What would be required to have a vehicle like the space shuttle in that it could launch from earth and travel through space and was reusable except that it also possessed the capability to land on the moon and return to earth. I am writing a science fiction novel where this occurs...just need a simplistic theoretical idea to make the journey in the book somewhat plausible even if it's not possible yet.
Being very minimalist you could achieve this trip with the following Delta V’s.
- LEO with 9.2 km/s Delta V
- LLO with 4,04 km/s
- Lunar surface 1,7 km/s
- Lift to LLO 1,7 km/s
- Back to LEO 1,31km/s (without the burn to slow down the craft therefore stressing the heat shield more)
Adding all that up gives us about 18km/s of required Delta V. That however is a very minimalist Delta V budget, absolutely no room for mistakes or non-optimal paths. Not only is that but the launch from earth uses metrics for dense launch systems which is very optimistic. The landing on the moon is also very tight so if distances are judged incorrectly the retrograde burn would waste more fuel. Assuming we managed to solve those two problems the very minimum Delta V would be the mentioned 18Km/s.
Using HydroLox Rockets the highest ISP of chemical rockets ever produced. At about 450s you would need e^(18/4,5)= ~55 . That means that your rocket would need a craft that could carry 55 times its own weight while inside earth atmosphere with at the very least 1,5 G’s of acceleration. The best rockets that can deliver the required acceleration with fuel easier to handle than hydrogen are three times heavier than that and current normal hydrogen rockets are about 6 to 8 times the target weight so rocket fuels are out.
If we use NTR (Thermal Nuclear Rocket) engines with the target specs of project Timberwind and considering that the hydrogen tanks had equivalent mass per volume of the External Shuttle Tank entirely for H2. We would them have about 150 Tons H2, 25 Tons for Tank, 9 tons engines. This is a realistic rocket up to the point where we notice that we ignored all other needed things like navigation, payload fairings, all the wiring, heat shields, landing struts, control structures, Etc. that said the Vac DeltaV is:
So the bare minimum weight is not quite slim enough. With a different design things start to look better. The High thrust portions are dealt with by the NTR and Ion engines for Lunar transfer and return. So you would need:
High thrust 9,2+1,7+1,7=12,6 Km/s = 72% weight
And another 12 Km/s for low thrust Lunar Transfer. (for some low thrust maneuvers you need more Delta V)
At 40 Km/s Exhaust speed you would further need=33% weight
Total fuel weight=1-0,28*0,67=0,79
The payload + ion engine weight is limited to 3% (100%-18%-79%=3%)
So we assume 1 % payload and 2 % “engine”
Let’s assume a high-power density of 500 W/kg. For every ton of land craft we have 20 kg of solar panels+engine.
10 kw/ton. Modest 50% Efficiency = 40mg exhaust / ton. Total exhausted fuel = 70 kg
1,75 Mega seconds=24 days thrusting for the moon and back (Actual time should be 2 or 3 times higher because the order in witch it was calculated didn’t take into account the fuel to burn on the moon. For all other purposes the calculations are correct.)
There are some approximations like 1000 sec is not 10 km/s but 9,82 km/s but the results are pretty accurate in the context they were used.
Conclusion, with a mix of NTR engines and Ion engines, ignoring all other things needed except propulsion (good enough for a book with significant but quite sci-fi improvements on current technology). Or you stop mid way to refuel. Leo before going to moon sound good and with current thecnology should be achievable.
There are of course other technology open cycle that with enough money and a decade we could “easily” make, but releasing nuclear fuel in the atmosphere is not such a good idea.
Getting from Earth into space is cheap (for rather large values of cheap...but ti has been shown that a missile (an ASM-135 ASAT) fired from an ordinary fighter airplane (an F-15A "Eagle") can make it into space (and shoot down a satellite there (https://en.wikipedia.org/wiki/ASM-135_ASAT))). Staying in space (achieving orbit) is expensive. Most of the fuel is consumed to bring the fuel into space (and have it stay there).
So...let's try it the other way around.
We need a fuel factory on the moon (or somewhere else near Earth, could be an asteroid or whatever). Getting into space from the moon and staying there (or going to Earth) is frigging cheap. So, if we can produce fuel on the moon, we could establish a cheap shuttle service from moon to Earth. The Moon-Earth-Shuttle won't land on Earth, but it can pick up payload which gets launched from Earth into space. Since it's cheaper to launch moon-sourced fuel into space than Earth-sourced fuel, this Moon-Earth-Shuttle would use this cheap "moon fuel" to brake hard near Earth to pick up the payload and then re-accelerate again for the trip back to the moon. Cheaper that way than to accelerate the payload with "Earth fuel" to get it into a Lower Earth Orbit.
So we will have two spaceships, one Moon-Earth-Shuttle and one Earth-Space-Shuttle.
The Earth-Space-Shuttle could be a conventional design, or maybe a laser-power spaceship. A laser-power spaceship does not need to carry its fuel along with it - the fuel stays on Earth and the energy is "beamed" to the vessel. One of the current designs uses the surrounding air as reaction mass. There are also other designs which carry reaction mass on board.
Note: I have not calculated the "orbital" maneuvers for the payload handover rendezvous. Also not that I have no clue on how to "mine" (produce) fuel on the moon. LOX might not be a natural resource on the moon :-). But some water is there, apparently (https://en.wikipedia.org/wiki/Lunar_water - also check the Ownership paragraph for some legal questions). Then again, using an asteroid as a fuel source could also be an option (https://www.space.com/1526-largest-asteroid-fresh-water-earth.html).
Obviously, the initial setup cost of a fuel factory in space or on the moon would be enormous. And this still does not answer the question why someone would want to travel to the moon (at least now that the space race is over). Oh, well - I know of the theory of the secret NAZI base there, and that Hitler might, due to the beneficial effect of low gravity, still be alive there. But you are wrong. The secret NAZI base is on Mars - which is a very well kept secret everywhere (when the NAZIs shot down the Mars Climate Orbiter, NASA even produced some cheesy cover story claiming some "unit discrepancy" (which is, of course, totally ridiculous - why would anyone in the US use an outdated unit system based on the "Imperial System"...did anyone miss the bit about the Boston Tea Party?)).
Note that the OP specifically didn't ask for a "hard scientific answer", but rather for some inspiration for a "soft" SF novel. I guess you can figure out where my answer deviates from the "hard scientific truth".
Also note that I interpret the requirement for a reusable spacecraft as the intention to build a regular Earth-Moon shuttle line. Hence my idea about accepting a much higher initial setup cost.
An other idea for launches from the moon was a rail gun (or linear motor), like in this question: Can we use a rail gun on the moon to launch stuff directly to mars?. However, for a "simple" return to Earth, it would probably not make sense to invest into a rail gun/linear motor, since launching from the moon to return to Earth is so cheap anyway.