I recently described how to fly to the Moon solo using SpaceX hardware. Someone asked me why I worked out an Apollo 8 style flight and didn't just do a simple free return trajectory.. after all, it's a lot easier - and that's actually the reason - it's too dog gone easy. In order to make this interesting I decided to try to think of the easiest way to do a free return trajectory. Preferably, we'd like to use an unmodified spacecraft and launch vehicle and not have to develop any other hardware.
For a start, let's forget this whole idea of an Earth Departure Stage - we'll just throw the Dragon spacecraft to lunar orbit. This sure is simple, but it only gives us 2585 kg to work with. This prompts the question, exactly what is the mass of an unladen Dragon.. yeah, yeah, I know - African or European?
Looking at the Falcon 9 Users Guide we find that it can throw 9358 kg to 51.6º with an altitude of 400 km. SpaceX will happily tell you that the Dragon can carry 3000 kg of pressurized cargo and 3000 kg of unpressurized cargo to the ISS, and has 1290 kg of propellant. So the dry mass has to be around 2068 kg. It's this big number that prompted me to suggest pulling out the heavy docking adapter, etc, but we're not doing that this time.
At some point there is going to be a bunch of used Dragon capsules, and maybe we can get one for cheap. The actual launch is around $56 million, if you can get SpaceX to stop placating NASA's worst fears: another crew lost and everyone asking why the hell they were flying in the first place. If they keep blowing money on a fancy launch abort system, then who knows.. but it'll probably still be smaller than the $150M per seat that Space Adventures is charging for a ride on Russian hardware.
For a single crew member weighing a maximum of 100 kg, you need 11.839 kg of cabin air, 25.83kg oxygen candles, 52.71kg LiHo CO2 scrubbers, and 45kg food and water. Total is 235.379 kg. From our throw mass to lunar transfer orbit we subtract the dry mass and the consumable mass to find 281 kg remaining.
Remember how we took the fuel out of the Dragon? Let's put 245 kg back. This gives us about 300 m/s of delta-v, which is about 10 times as much delta-v as we need to do a free return trajectory. So even if you're flying like Scott Carpenter you should be able to pull it off.
The remaining 36 kg is margin.. or you could take your dog along for the ride.
I have one last thing to say on this insanity. For a while I've been using 3140 m/s as the required delta-v to from Lunar Transfer Orbit directly to the surface of the Moon. Apparently, this estimate is horrible. According to the Lunar Polar Volatiles Explorer concept mission the required delta-v post-TLI breaks down like this:
|Thermal Control Maneuvers||70|
|Landing Site Navigation||25|
For some inexplicable reason they do the breaking burn with a solid rocket motor with 292 seconds of isp. Their maneuvering thrusters have 272 isp, and the terminal descent is done with 296 isp. With this reduced performance they turn 3492 kg at TLI into 1203 kg on the lunar surface.
They get the wet mass there by flying an Atlas V 401 on a 5 day minimum delta-v maneuver, and although that's just fine for cargo, it just means more consumables and radiation exposure for a human. The Falcon 9 has higher mass to LEO, but lower mass to GEO, but it's also 1/3rd the price, so let's stick with the 2585 kg that a Falcon 9 can throw direct to Lunar Transfer Orbit and use a decent storable propellant isp of 312 seconds. With that we can deliver 1038 kg to the surface.
With a inert mass ratio of 0.15 for the lander, the total payload mass is 651 kg. Using the crew/consumable mass above, and assuming 2.5 days to get there, we can spend 28 days on the lunar surface. Or you could try to fit in propellant to fly back.. I guess, if you wanna die in your bed or something.