Investigation: “Big Ship” Propellant From the Moon vs From Earth

This article is a follow-on to my earlier article (Ref. 1) about “big ship” propulsion for a large orbit-to-orbit transport between Earth and Mars.  The question has arisen:  “would it be better to make the propellant on the moon and ship it to low Earth orbit (LEO),  instead of shipping it up to LEO from the Earth’s surface?”  This article tries to answer that question,  at least in part. 

There are a lot of things that would impact any such propellant-making infrastructure on the moon.  The most important is “what resources are available with which to do this?”  One almost as important is “what is the difference between a resource-in-theory and an easily-recoverable resource?”.  Unfortunately,  too few consider that second question. 

Consider this:  there are oxygen and hydrogen atoms,  and some metal atoms,  locked up in the molecules making up the minerals that in turn compose the rocks and rock dust on the moon.  Those are “resources-in-theory”,  yes,  but they are most decidedly NOT “easily recoverable resources”.  To obtain them you would have to destroy the molecules into their individual atoms,  in order to separate-out what you want. 

What that really means is that you must turn solid rock particles into fully ionized,  fully dissociated plasma.  That takes a whopping amount of energy to do,  even on a small quantity,  and you would use far,  far more energy doing it,  than you could ever recover by burning the recovered atoms as propellants in some engine.  There is NO WAY AROUND that conundrum!

An easily-recoverable resource might well exist on the moon:  ice deposits.  There seem to be ices mixed into the regolith at least in the permanently-shadowed craters at the moon’s south pole,  and possibly elsewhere on the moon.  You merely need to physically separate the ice from the regolith,  melt it,  purify it if it is contaminated with salt or something else,  then electrolyze it for hydrogen and oxygen gases,  that you can then liquify to use as propellants. 

There doesn’t seem to be much in the way of carbon atoms on the moon,  certainly not as “easily-recoverable resources”.  What that means is that you cannot readily make methane fuel on the moon,  unless you import soot or carbon black from elsewhere,  such as from Earth.  But,  if the ice can really be found,  you can make liquid oxygen and liquid hydrogen as propellants on the moon.

In my previous article,  I looked at liquid oxygen-liquid methane as my chemical propellant combination,  something that cannot be readily made on the moon.  Most of the nuclear options use liquid hydrogen,  which can be readily made on the moon,  given ice to mine.  The electric propulsion items currently flying use things other than oxygen or hydrogen as their propellants.  The nuclear explosion drive uses fissionable materials,  something not yet found on the moon as a resource we can readily exploit.

That leaves liquid oxygen-liquid hydrogen chemical propulsion,  and the hydrogen-based nuclear thermal rocket options,  as something we could support with propellant-making infrastructure on the moon.  Nothing else seems to qualify. 

Therefore,  what I will evaluate here is the solid-core nuclear thermal (NERVA) concept for a “big ship” orbit-to-orbit transport,  using hydrogen delivered to LEO from the moon (versus shipped-up from Earth’s surface).  That delivery uses liquid oxygen-liquid hydrogen chemical propulsion to do the delivery from the moon,  appropriate in terms of boiloff risks because of the short flight times. 

That would seem to be the best fit,  to what might actually be an “easily-recoverable resource” (water ice) on the moon.  Emplacing the infrastructure to do this on the moon,  would be far easier than emplacing similar infrastructure on Mars,  because the moon is only 3-5 days away at a lower one-way delta-vee (dV),  versus Mars being several months away at a higher dV.

Picking a Delivery System Design

There would be a lot of ways to do this.  But,  the most reusable might be a delivery stage operating between LEO and low lunar orbit (LLO).  How such a stage is refilled at the moon is the real question here.  The most straightforward answer would be to land the stage,  refill it on the surface,  and relaunch it to LLO.  The most efficient way to do that,  would be to add a separate ferry stage that does the landings and takeoffs,  carrying the transfer stage as its dead-head payload.  That ferry stage never leaves LLO,  except to land on the surface,  refill,  reload,  and take off again. 

What are the Requirements?

