Lunar Starship and unnecessary operational complexity

By cjhandmer

This blog addresses the question of how SpaceX’s Starship could be used to ferry people and cargo to and from the Moon under a variety of different situations. It follows on from previous posts on Starship and Artemis, and Starship as a mechanism for space transport post scarcity. Broadly speaking, by the end of this post the reader should have a good idea of the variables and cost/benefit for various Starship-enabled transport systems.

It’s worth stating at the outset that Starship is in a league of its own in the current field of lunar landers. Within the HLS program, the NASA spec called for a capacity of at least 9 T, ideally 12 T, to the Lunar surface. Starship in its most basic configuration can do more than 200 T. One of these is not like the others.

The real strength of Starship is not in its transformationally large cargo capacity, but in its low cost of operations. Why fly 200 T once when we could fly it a few dozen times for less than the cost of the next cheapest vehicle?

Starship has enormous cargo capacity but by refilling fuel and oxidizer at intermediate locations, it’s possible to waste less fuel carrying fuel. This is the staging principle. So at the cost of the increased complexity of choreographing deep space fuel transfers, more cargo per given unit of fuel can be transported. Is this worthwhile? Let’s use math to find out.

My analysis uses numbers consistent with the Wikipedia article for March 2021: 240 T methane capacity, 960 T oxygen capacity, 120 T dry mass, 100 T LEO cargo capacity, 380 s vacuum ISP, 12000 kN thrust, 1100 m^3 cargo volume. Where variations in these numbers provides additional insight, I will adjust these parameters. Δv is derived from the vis-viva equation.

Summary

In this post I analyse four different mission profiles:

  • Flight of constant payload (such as a pressurized and occupied crew compartment) from LEO to the Lunar surface and back to LEO
  • Flight of cargo to the Lunar surface, with Starship returning empty to LEO
  • Flight of empty Starship to the Lunar surface, returning to LEO with as much cargo (i.e. rocks) as possible
  • Flight of cargo to the Lunar surface with an expended Starship

Against these four profiles, I analyse five progressively more involved fuel/oxidizer refilling schemes:

  • Refilling by tanker in Low Earth Orbit (LEO)
  • Refilling by tanker in LEO and Geostationary Transfer Orbit (GTO)
  • Refilling by tanker in LEO, GTO, and Low Lunar Orbit (LLO)
  • Fuel transport between LEO, GTO, and LLO by Solar Electric Propulsion (SEP)
  • Use of Lunar ISRU oxygen to refuel 80% (by weight) of Starship’s fuel/oxygen mix on the Moon

Against these 19 scenarios, I calculate the cargo mass transported by a single Starship, the number of supporting launches needed, and the mass/launch ratio as a figure of merit. The results are summarized in the table below.

RefillingCrew returnCargo to MoonCargo from MoonCargo to Moon expendable
LEO25, 13, 1.957.5, 13, 4.443.5, 11, 3.35216, 13, 16.5
GTO200, 31, 6.5539, 38,14.2326, 27, 12.1753, 41, 18.4
LLO670, 69, 9.71733, 96, 18.11092, 51, 21.41924, 101, 19.04
SEP670, 33, 20.31733, 59, 29.41092, 17, 64.21924, 62, 31.0 fast cargo
1924, 32, 60.1 slow cargo
ISRU1742, 63, 27.62263, 72, 31.42299, 11.5, 200NA
Payload (T), launches, payload (T)/launches

As a figure of merit, mass/launches can lead mission designers astray. For example, even though the huge SEP infrastructure concept roughly doubles the mass/launch of the expendable cargo Starship, the ratio does not capture the relative costs of maintaining this infrastructure, or of building a new Starship. In particular, thanks to heroic efforts by the crew at Boca Chica, both Starships and launches will be the cheapest part of the whole mission.

Instead, I need note only that 200 T of cargo will more than fill the Starship cargo bay, so any more is surplus to requirements, unless the cargo bay is literally filled with half an Olympic pool and some whales.

LEO refilling is more than adequate for expendable cargo launches and reusable crewed sorties. To put this into perspective, while Shuttle could lift 25 T to LEO, Starship can lift 25 T from LEO to the Lunar surface, and back to LEO, all without refueling. If capacity to fly 300 astronauts on a single flight is required, modest refilling in a sub-GTO orbit will suffice.

