Yeah, orbital refueling doesn't change the rocket equation unless you can manufacture fuel in space. The only benefit is that you don't need a bigger rocket.
Orbital refueling absolutely changes the rocket equation in a huge way. The standard NASA human Mars plan involves a mega rocket large enough to lift the humans and their supplies in one shot from earth, along with the fuel to get to Mars and the fuel to get back.
Starship enters LEO with empty fuel tanks, meaning it can lift much more payload per pound of fuel. Being refueled in orbit is cheap, because fully reusable flights are cheap. And for Mars, Starship only needs enough fuel to get there, it can make fuel on Mars. That means it doesn’t have to carry even more fuel to fly the return fuel to Mars.
We'll eventually get to the point where Starship-like rockets only ferry people, cargo, and, maybe, propellant to LEO for transfer to spaceships that don't need to go deep into any gravity well. These ships will then take you to orbit around your destination so you can board another shuttle to the surface.
You could probably aerobrake to get into orbit instead. But eventually it might make sense to build ships that are never supposed to touch atmospheres, or only upper layers. Some design constraints can be relaxed then.
There definitely is a place for Aldrin Cyclers, not soon, but eventually. It’s not to save on fuel, but to provide safer and healthier accommodations for the trip.
How it will likely work is passengers will take a Starship to orbit. It will be refueled in LEO, then accelerate to Mars injection velocity to match orbit with a passing Cycler. It will dock with the Cycler, passengers will switch to the Cycler for the duration of the journey. The Cycler will be much roomier, have better shielding, and likely rotate to provide Mars level artificial gravity. Passengers will have far better work, entertainment and workout options.
Once the Cycler approaches Mars, passengers will reboard their Starship, and it will Aerobrake to land, while the Cycler continues on in its orbit, which returns to Earth. The Cycler never slows to orbit either Earth or Mars, it just coasts between them but occasionally will need fuel for course optimizations.
The only problem is that Cyclers will take 9 months to go to or return from Mars. They will be like large cruise ships. Starship can make the trip to Mars in as little as 3 months, and some will still do that. They will be the equivalent of the long distance direct flight, trading a less comfortable and less healthy trip for a big time savings.
In the end you save a lot on fuel - you don't need to bring along shielding, life support equipment for the duration of the trip (only expendables and replacement parts).
The trajectory adjustments may be small enough that Hall thrusters, or even just reorienting solar panels or inactive radiators get enough light pressure to make it work. If we are OK with spending a little more propellant, the cycler can be put on a shorter quasi-cyclic orbit that requires course corrections on every pass (IIRC, the shortest trajectory Aldrin considered in his paper would enter Earth's atmosphere, or crust, I don't remember). The cycler maintenance cycles also don't need to coincide with in-transit crews and, in some passes, crews can bring more cargo (or the cycler can dock with autonomous cargo freighters).
If the cycler is large enough, it may have its own food production, so you don't need to carry that too, but then we can also imagine it as a full habitat that's permanently populated and passes by Earth and Mars every now and then and also plants us firmly into science fiction territory. IIRC, the shortest real cyclic path also takes a trip to the Asteroid belt before passing Mars on its way back to Earth. That, I imagine, would be a popular destination for future space colonists looking for resources in the belt to supply passing cyclers.
That would be a killer trip if it includes the belt. I’d pay for that!
But Cyclers won’t save much fuel. Starships (or their descendants) still have to accelerate and decelerate the same, and still need almost as much shielding (a solar flare during descent once you’ve left the cycler is still deadly).
Most of the starship mass isn’t radiation shielding, it’s reentry shielding, tankage, engines, etc.
But once we get to the Cycler stage I think fuel costs will be low on our lists of concerns anyways.
The most efficient propulsion methods are not suitable for atmospheric flight or landing because of their low thrust, but are excellent for long-duration interplanetary flight where you can "burn" for hours, or days, to change between parking and transfer orbits.
Sort of true. The rocket equation doesn't account for the added weight of lifting the rocket itself, just the added fuel. Multiple launches can reduce the practical overhead, even if not changing the overhead in the limit of 0% rocket mass 100% fuel mass.
Manufacturing fuel in space would be the way to go.
Or eg have giant solar panels in orbit that power a laser to shine at your spaceships. Either to propel them directly, or to transmit power for their ion thrusters etc.
