What tonnage can current heavy rockets land on the Moon?

Question

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?

Answer 1

Here's a table that shows the delta-v requirements in the Earth-Moon system:

         

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.

Answer 2

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.