant would cost about $1,000 per passenger. Including all of the other costs, rocket tickets from NYC to Shanghai might be priced around $10,000 – the same price as a first-class plane fare.

Caveats

1. I am not an engineer or a scientist; you are welcome to check my work.
2. Although I compute costs by assuming the worst case, my assumptions about CO2 impact are best-case due to my inadequate chemistry skills.
3. A single stage launch might be impractical; two stages might be more efficient, and a keralox first stage might be more affordable (though significantly less eco-friendly).

Assumptions

• Single-stage launch using only methalox engines.
• The BFR ship has a dry mass of 85 t. For Earth-to-Earth missions it would be equipped with 12 Falcon sea-level engines each providing 1,700 kN thrust with an Isp of 330. All burns are performed at sea level.
• A 100km high ballistic trajectory requires 6,000 m/s² delta v to ascend and 1,200 m/s² for braking.
• Methane can be purchased for $4 / 1,000 ft³ and O2 for $0.25 / kg.
• All methane is completely combusted, producing only CO2 and H2O in the exhaust stream.

Cost

A 245-passenger payload would expend 75% BFR's 1,500 t propellant capacity, costing $1,200 per passenger.

Environmental Impact

A one-way trip would have a carbon footprint of 640 t, or 2.7 t per passenger: slightly less than a business-class airplane ticket.

Conclusion

Earth-to-Earth rocket travel seems feasible, although SpaceX faces numerous regulatory, logistic and public-trust challenges. It is likely to be very expensive at first, a luxury for the super rich that drives the final nail into the coffin of first-class air travel – a market segment that, as a share of overall airline revenue, has been dwindling in importance for several decades.

I'm not sure that it's worth SpaceX's time to capture a mere 10% of air travel dollars; to truly line their coffers, they will need to improve engine efficiency and control costs enough to capture business-class (~30% of airline revenue) or even economy (60%) passenger dollars. Earth-to-earth rocket travel won't get SpaceX to Mars, but if they hone their technology through dozens of traditional low-earth orbit missions, ballistic rocket travel might eventually pay for SpaceX to stay on Mars.

If we scale up the rockets to carry 750 passengers, the environmental economics become superb compared to plane travel: 1.2 t carbon per passenger, compared to 2.2 t for a jet flight. To my mind, this is the most surprising part of the SpaceX proposal: once we scale it up, rocket travel could be 50% greener than jet travel.