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SpaceX Moonfuel: Part 1 – Background

Water Ice on the Moon holds promise as a propellant source for Space-Tugs operating between Low Earth Orbit (LEO) and Geosynchronous Earth Orbit (GEO) which fits the propulsion plans of the United Launch Alliance. But what about Space Exploration Technologies (SpaceX) and their technological commitment to the Methane-Oxygen Raptor engine?

Recent studies of the very early Moon suggest that a thin CO2 rich atmosphere could have formed and persisted, but it would potentially freeze out – presumably in the present day Cold-Traps. That’s the permanently shaded craters at the Poles, as well as the protected hollows formed by extinct lava-tubes and caverns. If there is significant Dry Ice mixed in with the water ice, then the SpaceX Raptor has a potential propellant supply on the Moon.

[Editorial Note: Originally I wanted to discuss Space-Tugs servicing the satellites in Geosynchronous Earth Orbit. However, in light of the hoped for LEO satellite networks, I’m not sure that’ll be an enduring market. Wikipedia’s discussion of SpaceX’s Starlink system notes that as of 2017 future investment in GEO satellites has slowed significantly.]

So, given a supply of methane-oxygen (“Methalox”) from the Moon, what’s the best way to use it? There’s three broadly-defined ‘places’ that fuel delivery can be useful, but if the Tanker delivering the propellant is to return to Moon Base Alpha for reuse the option which uses the least amount of propellant isn’t at all obvious.

To derive real numbers to answer the question, I’ve used the parameters of SpaceX’s proposed Starship, but as modified in recent Tweets by Elon Musk. First, Musk has described a stripped back version of the Starship for deep space work. With a Wet mass (fully fueled) of 1,200 tons and a Dry mass of 40 tons, the stripped vehicle is for purely Orbit-to-Orbit work. I’ll assume it can be modified for Moon Landing, which is much less arduous at 1/6 gee than landing on Earth.

The standard Starship holds 1,100 tons of propellant, 100 tons payload and masses 75-85 tons dry. For this study I’ll assume 75 tons, but harder figures will have to wait for real flight experience as the Starship moves from development to actual flight. It’s being developed so it can return from the Moon and re-enter Earth’s atmosphere to land at 1 gee. If we remove the requirement that it has to land on Earth, and accommodate a flight-crew, then a “Star-Tug” might mass ~60 tons dry.

Given its current parameters, the standard Starship using Raptors with a Specific Impulse of 380 seconds can achieve a delta-vee of 7.4 km/s. From LEO that’s enough to get to the Moon, but not enough to get back as well. Once the Moon Base is supplying propellant, then refueling for return flights is straight-forward. So Starships doing the Moon Run could be refueled in LEO from the Moon. That’s the first useful location.

If we’re not landing on Earth, but servicing different orbits around the Earth, then full re-entry is not required. Instead Aerobraking is used to shave speed off a Starship returning from the Moon’s orbit (or orbits near the Moon.) A Star-Tug acting as a Tanker to a another vehicle in a refueling orbit will be aerobraking with a partially loaded tank.

Aerobraking in this context means descending to a bit higher (~100 km) than Re-entry altitude (~63 km) and scraping off about 3 km/s of speed, rather than needing to endure a full re-entry. Depending on the thermal protection system parameters that might mean a series of Braking Orbits until LEO orbital velocity is attained, to minimise peak heating. The Ballistic Coefficient (vehicle mass divided by effective frontal area and coefficient of drag for the re-entering shape) is higher for a partially loaded vehicle undergoing re-entry, than a near empty Starship returning from the Moon or LEO. That means a higher heating rate, as more mass is being decelerated for the same frontal area, but because the idea is to scrape off some of the orbital velocity, rather than all of it, the required deceleration isn’t as arduous.

I’ll assume the following standard characteristics involved:

LEO, as a Parking Orbit to refuel, is about ~320 km (~200 miles) altitude, or 1.05 Earth’s equatorial radius of 6,378.137 km.

Lunar Orbit at 384,400 km, which varies throughout the month, of course.

Earth’s standard gravitational parameter is 398,600.4418 km3.S-2

The Moon’s standard gravitational parameter is 4,902.8000 km3.S-2

In the context of interplanetary journeys, there’s two options for Refueling Orbits, to make best use of the Oberth (or Gravity-Well) Maneuver. One is a Highly Elliptical Earth Orbit, which goes between LEO and about ~10 Earth radii or so. The other is the Earth-Moon Lagrange (EML) orbit number 1, which is between Earth and the Moon, at a distance of about 55 Earth-radii. Vehicles can wait at EML-1 for a small amount of station-keeping propellant almost indefinitely. It does cost more in fuel to access from LEO, but is easier to access from the Moon. What EML-1 doesn’t have is any option for aerobraking. All maneuvering requires propellant use.

To summarise, the Tanker delivery orbits are:

(1) LEO – at 1.05 Earth radii
(2) HEEO – at 10 Earth radii, max, LEO min.
(3) EML-1 – at 55 Earth radii, on average.

LEO is the parking orbit for Moon Missions, so can’t really be compared with the other two.

The Oberth Maneuver, if you don’t already know, is performing most of an interplanetary burn at the lowest point (perigee) of a highly elliptical orbit, to maximise the speed gain from burning that propellant. A concrete example is if we want to do a burn for a Solar Escape orbit. From LEO that’s means a speed of 16.5 km/s. In LEO, at 1.05 Earth radii, the orbital speed is already 7.72 km/s, so the delta-vee needed is 16.5 – 7.72 = 8.78 km/s. That’s too much for a Starship with a full tank. If instead it starts from a HEEO with a perigee speed of 10 km/s, then the delta-vee is a more manageable 6.5 km/s. And if the Starship has launched from EML-1 the speed can be ~11 km/s, requiring only 5.5 km/s delta-vee.

Ok, so that’s the background. What’s the results? That’s for Part 2.