My thinking is that
* Starship is going to spend around 10days flying to the moon and then on its surface. Absent dedicated cooling system all its liquid oxygen should boil off.
* In the absence of ground infrastructure on the moon, Starship would have to rely on the thrusters for both landing and launch.
* I recall that Starship would be using hot thrusters, and think that using the boiled off propellent can be used to fuel the thrusters. If after reaching the moon you have no use for the regular engines and huge proponent tanks, why not dual use them for this purpose
To quote (from memory) the book
Ignition!: "Space is a pretty good insulator, and when you have, in effect, a Dewar flask the size of the universe, you can store a low-boiling liquid a very long time". Yeah, they'll be able to keep more than enough LOX around for the purpose. Apollo was able to store liquid HYDROGEN of all things for the entire duration of every mission so storing the much-easier-to-store liquid methane/LOX shouldn't be an issue.
There are two kinds of gaseous propellant in a rocket: the kind you might want and the kind you don't. The kind you might want is what SpaceX is thinking of doing, pressurizing their tanks with some of the hot exhaust from their gas generators. i.e., a mixture of CO2 and H2O (the end products of the reaction that goes on in their engines) and unburnt methane (in the fuel tank, coming from the fuel preburner) OR excess O2 (in the oxidizer tank, coming from the oxidizer preburner). This is going to be there in Starship but can't be used for fueling the lunar landing thrusters A. because it's gaseous and you DON'T build a system that can only pump a gas when there's a liquid in the tank and B. because it's partly composed of things that aren't useful propellants anymore.
The kind you DON'T want is "ullage", where fuel or oxidizer evaporates to maintain vapor pressure over the propellant; for LOX boiling at the temperature of "very, very cold" this vapor pressure is fairly high and therefore a lot of the propellant tries to evaporate into the ullage. Methane is a bit better off but still has a high vapor pressure. This is why SpaceX wants to use autogenous pressurization; to keep pressure in their propellant tanks without having it all evaporate and be more difficult to handle.
The "regular engines" are still being used to change orbits, boost Starship into earth orbit after the first stage is exhausted, etc. They're not optional even if they're only necessary for the launch. The fuel tanks are carrying the propellants for every kind of thruster (attitude control, main propulsion, lunar landing) on the Starship, so they're not unnecessary. So Starship uses main propulsion to reach the Moon and then the specialized lunar landing thrusters to make the final descent and touchdown so as not to do exactly what Super Heavy just did to itself. But in all cases these thrusters are fueled by LIQUID propellants because pumps don't like to pump a mixture of gas and liquid propellant and liquids are denser, therefore you use liquid and actively try to avoid the gaseous propellants.
Sorry for the massive post but I like this stuff. And also I'm too tired to trim it down so have fun reading the disorganized thoughts of an exhausted madman
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