The moon circles the Earth in an elliptic orbit of low eccentricity:  not quite circular,  but fairly close.  This affects the perigee and apogee speeds of any transfer orbit from Earth to the moon.  The non-circular lunar orbit effects are not large,  but they are quite real,  as depicted in Figure 1.  What I have shown is the 2-body approximation that led to the figure-8 trajectory into retrograde lunar orbit that was used by Apollo.  The moon spins so slowly that the retrograde LLO orbit penalty is trivial. 

Figure 1 – Basic Astronomical Data Regarding Earth and Moon Orbits and Transfers

A craft approaching the moon on a transfer ellipse has an apogee speed far less than the moon’s orbital speed about the Earth,  as indicated in the figure.  In effect,  the moon is trying to “run over” the craft from behind.  The difference between these speeds is the craft’s speed with respect to (wrt) the moon,  before any effects of the moon’s gravity come into play. 

There is an approximation to this “third-body effect” of the moon,  shown in Figure 2.  That is the “far” versus “near” speed estimates relative to the moon.  But,  to get this “right”,  requires an orbital trajectory analysis computer program that can handle 3 (or more) bodies interacting gravitationally.  That is where the Apollo figure-8 trajectory actually came from.

As noted in the figure,  I used a nominal 300 km altitude for LEO,  and a nominal 100 km altitude for LLO.  These values are consistent with typical practices here at Earth,  and with the Apollo experience at the moon.  At Earth,  the difference between the transfer orbit perigee velocity,  and the circular orbit velocity at 300 km altitude,  is the dV required to depart (or arrive) at Earth. 

It’s a bit more complicated at the moon,  because of the 3^rd-body approximation,  and having to obtain speeds with respect to the moon.  This in indicated in the figure.  For purposes of evaluation,  a nominal arrival/departure dV in LEO would be about 3.110 km/s.  A similar nominal arrival/departure dV in LLO would be near 0.830 km/s.  The gravity and drag loss-factored dV to get from Earth’s surface to LEO is some 8.705 km/s.  The gravity loss-factored dV to get from the moon’s surface to LLO is about 1.819 km/s.  Course correction budgets and rendezvous budgets have yet to be considered.

Figure 2 – Processing Astronomical Values into Rocket dV Requirements

Figure 3 shows the nominal dV values associated with the transfer stage flying to and from Earth,  to include an assumed dV budget for multiple course correction burns along the way,  each way.  As the figure indicates,  on the trip from LLO to LEO,  the transfer stage is heavy with propellant,  being completely full at departure from LLO.

The same dV’s apply to the return from LEO to LLO,  except that the transfer stage arrives depleted of all propellants in LLO.  One thing to remember is that some propellant is off-loaded while in LEO!  That off-loaded propellant is the “payload” delivered from the moon to LEO,  for loading into the “big ship”.  

Figure 3 – Determining Delta-Vee Requirements for a Transfer Stage/Ferry Stage System

What is not shown in the figure is the rendezvous budget needed by the ferry stage between the lunar surface and LLO.  This is not needed for launch,  since the transfer stage is the dead-head payload pushed by the ferry stage.  It is needed for lunar arrivals,  as the ferry stage must find the transfer stage in LLO,  then rendezvous and dock with it,  in order to carry it back down to the lunar surface.  There,  both are refilled for the next flight.

The rendezvous budget adds to the surface-LLO dV of 1.819 km/s,  but only for ferry stage upon transfer stage arrival.  Being airless,  for the ferry stage at the moon,  the basic factored landing dV is the same as the factored launch dV = 1.819 km/s,  as shown in the figure.  So,  with a rendezvous budget of 0.1 km/s,  the factored landing dV = 1.919 km/s.  This is shown in Figure 4.  Factoring reflects 0.825% gravity loss.

For the ferry stage,  these two burns occur at different weight statements.  As explained in Ref. 1,  you have to do two separate rocket equation calculations for these burns,  precisely because of the difference in weight statements.  You do the second burn first,  so that its propellant is part of the burnout mass for the first burn. 

