What is the cheapest possible way to land a crew of 2 on the moon?

Question

During the Apollo moon missions, a single very large rocket sent both the Apollo CSM and the LM to the moon in a single shot and it took only around 3 days to get there. However, after the Apollo missions, significant research has been done on low energy transfer orbits, aerobraking in the earth's atmosphere and unmanned probes.

For the below scenario please assume the mass of LM to be similar to that on apollo (approx 15-16 metric tons), or maybe somewhat smaller since computers have shrinked since then.

So let's say we have a medium class rocket somewhat smaller than the delta iv heavy (around 25 metric tons to 300 km LEO) and with an upper stage fueled with something other than LH2 (something that can withstand being in space for months and not leaking), and we launch only the LM using this rocket, and instead of going directly to the moon like Apollo style, we launch it in a short elliptical orbit and let it gradually keep increasing it's apogee using the rocket's upper stage (or maybe using a separate transfer stage, in which case we can use LH2 as the fuel for rocket's upper stage). We keep increasing the apogee till ballistic capture takes place and then when the LM is in orbit around the moon, we similarly gradually bring it closer to moon till it is in the desired orbit. Let's say this whole process to put the LM in Low lunar orbit takes 3-8 months. Some of the missions that used low energy transfers:

1)Chandrayaan-2

2)GRAIL

3)Hiten

And then we launch the crew using another rocket of the same class, maybe somewhat smaller. And let's say we leave the reentry module in a Low earth orbit of around 200-250 km (since crewed lunar landing missions can be completed in a week or two, the reentry module only needs to stay in orbit for that much time, so we can minimize the altitude at which we leave the reentry module in orbit). Then the service module is taken to the moon by the rocket's upper stage in 3 days (in same Apollo style). Then the service module and LM dock in low lunar orbit and the landing happens, then again in the same Apollo style, the crew launches from moon, docks with service module, leaves the lander on moon's surface and ascent stage in moon's orbit and heads towards earth.

Then upon reaching earth, the service module performs aerobraking similar to the Japanese Hiten spacecraft. After performing 2-4 aerobraking maneuvers (with each one shedding off around 1.5 - 1.7 km/s similar to the Hiten spacecraft), it seems like it should be able to reach the reentry module and dock with it. After that we leave the service module in LEO for another moon mission and bring the crew on earth in the reentry module. To reuse the reentry module, we either land it on land (boeing's starliner style) or we snag it off air using helicopters above the ocean.

So in this way, we are using 4 things to reduce costs here:

1. Using low energy path for LM to reach moon (As a result we need to launch the crew separately later to avoid months of deep space exposure).

2. Leaving the reentry module in LEO and later using aerobraking to dock with it.

3. After crew transfer to reentry module, leaving the service module in LEO to reuse it for more missions.

4. Reusing the reentry module by landing it on land (boeing style) or snagging it mid-air by helicopters over the ocean.

Most of these points have been successfully demonstrated, and I see no obvious roadblocks.

My only few concerns here :

1. Is a delta iv heavy class rocket powerful enough to be used to ferry the LM to the moon (even with a fuel efficient trajectory) ? Just how much fuel efficient are fuel efficient trajectories ? We basically want to take the LM (about the same mass as in Apollo i.e 15-16 metric tons) to low lunar orbit as fuel efficiently as possible. Is it really possible to do it with a rocket capable of putting only 25 metric tons in 300 km LEO ? If not, then what is the least possible mass a rocket should be capable of putting in 300 km LEO to pull this off ?

2. When ballistic capture takes place, to bring the LM in low lunar orbit, do we use the rocket's upper stage (or the transfer stage) and then discard it in low lunar orbit, or do we use the LM's own descent engine (and thus use a restartable engine in the descent stage) ?

3. To perform the required number of aerobrakings, how much time will it take (one day ? Two days ? Three days ?)

It would be great if you can share your thoughts on the above scenario, answer the above questions and mention any other possible mission architectures that can reduce the cost of a crewed lunar landing.

Answer 1

While the overall scope is too broad, let me address the "low energy transfer" part.

Firstly, the idea of "gradually increasing apogee" doesn't save you any fuel. Chandrayaan-2 did that because of limited thrust. The only saving to be had here is picking an engine with a slightly lower mass.

Secondly, a "ballistic capture", as performed by Hiten, was done to correct a tiny deficit of 50 m/s. A 3150 m/s burn is still required to get an apogee that high, so a 1.5% saving.

The last way, a GRAIL-like profile, saves at most 110 m/s for the Lunar orbit injection. While that isn't much either, it's more notable since that saves on-board propellant instead of upper stage propellant. You still have to spend about 710 m/s to enter low lunar orbit.

Sending a payload into a lunar transfer orbit is going to take at least 3150 m/s of $\Delta v$. For a hydrogen burning upper stage, that's a very neat mass ratio of nearly exactly 2.00
So of your 25 tons of LEO payload, 12.5 tons is the mass of the Lunar module, the propulsion system to enter LMO, and the dry mass of the upper stage. Since the Apollo lunar module alone was over 15 tons, you would have to slim it down considerably to fit your constraints.