Simplest case, LEO refilling

Simplest Starship Lunar mission

In this version, a Starship flies to LEO, where it is quickly refilled by 12 fully reusable tanker flights for a total of 13 launches. It then flies to the Moon, lands, does whatever it has to do, then flies back to Earth where it lands back near the launch pad. While the alternative bids for the Artemis HLS require three stages just to get from Gateway to the surface and back, Starship is actually just capable of flying from LEO to the Lunar surface and all the way back to Earth.

The required Δv is 2.44 (GTO) + 0.68 (TLI) + 0.82 (LLO) + 1.72 (Lunar surface) + 1.72 (LLO) + 0.82 (TEI) + 0.1 (landing on Earth) = 8.3 km/s.

On this flight, Starship can support a payload of 25 T, or 1.9 T/launch. This includes life support, space suits, people, food, rovers, etc. Whatever mass is expended on the Moon (ie rovers) can be replaced with rocks on the flight back. To put this into perspective, the Shuttle could carry 25 T to LEO. Starship can carry it to the Moon, and back.

If only cargo delivery is required one way, Starship can deliver 57.5 T of cargo while reserving only 124 T of fuel for the flight back, or 4.4 T/launch.

If cargo is only to be transported from the Moon (such as an enormous haul of Moon rocks), then a Starship launched empty can transport 43.5 T back to Earth and requires only 11 tanker flights as the Lunar Starship, launched empty, can retain a tanker load fuel. This works out to 3.35 T/launch.

If Starship is to remain on the Moon as a habitation module, it can deliver 216 T of additional cargo, plus whatever mass can be salvaged by omitting aerodynamic flaps it will not need, or 14.2 T/launch. This is nearly 4 times as much with a reused Starship, so we can place a constraint on costs of reflight vs new build.

Let’s say a Starship costs $5m to build and $5m to launch, then the marginal cost of delivering 216 T to the Moon is $70m, including the tanker flights, or $324k/T. The marginal cost of delivering 57.5 T with reuse is $65m for flights alone, no new Starship included, or $1.13m/T. This strongly favors littering the Moon with Starships. Indeed, this holds unless the cost of construction is more like $180m per Starship, which seems very high.

Of course, Starship needs to retain a return capability to bring people and rocks back to the Earth, but there seems to be limited utility in returning Starships for any other reason.

Let’s refill in LEO and Geostationary Transfer Orbit (GTO)

Top up fuel in GTO or similar high energy orbit

Can we exploit the staging principle to increase cargo capacity per launch? The next most obvious step is to refill Starship in GTO, as well as LEO.

A fully fueled Starship in GTO needs Δv = 0.68 (TLI) + 0.82 (LLO) + 1.72 (Lunar surface) + 1.72 (LLO) + 0.82 (TEI) + 0.1 (landing on Earth) = 5.86 km/s.

Two way cargo transport can carry 194 T, with the caveat that landing 194 T of cargo back on Earth is somewhat beyond the core requirements of Starship. In this case, a Lunar Starship would aerobrake into LEO and be refilled there for another flight. Removing the Earth landing Δv bumps total payload up to 204.7 T. Lunar Starship’s cargo could be returned to Earth using some of the Starships that are bringing up more fuel.

One way cargo flight with returned Starship is 539 T, one way cargo return is 326 T (to LEO), while a Starship sent one way to the Moon could carry 753 T from GTO to the Lunar surface. Due to low lunar gravity, Starship has adequate thrust to land even these rather heavy payloads on the Moon.

There are other constraints, however. The total payload volume of Starship is “only” 1100 m^3. For a 750 T payload we’re approaching the density of water. Which, incidentally, is why mining lunar water is not that exciting.

Further, we have to consider how to get these payloads to GTO in the first place.

The 200 T return payload could be launched with two Starships. 12 more launches refill the Starship. After flying to GTO, it has 470 T of its original 1200 T fuel load remaining, so needs 730 T of fuel. A fully loaded Starship tanker would arrive at GTO from LEO with 566 T of fuel remaining, while one with 814 T of fuel in LEO would arrive with 365 T in GTO, so only two such tankers would be needed. Together they would require 17 Starship launches. In total, 31 Starship launches are required to transport 200 T to the Moon and back, or 6.5 T/launch, compared to just 1.9 T/launch for LEO refilling only.

Similar calculations show that a 539 T payload with empty Starship returned requires 6 cargo launches, 12 tanker launches to refill the Lunar starship, and 20 tanker launches to fly two tankers to GTO, for a total of 38 launches. This works out to be 14.2 T/launch, compared to 4.4 T/launch for LEO refilling only.

