First a disclaimer: In a nutshell, the moon moves and landing sites are not all in the same place. This makes this discussion a generalization. We will use typical values for what we need in time/distance/propellants.
We have several distinct flight phases to get a payload from the earth to the moon and ,optionally, back.
1) First the launch. There are several options to choose from. Each has a different price and capability. At this point in the document we will just postulate a ride to Geostationary Tranfer Orbit (GTO) with what ever mass we require. This is a common type of launch for commercial communication satellites bound for Geostationary orbit (GEO).
We will revisit this later with other options.
2) Next our spacecraft needs to go from GTO to a Low Lunar Orbit (LLO). This requires about 1.5 Km/Sec in Velocity Change (DeltaV). With the rocket equations DeltaV = Isp*9.8*Ln(Mass full/mass empty) gives us the requirement of carrying about half the mass in propellant. (Isp ~ 300 sec, Mf = 1.66/1.0, 40% Burned Propellant )
Results: about twice the mass in GTO as in LLO
3) Next we need to land on the surface with a vehicle that has more thrust than weight, and landing legs. The DeltaV requirements are about 1800 m/s. This give us a Mf = 1.85 or 46% burned propellant.
Results: about twice the mass in LLO as on Lunar Surface
4) On the surface we would probably do something with the payload. Lander designs vary, but payload may represent between 10% and 80% of the landed mass.
Results: put the cargo in here. say vehicle is 7 times as massive loaded.
5) Now, if whe choose to, we start coming home. We will need to launch back up to LLO with a vehicle that has more thrust than weight. The DeltaV requirements just to undo that last landing step (1800 m/s). This give us a Mf = 1.85 or 46% burned propellant again. We do, however, have the option to leave the landing gear behind!
Results: about twice the mass on Lunar Surface as in LLO.
6) Now we Need to go back toward the earth. With the ability to slow down via air drag, all we need to do is hit the earth from LLO. This takes about half as much DeltaV as going from GTO to LLO. (750 m/s). this works out to a Mass Fraction Mf = 1.27 or 22% burned propellant. This propellant can be stored in LLO on the way down, so it need not be landed nor launched.
Results: about 1/4 the mass in LLO needs to be stored in LLO in step 2
7) Earth reentry and recovery. Technically the parachutes and heat shield could have been stored in LLO like the stage 6 propellants or it could be included in the landed payload mass. For sake of argument, we will assume 7:1 (14%)
Example 1: Mission 1-2 (calculated numbers with 5% tank mass)
Payload 300 lbs Mass on Lunar surface = 350 lbs Mass in LLO = 700 lbs (663) Mass in GTO 1400 lbs (1221 or 1123)
Example 4 Mission 3-4
Returned Payload 300 lbs Mass at reentry = 350 lbs Mass in LLO = 350 + 88 or 4lbs (300+167, 350+117 or 467) Mass on surface 875 (907) Mass in LLO first time 1750 lbs (1762) Mass in GTO = 3500 lbs (3071)
The problem of GTO vs Low Earth orbit: The multiple options of launch vehicles will give different mass capabilities at different orbits. Assuming the worst case of only Low Earth Orbit (LEO) is possible, then our vehicle needs to make up the extra propulsion. LEO to GTO is a DeltaV of about 2500 m/s. We need additional propellant (and tanks) depending on how much we need to make up. At an Isp of 300 we need:
2400 m/s shortfall (LEO) needs 2.38 lbs on the Launch Vehicle per 1 lb of GTO mass 1200 m/s,,, 1.58 lbs ... 600 m/s,,, 1.29 lbs ... 300 m/s,,, 1.16 lbs ... 100 m/s shortfall needs 1.09 lbs on the Launch Vehicle per 1 lb of GTO mass
Launch vehicles have some advantages so the trade between us supplying the extra DeltaV and them doing it may not be so simple.
Example 1a from LEO Launch vehicle required to deliver 3332 lbs to LEO Example 4a from LEO Launch vehicle required to deliver 8330 lbs to LEO
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