The energetic cost of removing a kilogram of stuff from some body is proportional to the mass of that body, and inversely proportional to its radius:

For the moon, this is about 2.8 MJ /kg; for Earth, 63 MJ / kg. That makes escaping the moon over twenty times cheaper, energetically, than escaping the Earth entirely^{1} - is there then a business case for exporting lunar commodities like water, oxygen, rock, or metal elsewhere in space?

No - at least, not until there is *already* civilization on the lunar surface. What the Earth lacks in gravitational lassitude, it more than makes up for in human population, engineering knowledge, and industrial infrastructure. This is a point Casey Handmer has made well already - this page is just a prettification of the notes I used to prove it for myself. I'll compare the cost of shipping stuff to GEO, the highest populated Earth orbit, from Earth and from the Moon.

- The change in velocity, Δv, required to for a spacecraft to reach its destination.
- The propellant mass required to provide that Δv.

As for the propellant mass - with a piece of paper, a pen,
and the conservation of momentum, you can convince yourself that the change in velocity for a nonrelativistic rocket moving freely in vacuum, ejecting
propellant with a relative speed *c*, is

where m_{i} is its total initial mass and m_{f} its final mass. In terms of the dry vehicle mass
m_{v}, the payload mass m_{p}, the propellant mass burned m_{prop}, and the residual propellant mass
m_{prop,res} afterwards, that's

With no residual propellant, the mass breakdown of the vehicle before / after the burn looks like this:

This lets us compute the payload we can carry if we fill the rocket's tanks to the brim:

We'll also want to consider round trip deliveries, where the payload is the only thing that gets left at the destination:

The outbound and inbound velocities Δv_{1} and Δv_{2} will differ if the start and stop states differ, or if the spacecraft passes through an atmosphere. Applying the one-way equation from above twice, you'll find that the payload capacity with a total prop mass m_{prop} is

Note how you have to pay for the vehicle going both ways!

- Vehicle mass: 120 tons
- Propellant mass: 1200 tons
- Super Heavy booster propellant mass: 3400 tons
- Vacuum specific impulse for the engines: 380s
- Payload capacity to LEO, reusable, using booster: 150 tons

I'll assume a $10M marginal cost per starship launch, which is a number Elon has thrown out that doesn't seem crazy. That corresponds to $67 / kg from Earth surface to LEO. Since we need cost estimates for flights that are not just between Earth surface and LEO, I'm going to make the simplifying assumption that cost of any Starship flight is proportional to the propellant consumed. Since the $10M flight burns 4600 tons of propellant, that means assigning a cost of about $2200 per ton of propellant used. In reality there will be operational costs that don't scale this way, but since almost all of the Starships involved in the operations described below fly with full tanks, it's not a huge source of error.

I'll also assume that lots of Starships and corresponding boosters are available, and that in-orbit refueling of Starships can be done reliably.^{2} That means that a Starship which expends its tanks reaching LEO from Earth surface can be refilled by 1200 / 150 = 8 starship tanker flights which carry up propellant for it. We need this capability to perform high Δv deliveries without using another spacecraft.

Since going from Earth surface to LEO costs a huge 9 km/s^{3}, we need refueling in LEO to do anything useful. For a LEO -> GEO -> Earth surface trip, the outbound and return Δv requirements are Δv_{1} = 3.9 km/s and Δv_{2} = 1.47km/s, where the savings in the return comes from braking in the Earth's atmosphere. Using the Starship numbers from above, this works out to a 437 ton payload capacity to GEO.
So here's how we can do GEO deliveries:

- Launch three starships carrying a total of 437 tons to LEO, and transfer the payloads to one vehicle.
- Launch eight tankers to fuel it
- Burn to enter geostationary transfer orbit (GTO), then again to enter GEO, drop off the payload, and re-enter GTO
- Aerobrake into the Earth's atmosphere

- Starship
- A different rocket

The Δv cost from LTO to GEO is only 2.15km/s, which means the vehicle can carry an impressive 1200 payload tons. The methane propellant, 300 tons, will have to be flown from Earth at $180k/ton. The oxidizer can have a much lower marginal cost if produced locally and brought to LTO - the question of *how* much lower is not important for the conclusion here, so I'll be generous and say it's free.

As for the other leg of the trip - we want to take off with a full tank of methane from the lunar surface. We'll fly a Starship down to the surface with 300 tons of methane, which requires burning about 100 tons of methane. We can then take off with a full payload, about 1100 tons, again using *free* lunar oxidizer. That makes about 400 tons of methane total for this leg.

So in this (crude) model, the marginal cost is set just by the methane used, which comes out to roughly **$110k / ton** payload in total, $150k/ton cheaper than direct Earth delivery!

However, we have to pay for the machinery used to produce thousands of tons of lunar liquid oxygen. If it costs, say, $1B all-in to set up and working, and it lasts for ten years, then we need to be shipping ($1B / 10 yr) / ($150k / ton) = 667 ton / year of payload from the lunar surface to break even.^{5} For comparison, a twice-a-week launch cadence for Falcon 9 carrying Starlink is about 1500 tons / year.

In short, yes, lunar deliveries are *theoretically* cost competitive, if:

- Somebody needs thousands tons of rock or water in a high orbit
- You can compete with SpaceX's current launch cadence in a very expensive wilderness
- You're willing to wait for the better part of a decade before breaking even, while selling a commodity.

To be clear, this is not any kind of chicken-and-egg problem. Putting people on the moon is a plain good idea (and with Starship, unintuitively cheap), and we should just do that first, right away. You can do all kinds of great things there, like:

- Racing cars and jumping them over craters
- Admiring the Earth from 1/6 g swimming pools
- Working remote, at high latency and low productivity, for Google
- Building massive telescopes
- Building a copy of the Library of Congress
- Building military bases for national prestige (and fun)
- Playing golf
- Sneaking into prestigious military bases to play golf
- Etc, etc