The total propellant mass needed for the two burns is what sets the ferry stage stage inert mass,  easily estimated from the ferry stage-only propellant mass fraction R assumed for the analysis.  What I assumed for chemical propulsion in Ref. 1 (R = 0.97),  is not what I will assume here for this chemical propulsion stage.  While boiloff effects are far higher with liquid hydrogen,  flight times are far shorter.  However,  this ferry stage needs landing legs and the structural “beef” to support the transfer stage.  I used R = 0.97 for the transfer stage,  and R = 0.90 for the ferry stage. 

Figure 4 – Delta-Vee and Weight Statement Information for the Ferry Stage

The transfer stage is the dead-head payload for the ferry stage.  Thus,  it has to be defined first,  so that appropriate dead-head masses can be used in the rocket equation analysis of the ferry stage.  What that means is one sizes the transfer stage first,  then the ferry stage.    Appropriate dV and weight statement information for the transfer stage are given in Figure 5.  This includes course correction budgets.  The big item here is just how much liquid hydrogen is off-loaded in LEO for loading into the NERVA-powered “big ship”.  This is very probably best done as an off-load to an orbiting propellant depot facility,  for later loading into the “big ship”.  Ref. 2 is my take on what such an orbital propellant depot facility might look like.  The value I chose (500 metric tons) is arbitrary!

What that means is that the incoming-to-LEO transfer stage needs a rendezvous budget to meet up with either the on-orbit propellant depot or the “big ship” itself.  Since Earth’s gravity well is stronger and its orbital speeds are higher,  I used 0.2 km/s for that course correction budget instead of the 0.1 km/s I used at the moon.  The figure reflects that. 

The independent variable here is just how much liquid hydrogen I am going to off-load in LEO as payload,  to be loaded (immediately or eventually) into the “big ship”.  The smaller that number,  the more “reasonable” will the ferry and transfer stage sizes be,  but the higher the number of required flights will be,  from the moon.  That choice is entirely arbitrary,  and I have no clue how best to set it. 

If I use about 6000-8000 tons of liquid hydrogen in a NERVA-powered big ship also refilled at Mars,  per the recommendations from Ref. 1,  and I want no more than about 12 or 16 flights from the moon to refill it,  that would set the off-loaded liquid hydrogen “payload” number at around 500 metric tons per flight from the moon.  And that totally-inadequate estimate is the “best” that I have at this time.  

Figure 5 – Delta-Vee and Weight Statement Information for the Transfer Stage

Stage Sizing Results

Figure 6 shows both the spreadsheet image and a pictorial sketch for the sized transfer stage.  It operates between LLO and LEO,  and offloads 500 metric tons of its propellant while in LEO,  to serve its tanker function.  This stage does not land itself upon the moon for refill,  nor does it get serviced by a tanker up from the moon’s surface.  It is the dead-head payload for a ferry stage that operates between the lunar surface and LLO. 

Figure 7 shows both the spreadsheet image and a pictorial sketch for the sized lunar ferry stage.  It operates between the lunar surface and LLO,  with the transfer stage as its dead-head payload.  Because this stage must support the transfer stage,  and because it must have landing legs,  I significantly reduced the stage propellant mass fraction for this design.  It takes off with the transfer stage fully loaded,  and it lands with the transfer stage fully depleted.  It needs a rendezvous budget to meet and dock with the transfer stage,  but only after the transfer stage returns to LLO,  before landing. 

The fact that these two stages are roughly about the same size suggests that this design approach is probably not very far from an optimum.  It takes about 2385.1 metric tons of LOX-LH2 propellant made on the moon to deliver 500 tons of propellant to LEO.  That ratio is 4.770:1,  which is even more favorable than shipping up propellant from Mars.  That outcome is not so surprising,  since the moon has a far shallower gravity well than Earth.  Thus there is plenty of capability to travel between LEO and LLO,  as well as for shipping propellant up from the lunar surface to LLO.  That 4.77 ratio (ton for ton) is quite a bit more attractive than the estimated ratio shipping propellant up from the surface of the Earth (26.9),  by a factor of roughly 5! 