The 326 T Moon rocks payload would arrive empty at GTO needing 634 T of fuel, or 15 tankers, for a total of 27 launches. This works out to be 12.1 T/launch, compared to 3.35 T/launch with LEO refilling only.

Finally, the 753 T payload with a one way flight of Starship. 8 cargo flights, 12 tanker flights to get Starship to GTO, and 21 tanker flights to get two nearly full tankers to GTO, for a total of 41 Starship flights. This works out to 18.4 T/launch, compared to 14.2 T/launch for GTO refilling of a reused Starship, and 16.5 T/launch for LEO refilling of a disposable Starship. Interestingly, in the case of disposal it seems that there’s limited overall benefit to refilling in GTO and this makes sense given the relative Δv capacity of Starship and the relatively tiny hop from GTO to the lunar surface.

In this discussion, I have mostly conflated the return of payloads greater than 100 T to LEO of the Earth’s surface. Starship is not designed to return more than 100 T aerodynamically, but as we will see there is never a shortage of downmass available from tankers returning empty back to Earth.

Refilling in LEO, GTO, and Low Lunar Orbit (LLO)

The idea here is that there’s not much point in flying a bunch of fuel from LLO down to the lunar surface, only to fly it back up a week or so later when it’s time to come home. At this point doing calculations on a mission by mission basis becomes a bit cumbersome, so instead I’m going to refer to “gear ratios”, which encapsulate how much fuel is needed to transport other fuel around.

For example, a fully fueled tanker in LEO will arrive in GTO with 565.5 T of fuel remaining, a ratio of 0.47. A fully fueled tanker in GTO will arrive in LLO with 762.4 T of fuel, a ratio of 0.64. Combining these two ratios, a tonne of fuel in LLO costs 3.34 T in LEO. In fact, we could split the Δv between LEO and LLO more cleanly with two sequential 1.97 km/s hops, each of which has a ratio of 0.55, reducing the fuel required in LEO to just 3.329 T, a whopping improvement of 0.34%!!

With LLO refilling, the longest unsupported Δv hop is from LLO to the lunar surface and back, requiring 1.72 km/s each way.

A fully fueled Starship in LLO can carry 670 T from LLO to the Moon and back to LLO, 1733 T to the Moon with Starship return, 1092 T from the Moon to LEO, and 1924 T with the Starship left on the surface.

670 T of cargo requires 7 launches, while refilling requires 12 launches. In GTO, 957 T of additional fuel requires 21 tanker launches to LEO, while in LLO 660 T of additional fuel requires 1400 T in GTO or 2204 T in LEO, for 22 additional tanker launches. Once back in LLO, 195 T of fuel are required to return to the Earth’s sphere of influence, necessitating 7 tanker launches via GTO. In total, 69 launches are required, or 9.7 T/launch, compared to 6.5 T/launch with GTO refilling and just 1.9 T/launch with no refilling.

1733 T of cargo one way requires 18 cargo launches, 24 refill launches in LEO. The cargo has to be split until GTO, with one Starship (carrying 1177 T) arriving empty, transferring the cargo and returning to LEO, and the other (carrying 556 T) arriving with 298 T of fuel remaining. 19 tanker launches refills it, where it flies to LLO with 188 T of fuel remaining. 34 more tankers and it can drop the cargo on the Moon before returning to LLO, where it needs just 29.6 T of fuel to return to LEO, or one additional tanker. In total, 96 flights or 18.1 T/launch, compared to 14.2 T/launch (with GTO refilling) and 4.4 T/launch without GTO refilling.

1092 T of Moon rocks requires 11 tanker launches (it goes up empty and can save a tanker load of fuel) in LEO, 15 tankers-worth in GTO, 15 tankers-worth in LLO, and and 10 more after returning to LLO laden with rocks, for a total of 51 flights, or 21.4 T/launch, compared to 12.1 T/launch with GTO refilling and 3.35 T/launch with LEO refilling only.

Finally, in the expended Starship case, 1924 T of cargo requires 20 cargo launches, 24 refill launches in LEO. Two cargo Starships reach GTO, one of which has 206 T of fuel remaining, requiring 21 additional tanker launches to refill. It arrives in LLO with 124 T of fuel, requiring 1076 T to fill up, or 36 additional tanker launches. In total, 101 launches or 19.04 T/launch, compared to 18.4 T/launch for GTO refilling and 16.5 T/launch for LEO refilling of an expendable Starship.

