SpaceX has said two Falcon Heavy launches would be required to carry a manned Dragon to a lunar landing. However, the 53 metric ton payload capacity of a single Falcon Heavy would be sufficient to carry the 40 mT (Earth departure stage + lunar lander) system described below. This would require 30 mT and 10 mT gross mass Centaur-style upper stages. This page gives the cost of a ca. 20 mT Centaur upper stage as $30 million:
A 30 mT Centaur would be somewhat more than this and a 10 mT Centaur-style stage would be somewhat less, so the total for both about $60 million. Note it could also be done with two 20 mT Centaurs at slightly reduced performance.
The 53 mT to LEO capacity of the Falcon Heavy would also allow large lunar cargo transport using two of the 20 mT gross mass Centaurs that already exist either using the Dragon to carry the cargo or by carrying somewhat more cargo just within a lightweight container.
An important cargo delivery to the Moon would be in-situ resource utilization (ISRU) equipment, specifically for producing propellant from the water discovered to lie within the shadowed craters near the lunar poles. Elon Musk has said a key goal of his is to mount a manned Mars mission within 1 to 2 decades. Such a mission could be mounted more cheaply if the large amount of propellant required did not have to be lofted from the Earth's deep gravity well but could be taken from the Moon.
Another important cargo delivery would be to carry a rover that could do a sample return mission from the near polar locations. Lunar orbiter observations suggest there may be valuable minerals concentrated in such locations:
"There is water on the moon ... along with a long list of other compounds,
including, mercury, gold and silver. That's according to a more detailed
analysis of the chilled lunar soil near the moon's South Pole, released as six papers by a large team of scientists in the journal, Science Thursday."
NASA's Commercial Orbital Transportation Services: A New Era in Spaceflight - History of International Space Station (ISS) Cargo and Crew, SpaceX, Orbital Sciences, Bigelow
eBooks (Progressive Management)
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