Manufacturing fuel in orbit requires sending the plant in orbit, extracting the raw materials, packaging them then bringing them up there and also involves sending a ship every time a maintenance is needed, unlike Mars where the raw material (water, CO2) are already nearby. ISRU (in situ resource utilization) is the best way to go, i.e. you bring the plant to Mars but at least you use the local raw materials.

I've heard about approaches for manufacturing fuel on the Moon, but I can't imagine how you might manufacture it in earth's orbit. What are the leading ideas around this approach?

edit: i know we can launch more fuel into orbit, and I really emphasize the "manufacturing" in orbit part.

The main problem would be getting the necessary atoms to your factory. It likely would be easier to construct fuel on earth or on the moon and send it up. (If your rocket exploded the ‘BOOM’ might be a bit louder if its cargo were rocket fuel instead of raw materials for rocket fuel, but the practical difference would be zero)

Your best bet would be to use mass that’s present in space, but unfortunately (1), there isn’t that much in orbit. In theory, one could scope up cosmic dust, tiny meteorites, and old satellites in orbit. It would be a challenge to scale that up, though. https://en.wikipedia.org/wiki/Stardust_(spacecraft) didn’t catch kilograms of stuff, even though it explicitly went for a comet.

Capturing a larger meteorite would work, but larger meteorites are harder to catch.

If you’re extremely ambitious, build a solar powered particle accelerator in space, use it to create electrons, neutrons and protons (https://en.m.wikipedia.org/wiki/Matter_creation), turn those into atoms, and build fuel from those (apart from the practical problem of scaling that up, there are ‘a few’ Ph.D’s to be earned there.)

(1) or fortunately, as having lots of mass there would make space flight dangerous (https://en.wikipedia.org/wiki/Space_debris)

Collect a water-ice asteroid or cometary nucleus or some such, park it in orbit, and electrolyse it.

I'm not aware of a less outlandish plan!

Now, if you want oxidiser, you could skim air off the top of the earth's atmosphere. I have no idea if that has been considered outside of science fiction [1], though.

[1] okay, here they're skimming nitrogen, but: https://en.wikipedia.org/wiki/Fallen_Angels_(science_fiction...

If you were electrolyzing water ice, wouldn't you get both hydrogen (fuel) and oxygen (oxidizer), by definition?

Yes. But if you only wanted oxidiser, you could skip the awkward "capture a cometary nucleus" step by scooping air. Since oxygen is much heavier than hydrogen, this could save you a lot in mass launched from the Earth.

Also if you had enough power (solar or possibly nuclear) you could use the captured gases directly for slightly inefficient propulsion by heating them NERVA style or accelerating them by a modifiedion engine.

I remember some concepts for very low altitude satellites that compensate for drag by running a solar powered ion ramjet. :)

About 80% of the methalox propellant used by the Raptor engine is oxygen. If you manage to scrub oxygen from the very low earth orbit (VLEO), and then bring it to LEO, you are in business. The Japanese Space Agency put a satellite in VLEO in 2019 [1].

[1]https://en.wikipedia.org/wiki/Super_Low_Altitude_Test_Satell...

Oxygen can be obtained from regolith on the moon.

I'm in-favor of robots on the moon bootstrapping a fuel and solar-furance refinery of materials construction plant. The speed of light delay is annoying, but not fatal for higher level remote supervision and planning of automated processes.