Once again, the overall improvements are very marginal although it is worth noting that with GTO and LLO refilling, the mass/launch of a fully reused Starship finally exceeds that of an LEO-refilled expendable one. Whether that is worth the huge increase in complexity is left to the judgment of the reader.

Fuel transport by Solar Electric Propulsion (SEP)

This modality is basically identical to the one above, except that fuel is transported from LEO to GTO and LLO with solar electric propulsion (SEP). This takes a long time but uses very little fuel, so if there’s a constant and predictable demand for fuel at GTO and LLO (complexities of orbital phasing aside) then the respecting gearing ratios for these intermediate stops can be improved to near 1. Unlike previous steps, here there is an incentive to use only what fuel is needed to get to the next fuel depot, which also slightly reduces fuel needs.

670 T of cargo requires 7 launches, while refilling requires 8 launches for the 731 T of fuel to get to GTO. In GTO, 392 T of additional fuel requires 4 tanker launches to LEO, while in LLO 1200 T of additional fuel requires 12 additional tanker launches. Once back in LLO, 195 T of fuel are required to return to the Earth’s sphere of influence, necessitating 2 tanker launches via GTO with SEP. In total, 33 launches are required, or 20.3 T/launch, compared to 9.7 T/launch with GTO and LLO refilling, 6.5 T/launch with GTO refilling and just 1.9 T/launch with only LLO refilling.

1733 T of cargo one way requires 18 cargo launches, and 19 refill launches in LEO. The cargo has to be split until GTO, with one Starship transferring the cargo and returning to LEO, and the other continuing on. 9 tanker launches refill it, whereupon it flies to LLO. 12 more tankers and it can drop the cargo on the Moon before returning to LLO, where it needs just 29.6 T of fuel to return to LEO, or one additional tanker. In total, 59 flights or 29.4 T/launch, compared to 18.1 T/launch (GTO and LLO refilling), compared to 14.2 T/launch (with GTO refilling) and 4.4 T/launch without GTO refilling.

1092 T of Moon rocks launches empty all the way to GTO, where it needs just one tanker load to reach LLO. In LLO it takes on 12 tankers worth, flies to the surface, picks up rocks, and flies back to LLO. In LLO it takes on 299 T of fuel (3 tankers) to return to LEO, for a total of 17 flights, or 64.2 T/launch, compared to 21.4 T/launch with GTO and LLO refilling, 12.1 T/launch with GTO refilling and 3.35 T/launch with LEO refilling only.

Finally, in the expended Starship case, 1924 T of cargo requires 20 cargo launches, 20 refill launches in LEO. Two cargo Starships reach GTO and transfer cargo, with the empty one returning to Earth. The other requires 10 more tankers. It arrives in LLO and needs 12 additional tanker launches. In total, 62 launches or 31.0 T/launch, compared to 19.04 T/launch (GTO and LLO refilling), 18.4 T/launch for GTO refilling and 16.5 T/launch for LEO refilling of a disposable Starship.

Of course, cargo is not always time sensitive, in which case 1924 T of cargo could be delivered expendably to the Moon with 20 cargo launches, 12 refilling launches, followed by a long SEP transit to LLO, upon which chemical propulsion performs the final landing. This requires just 32 launches, or 60.1 T/launch, which compares favorably to Starship’s LEO capacity of 100 T/launch and also does not require any GTO or LLO refilling.

Using Lunar oxygen for ISRU

At some point in the distant future it may be possible and even cost effective to produce thousands of tonnes of liquid oxygen on the Moon from lunar resources, most likely by melting rocks. Given that 80% of Starship’s fuel weight is oxygen, even more cargo capacity can be wrung from the system.

With lunar surface oxygen refilling, a fully fueled Starship in LLO can carry 1742 T of payload to the Moon and back, 2263 T from LLO to the surface, and 2299 T from the surface back to LLO (limiting case is methane tank capacity). Lunar ISRU isn’t relevant for the expendable cargo Starship case unless Lunar oxygen is cheaper to get in LLO than Earth oxygen – a very tough proposition.

All these masses are within Starship’s thrust capability on the Moon, but really stretch the limits of its 1100 m^3 fairing volume. It is hard to imagine, but flying 2299 T of Moon rocks would fill the fairing almost 3/4 of the way to the top. Depending on arcane details of ballistic coefficient and heat shield performance, aerobraking at LEO could also be much more difficult. The reader should understand that, like all approximations, these calculations are being taken to a point well beyond the realm of the sensible!

