A Water Economy in Space: Some Quick Numbers v 2.0

Momentus Space is a space tech company offering a ‘water plasma rocket’ – basically a helicon thruster that uses water as propellant (not ‘fuel’ as the energy has to be added via a power source). A helicon thruster is an electrodeless electric thruster that uses microwave energy from a ‘helicon’ antenna to flash heat the propellant into plasma. As the hot water doesn’t touch the electrode supplying the energy, there’s no corrosion of the drive system. Thus it can run for long, long periods of time. The water plasma (ions of hydrogen, oxygen and hydroxide plus their loose electrons) rushes out and produces a Specific Impulse (Isp) of 700 seconds in the small initial system being marketed. That’s better than burning hydrogen and oxygen to make hot fast steam, like a Space Shuttle Main Engine, which typically gets about 460 seconds Isp in space. And most long term propellant mixes that store well in space, like monomethyl hydrazine+nitrogen tetroxide, manage about 300 seconds.

But… there’s a down-side to all electric rockets. Power has to be supplied to the engine and it’s a LOT. Unlike chemical fuels, which react to release the energy they store, an electric rocket needs electrical power to turn Propellant into Push (3 P’s, Power-Propellant-Push). An Isp of 700 seconds translates into an effective jet velocity of about 6,865 m/s, which means a kinetic energy of 23.6 megajoules per kilogram of propellant shot out the back of the drive. Jetting that 1 kilogram in a second at 6,865 m/s produces a push (an impulse) of 6,865 newton-seconds. If the satellite+rocket combination masses 300 kilograms, then it’d accelerate at 6,865 kg.m/s2 / 300 kg = 22.9 m/s2, which is probably excessive for a satellite already in orbit. It’d also require powering the jet with at least 23.6 megawatts of power – and probably more like 32 megawatts of power, if we take rocket efficiency into account.

If we dial down the impulse per second to just 1 newton, rather than 6,865, then the acceleration would be a leisurely 3.33 mm/s2 and the power needed more like 4.5 kilowatts. That’s still a lot, but more feasible to provide. If half the mass on board is propellant, then the total time to use it is 12 days. The mass-ratio of empty to full is 2. Thus, thanks to the Rocket Equation, we can compute the total delta vee as LN(2) x 6,865 m/s = 4,758 m/s. If we start in Low Earth Orbit (LEO) that’ll get us much of the way to Geosynchronous Earth Orbit (GEO), but much of the time will be spent in the worst bits of the Van Allen radiation belts. The satellite can be hardened to take the punishment, but it eats into the actual ‘payload’ we’re delivering to its new orbital home.

The other option, if we’re using water, is to turn it into hydrogen and oxygen, to then fill up a rocket that can burn it at high thrust and deliver our GEO bound satellite in mere hours rather than days (NB: most available electric rockets would actually take months, due to their higher power demands and smaller thrust.) If we react hydrogen and oxygen to make water, then the energy released per kilomole (18.015 kilograms of H2/O) is 241.83 megajoules. That’s 13.42 megajoules per kilogram of fuel mix. So the reverse process, breaking water into hydrogen and oxygen, means applying at least that much to water to break it apart. The usual process assumed is electrolysis, which uses electrical potentials to break up the water molecules, and it’s typically 70-80% efficient. Then the resulting gases need to be cooled and compressed into liquid form so they can stored. Total is 15.33 megajoules per kilogram. At 80% efficiency that means 19.16 MJ/kg.

An Orbital Fuel Depot, splitting water to make fuel, powered by ~20 megawatts, would then make 1 kilogram of fuel per second, thus over 30,000 tons per year. That’d deliver about 20,000 tons of annual payload to GEO, which is much more than present traffic levels. If there’s about 450 active GEO satellites, with average lifespans of 15 years, and each masses about 6 tons, then 30 replacement satellites need to be launched each year, thus about 300 tons of fuel per year is a good starting goal.

A side note: At the end of its useful life, of about 15 years, a GEO satellite is then is parked in a higher orbit – a ‘graveyard orbit’ – to open orbital space for functional satellites. At least if the satellite owners are responsible corporate citizens.

