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Mass to LEO is somewhat of a standard in superficially comparing the payload capacity of different rocket, at least for the googling general public. There are many LEOs and it depends on where the launch takes place and whatnot. But especially when it accounts for what has actually been lifted to LEO, it is a rough guideline and useful for relative comparision (I hope).

I wonder if such a mass to LEO could be easily and roughly converted to a mass on the lunar surface? And if so, in a couple of distinct scenaria such as to the equator or to a lunar pole, if that matters much. And for simplicity lets not consider long term low thrust propulsion, just chemical rocketry.

With heavy rockets I mean the 12-23 tonnes to LEO types (Atlas, Delta, Ariane, Proton, Zenit, Mitsubishi, Long March, Falcon). How much can they land softly on the surface of the Moon today?

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  • $\begingroup$ Actually, LEO to lunar surface is what I'm looking for. And a conventinal lander, stuff that has been done or could reasonably be done within a few years. Or how much difference feasible innovation could make. If the particularities matter too much for a rough estimate, then too bad. $\endgroup$ – LocalFluff Jun 12 '14 at 18:39
  • $\begingroup$ Thanks for clarifying! I believe that by assuming some reasonable fraction of lander to payload mass, this can now be answered. $\endgroup$ – TildalWave Jun 12 '14 at 18:59
  • $\begingroup$ "I wonder if such a mass to LEO could be easily and roughly converted to a mass on the lunar surface?" Not really, given that a craft/load in LEO can then use ion engines or solar sails to visit places far from Earth (given enough time). E.G. Acounting for the payload, engines and fuel, if ion engines were used to move a load from LEO to LMO (low moon orbit) that would presumably increase the mass that could be transported to the lunar surface. $\endgroup$ – Andrew Thompson Jun 18 '14 at 5:11
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Here's a table that shows the delta-v requirements in the Earth-Moon system:

         Delta-V Budget. Earth-Moon space.

By this it takes 5,930 m/s to go from LEO to the lunar surface. The Centaur V2 upper stage could do this as a single stage one-way. It has a loaded mass of 23 metric tons (mT) and empty mass of 2.2 mT, with an Isp of 451s. Then it could carry 5 mT from LEO to the lunar surface:

$$ 451 \cdot 9.81 \ln{\frac{23 + 5}{2.2 + 5}} = 6,010 \text{ m/s} $$

It would need landing legs but these are typically a fraction of the landed weight and would need even less mass for the 1/6th gravity of the Moon.

The total gross mass, loaded stage plus payload, of 28 mT could be carried to LEO by the Delta IV heavy which has been upgraded to carry 28 mT to orbit.

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    $\begingroup$ It would also need substantial upgrades in tank insulation to reduce LH2 boiloff to manageable levels. And new electrical power, guidance and communication systems. $\endgroup$ – pericynthion Dec 12 '14 at 20:16
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The accepted answer assumes a single hydrogen-fueled stage for the whole TLI-to-landing thing, which isn't how it's normally done, because cryogenic hydrogen would boil off along the way.

So for a more accurate estimate, you have to split the LEO-to-moon delta-V requirement into 3300 m/s for the translunar injection (to be done on a hydrogen-fueled upper stage with an ISP in the 400s) and 2600 m/s orbital insertion and landing (to be done on a non-cryogenic hypergolic with an ISP in the 300s).

Then you run the rocket equation once for each leg of the trip, and find you need about 2.1 tons of TLI stage to get 1 ton from LEO to the lunar intercept, and about 3.6 tons of orbiter/lander at lunar intercept to soft-land 1 ton. So there's a total mass ratio of about 7.5 involved.

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