1742 T of return payload requires 18 cargo flights, 19 refill launches in LEO, 9 tankers in GTO, and 12 in LLO. Once returned to LLO, the Starship requires a further 5 tankers, for a total of 63 flights. This works out to be 27.6 T/launch, compared to 20.3 T/launch with SEP, 9.7 T/launch with GTO and LLO refilling, 6.5 T/launch with GTO refilling and just 1.9 T/launch with only LLO refilling.

2263 T of Lunar-destined cargo requires 23 cargo flights to LEO, 24 refill tankers in LEO, 12 in GTO, 12 in LLO, and 1 more on the way back, for a total of 72 launches. This works out to be 31.4 T/launch, compared to 29.4 T/launch, 18.1 T/launch (GTO and LLO refilling), 14.2 T/launch (GTO refilling) and 4.4 T/launch without GTO refilling.

2299 T of Moon rocks flown back requires 1 tanker at GTO, 4.5 tankers in LLO (2.5 of methane, 2 of the usual mix), and 6 more on the return trip, for a total of 11.5 launches. This works out to be 200 T/launch, compared to 64.2 T/launch with SEP, 21.4 T/launch with GTO and LLO refilling, 12.1 T/launch with GTO refilling and 3.35 T/launch with LEO refilling only.

Ironically ISRU is only really compelling in the case of needing to bring large quantities of lunar stuff back to Earth. If, for example, a very rare metal oxide was discovered on the Moon, refining the ore would automatically generate more than enough oxygen to fly the rest back to Earth. For a flight cost of $10m, transport costs from the Moon work out to be $50,000/T.

This is vaguely in the same range as things like Neodymium, Praseodymium, and other metals where 2299 T of refined ore would drastically change the shape of the market. Remember that in order to make money, processing AND transport from the Moon needs to be cheaper than the same on Earth – a tall order given that as far as anyone knows, the Earth has both far better ores and an abundance of breathable air.

On the other hand, 2299 T of Moon rocks is enough to give 150 g to every middle school child in the US – a bigger chunk than the piece President Biden has in the Oval Office. And at 0.016% of the annual education budget, it’s a bargain!

Some heuristics

While it is fun to imagine a fleet of solar electric propulsion fuel tugs operating between enormous fuel depots in LEO, GTO, and LLO, the numbers are quite clear. For cargo transport to the Moon, it is more cost effective to expend the transporting Starship on the Moon, or better yet use it as part of a Moon base. With 2200 cubic meters of pressurizable volume, each is about 4 times the size of the entire ISS.

For crew transport to and from the Moon, expansion of the payload beyond the 25 T enabled by LLO refilling requires either steady improvements in mass fraction, ISP, or refilling in a higher energy orbit between LEO and GTO. Under sensible assumptions about payload mass (< 200 T), there is no marginal benefit to doing refueling in LLO, using SEP into cis-Lunar space, or surface ISRU. While it is true that SEP can increase total cargo mass per launch for things that aren’t time sensitive, it’s worth questioning what program constraints would make that worthwhile.

In particular, the cargo itself is value dense and cost of goods in transit is almost certainly higher than the marginal cost of more launches from Earth. If there is launch site congestion, build more launch pads. If there is a shortage of Starships, build another tent factory on a sand bar in Boca Chica. The whole point of Starship, illustrated by the calculations that underpin this blog, is that launch mass is no longer a constraint.

So what might a 2024 Artemis mission with Starship look like?

A single Starship flight to the Moon can transport 25 T of mission-related cargo there and back, which is more than enough to support a crew of 10 for weeks, and give them a Moon rover each. Add to this the beginnings of an enormous lunar space station built inside an expendable Starship-based lander and not only is the Artemis program affordable, it’s also achieving something like an exciting science-fiction based vision for what a Moon base should look and feel like.

Artemis base building for cheap, no nonsense.

No NRHO phasing requirements, no launch windows, no decades-long roll out of incredibly expensive deep space infrastructure. Just a vehicle built around the given task and committed to achieving it without compromises. A mission architecture capable of deploying a large lunar base for a cost comparable to the NSF’s new(ish) South Pole Station. With a budget of $1b/year, NASA could fly this mission (or variations on the theme) every 90 days – a big step change improvement over space access with the ISS.