Thus the Orbital Fuel Depot needs about 0.2 megawatts of power to provide fuel for Space Tugs serving the GEO satellite trade. If we use solar power, that’d be the largest single array ever launched, but it doesn’t have to be heavy. Reflectors that concentrate sunlight onto high temperature solar cells can minimise the mass and the total area of expensive semi-conductors such solar cells are made of.

Question is: What’s the best source for the water?

Of course Earth might seem a logical choice. The Throw-Away Falcon Heavy promises about 60 tons of payload to LEO. Thus 5 Falcon Heavies per year could supply the water. Total RP-1/LOX propellant required 1,400 x 5 = 7,000 tons. Fully Reusable Falcon Heavies might deliver 30 tons to LEO, so 10 launches of those would be enough. Some 14,000 tons of RP-1/LOX. A bit further along and the Big Falcon Rocket promises 100 tons to LEO. Just 3 launches required, but about 4,000 tons of LCH4/LOX required per BFR, thus 12,000 tons total. Another option is to mine water on the Moon, then deliver it to LEO via H2/O2 rockets. A Moon Tug could launch from the surface into an Earth Transfer Orbit for a delta-vee of about 2.5 km/s with aerobraking into LEO. The Moon Tug plus a payload of 100 tons water masses about 120 tons, but needs about 173 tons of H2/O2 to launch from the Moon, then return the empty Tug to the Moon. That does put the whole process into question, since supplying 300 tons of water in LEO to make into H2/O2 also means having to make about 519 tons of the same to use on the Moon. Thus about 2.5 megawatts of power supply delivered to the Moon. That might not be excessively onerous, especially if the Moon’s regolith (‘soil’) can be turned into solar panels as some have suggested.

Momentus Space’s Water Rocket becomes relevant at this point. If the Moon Tug delivers water to a waiting Water Rocket in Low Lunar Orbit (LLO), which then returns it to LEO via aerobraking, then it only needs about 100 tons of H2/O2 for every 100 tons water delivered. The orbital design will require some finesse. Low thrust orbits aren’t like high-thrust orbits. The total delta-vee required is significantly higher. In the case of the LEO-to-LLO round-trip mission, the total delta-vee can be up to 18.8 km/s, which would be a prohibitive additional water cost. That’s LEO-to-LLO and back, solely under thrust. So rather than thrusting the whole way, the Water Rocket thrusts away from LLO into Earth’s Sphere of Influence and a low perigee aerobraking orbit, the delta-vee I’m assuming is more like 2 km/s one-way. Getting back to the Moon however incurs the low-thrust delta-vee penalty, but only the Water Rocket is returning, sans 100 tons of payload. The return delta-vee could be up to ~9.4 km/s, but hopefully it’ll be less via careful orbital design. Alternatively, we might make water containers that can aerobrake themselves, and then be repurposed as pressure vessels in LEO once emptied. The Water Rocket could then free-return to the Moon after delivery, so long as perigee isn’t too low.

5 Responses to “A Water Economy in Space: Some Quick Numbers v 2.0”

  1. Hop David says:

    A lot of people take Spudis’ very optimistic estimates of lunar ice deposits as a given. I don’t.

    The best data I know of is from the LCROSS ejecta. Which at one time was estimated to be 5.5% water. It also had other volatiles. But a year later the team downgraded their volatile estimates by a factor of 5.5.

    I’m skeptical lunar propellent mines would be worthwhile if highest water ice concentrations turn out to be 1%.

    I’m happy Bridenstine, Bezos and others are expressing an interest in lunar ice. But I don’t think we should count our chickens before they’re hatched.

  2. Adam says:

    Hi Hop
    There’s more evidence of actual water ice than LCROSS – a very recent paper has made that case [ Direct evidence of surface exposed water ice in the lunar polar regions ]. However it’s not the easiest accessible water in Near Earth Space thanks to being on the Moon. If an NEA was proven to be an inactive comet, then we’d really be in business. Water Rockets would then be prime propulsion options for retrieval, though to exactly which orbit would require further analysis – LEO is a *bitch* for low thrust drives.

  3. Andrew_W says:

    Hi Alan, where to you get the figure of 10% for the efficiency of electrolysis? From what I can find it’s around 70 – 80%.