Starship lift power to moon

Starship is one of the candidates in the Artemis program. I have heard it would require additional refueling before it gets to the Moon.

It is a bit surprising since Beresheet got to the Moon with Falcon 9, which is capable of carrying 10 times less payload to LEO.

I guess it is because of the fuel requirements for the way back. I wonder up to where can it reach without refueling, following the landing on the Moon (how close to Earth). Would it be possible to get to a gateway around the Moon?

Also, does all the candidates rely on refueling?

• @fasterthanlight Sorry it is "Beresheet" on the Wiki. – peterh - Reinstate Monica Jun 3 '20 at 20:07

It's pretty simple: Beresheet has a dry mass of 150 kg. Starship has a dry mass of 120 t. So even though Super Heavy is 10 times as powerful as Falcon 9, that's nowhere near enough to make both situations similar – even without needing also fuel for the return.

• With refueling, how much tons could it bring to the surface? – user2679290 Jun 1 '20 at 8:45
• I don't know; I think you could well ask this as a separate question. – leftaroundabout Jun 1 '20 at 8:47
• I thought why not replacing the second stage with something lighter. Lets say 10 tons of gross weight and 5 fuel. Probably be enough just to land. – user2679290 Jun 1 '20 at 8:50
• @user2679290 "Starship" is the second stage. You could, with a lot of work, use the Superheavy 1st stage booster to launch a different upper stage, or even just take a fueled upper stage up in. a cargo starship, but is SpaceX can make the refueling work (a) it shouldn't be very expensive and (b) it's a step towards their Mars plans. – Steve Linton Jun 1 '20 at 10:09
• @user2679290 well SpaceX hasn't been very, let's say, rigorous with its terminology... Big F... Rocket and so on. At the moment, “Starship” can apparently refer both to the 2nd stage alone, and to the combination of 2nd-stg-Starship on top of the Super Heavy booster, i.e. the entire launch system. That's what we're taking about when comparing LEO lift capabilities. — Also, generally, stage identifiers are not, like, mathematically well-defined quantities. In some cases it's clear-cut (Saturn V, Falcon 9), but as soon as any sort of side boosters enter the picture it becomes murky. – leftaroundabout Jun 1 '20 at 20:43

The relevant quantity here is delta-V. Starship, when fueled in orbit will have about 6500 m/s of Delta-V budget available with 100 tons of cargo. It takes pretty much that whole budget to land the cargo on the moon (about 5500). Unloaded, it's weight is reduced by a third, which isn't a whole lot, so the remaining fuel is nowhere near enough to bring Starship back to earth orbit. So you'd need to de-rate Starship for these missions. By how much depends on the question whether you want to bother with refueling a second time in earth orbit, just for the Earth landing phase.

This makes sense, of course. Starship's design is for Mars surface refueling, and the delta-V to Mars surface is approximately the 6500 m/s that Starship is designed for. The way back is somewhat cheaper as Starship can aerobrake on the return mission to Earth surface, but you still need some fuel for a soft landing.

As @MSalters says the key measure is delta-V, the total amount by which the spaceship can change the velocity of its payload.

Starting from the ground you need about 10 km/s to reach a stable orbit. From there you need about 5.5 km/s to land softly on the Moon and about another 2.5 km/s to get from the Moon's surface back to Earth where you can use the atmosphere to slow down.

How much delta-V a rocket gives you depends on the fuel used and the engine efficiency, which together give a number called the specific impulse $$I_{sp}$$ and the mass ratio, the ratio of the dry mass (engines, empty tanks, cargo, crew, etc.) to the fuelled mass (all the above plus fuel and oxidiser).

The Starship concept comes with a first stage booster called Superheavy, which has not yet been built. Current estimates (from wikipedia) put its dry mass at 230 tons and its wet mass at 3530 tons for a mass ratio of about 14.7. The $$I_{sp}$$ of the Raptor engine is about 330s.

So if you had no upper stage at all, you can calculate the delta-V of Superheavy as about 8.8 km/s. Not quite enough to reach orbit, although it's close. So no matter how small you make the second stage it's not going to be able to launch it to the Moon. The reason is that you are lifting the huge superheavy tanks and engines to orbit, which is wasteful.

If you add an upper stage, you get less delta-V from Superheavy, because you have increased the dry mass, but you get to add the delta-V from the upper stage. So Starship has a wet mass of about 1320 tons and a dry mass (no cargo or crew) of about 120 tons for a Mass ratio of 11 (less than SuperHeavy because it needs a crew cabin and stuff and because bigger tanks naturally have less surface area compared to their volume). The $$I_{sp}$$ is a bit higher because the engines work better in vacuum, so you get about 8.8 km/s of delta-V from Starship (with no cargo).

If you put a fuelled starship on a superheavy, the "dry" mass (when the Superheavy is out of fuel) is now about 1550 tons, and the fuelled mass about 4650 for a mass ratio of 3, and we get about 3.5 km/s of delta-V from Superheavy, so ignoring many details, we make orbit with a fuel reserve enough for about 2.3 km/s. Not quite enough to get to the Moon, let alone land.

We could try different upper stages. The Centaur, for example, has a wet mass of about 23 tons (there are multiple variants) and a dry mass of 2.2 tons, with an $$I_{sp}$$ of 453s (using liquid hydrogen fuel). This gives a delta-V of just over 10 km/s with no payload. With only this payload superheavy gets about 8.5 km/s. So this configuration has, in principle, enough delta-V to get to the Moon' surface and back, probably with enough left over for a few hundred kg of payload.

This is, however, a fantasy experiment, for a whole bunch of reasons. First of all, the centaur upper stage fuel won't remain liquid for long enough to get to the moon and back. Adding active cooling would add a lot of mass. Secondly landing on the Moon would need legs and other added mass. Thirdly the upper stage could be quite a lot bigger and still not reduce the delta-V of Superheavy that much.

At the end of the day, though, the question is "why?". If spaceX can make refueling work it will be a cheap and effective solution to the problem. If not, the obvious way to the Moon is more stages (Apollo style).