It's not particularly hard. Just like with regular rocket upper stages that require multiple burns to complete the mission, you can use small ullage thrusters to settle the propellant and make sure liquid (instead of pressurant gas) is transferred from one tank to another. The physics is exactly the same as making sure the engine receives fuel. Just need the thrusters to be fired longer.

SpaceX has done experiments with how much thrust is necessary for ensuring propellant settling. That's one reason you often see a video feed of inside the upper stage liquid oxygen tank during a Falcon 9 mission. It doesn't take much thrust to ensure propellant settling. Not at all an open question.

This always struck me as one of the least questionable new things in SpaceX's architecture. Much less Kerbal than most Mars architectures which require assembling a massive craft in LEO or whatever.

(One would be remiss to not mention the history of refueling... SpaceX's competitor ULA had been pushing refueling and orbital depots, which it called "distributed launch", since its formation, but has only been able to do small experiments since one of its parent companies, Boeing, sees orbital refueling as a threat to NASA's SLS rocket, which Boeing is the main contractor for. That's a huge reason for a lot of the "skepticism" about orbital refueling you sometimes see in aerospace circles, besides the usual pathologically conservative mindset of many grey beards...)

Out of curiosity, which of the engineering problems posed by the Starship/Superheavy system are the biggest potential showstoppers? My instinct is the belly flop/heat shield required to make Starship reusable, but I know nothing about rocketry.

Yes but ullage thrusters would have to fire continuousky for the duration of the transfer. That is a significant burn time. If they are going to be draining the fuel using only the ullage thrust, it will take more than a slight nudge.

They would be using a pressure differential to transfer the fuel, not relying on just ullage thrust.

You'd be surprised at how low of an acceleration is required for propellant settling and transfer. On the order of 0.0001-0.01m/s^2. At a 310s Isp for the ullage thruster, that's between 0.01kg and 1kg of propellant usage per second. Even if it takes an hour to transfer fuel (on the ground, fuel is transfered in about 20 minutes and in flight, all the propellant is transfered from the tanks to the engines in ~8 minutes), we're only talking about maybe 1% of the propellant needing to be used for ullage thrust and perhaps as low as 0.01%.

ULA has published a paper on the topic: https://www.ulalaunch.com/docs/default-source/extended-durat...

They would build a dedicated cargo section and fairing for this, all of that would be fairly straightforward to accommodate. I don’t know if SpaceX has acknowledged the idea but there was discussion of installing ’retro-rockets’ up in the fairing for the moon lander (to reduce exhaust blast on the regolith), could use the exact same technology.

If they were so inclined they cold even recover the helium from the tanks they are filling and use that to assist with pumping pressure.

Wouldn't the thrust just be to settle the fuel so pumps could move it over?

Usually when you ignite an engine on orbit a short kick of ullage trusters is enough. It is because once the fuel settled enough to start the engine the trust of the engine will keep the fuel settled. This is not true in the fuel transfer situation, there a single kick is not enough. If you are using ullage motors and not internal bladders, you have to keep producing the micro-trust for the whole transfer duration. Be mindfull that pumping a rocket-full of fuel won’t be an instantenous process.

You need acceleration to settle the fuel and to keep it there. Once the acceleration stops, the fuel begins to unsettle.

At the last presentation on Starship, Elon said they planned to do the refueling by applying a small amount of thrust during the procedure, giving a small g-force that's enough to drive the fuel from one ship to the other.

SpaceX did at one point describe using RCS to accelerate the paired vessels to facilitate fuel transfer [slide][video].

[slide] https://spaceflight101.com/spx/wp-content/uploads/sites/113/... [video] https://youtu.be/tdUX3ypDVwI?t=1411

Some rockets have already used small acceleration prior to engine ignition to settle the propellant in zero gravity situations: https://en.wikipedia.org/wiki/Ullage_motor

Transfer tanks, not fuel. In-orbit servicing using robots, please. or just dock the tanks as vehicles.

Sounds like a good idea. The problem is that for weight efficiency reasons in modern rockets the tank is the rocket. (So much so that they often crumble if you are not providing sufficient internal pressure.)

I'd accept a future in which weight efficiency is slightly reduced to enable in-orbit refueling with standardized tank delivery. As others have noted, it seems extremely challenging without it.