Figure 6 – Sized Transfer Stage LLO-LEO for Delivery of 500 Tons Propellant to LEO from the Moon

Figure 7 – Sized Ferry Stage to Take Transfer Stage To-and-From Lunar Surface From LLO

Using the NERVA “Big Ship” Study As a Comparison Basis

The best NERVA configuration for the “big ship” was a one-way design refilled at Mars,  using a NERVA-powered space tug and an elliptic capture orbit,  to assist with Earth departures and arrivals.  This minimized both Earth and Mars propellant manufacturing quantities and rates.  The real emphasis on that selection was minimizing the infrastructure needed on Mars.  However,  the same held true when making and shipping the propellant from the moon to LEO.

The total propellant manufacturing quantities per “big ship” mission are compared in Figure 8.  These totals are propellant deliveries to LEO (and to LMO),  plus all the launch and transfer propellant needed to get it there,  at both planets.  All the NERVA-powered “big ship” scenarios from the original study are there,  and making propellant on the moon versus on Earth does not change the selection of the “best” option:  refill at Mars,  use a space tug only at Earth (scenario 4). 

However,  making propellant on the moon and shipping it to LEO makes almost a factor-5 reduction on the Earth total propellant quantity!  The total quantities to make and ship-up at Mars are unchanged by the Earth vs lunar choice.  This mission looks far more attractive,  using the lunar propellant option. 

That does require emplacing significant propellant manufacturing infrastructure on the moon,  in turn pre-supposing that ground truth will verify the presence of easily-recoverable ice resources there.  It will be far easier to construct infrastructure on the moon,  which is only 3-5 days away,  than it will be on Mars,  which is 6-9 months away.  That is why selecting option 4 is the best choice available,  once one presumes that at least some propellant-making infrastructure at all must emplaced on Mars.

The other issue is exactly where those easily-recoverable ice resources will be located on the moon.  For this study,  I presumed equatorial locations.  If polar,  the higher dV will raise the launch-and-ship/delivered propellant ratio from 4.77 to something a little higher.  But it will still be attractive. 

Figure 8 – Propellant Quantities Comparisons For Ship-Up From Earth vs Ship From Moon

The manufacturing rates comparison is given in Figure 9.  It tells basically the same tale as Figure 8,  plus the far more reasonable rate numbers that will in part size any propellant-making infrastructure on the moon and on Mars.  These are simply the total quantity numbers divided by the 52 month interval between successive missions flown by the “big ship”,  as indicated in the original Ref. 1 article.  

Figure 9 – Propellant Rates Comparisons For Ship-Up From Earth vs Ship From Moon

“Tanker Flights” Required

This study presumes the use of the SpaceX Starship/Superheavy as the supply tanker for shipping propellant up from Earth’s surface to LEO,  at 171 metric tons deliverable per flight.  To fill the NERVA-powered “big ship” in LEO from the surface requires something like 51 tanker flights!  Plus something similar to refill the tug. 

At 500 tons per flight from the moon,  something like only 17 or 18 transfer/ferry stage flights are required to LEO from the lunar surface,  which is far more reasonable to expect!  Doing propellant from the moon really does make a large improvement for this kind of “big ship” transport mission.  It just presumes the necessary easily-recovered resources really are there,  on the moon,  for us to exploit.  That is not yet determined to be true with real ground truth.

At Mars,  this study presumes the SpaceX Starship is flown single stage,  at about 200 metric tons delivered to LMO.  Something near 12 tanker flights are needed at Mars to refill the “big ship” while it is there.   That’s not too bad,  really!  This also presumes the easily-recovered ice resources really are there to exploit.  That still requires confirmation with real ground truth,  although the remote sensing is promising indeed.

The tanker issue is affected by the 500 ton choice I made for sizing vehicles.  Fewer flights are required if that offload-payload is larger,  but the sized vehicles are also larger,  and because the ferry stage has to land with the transfer stage as its payload,  the square-cube scaling laws versus intrinsic material strengths get involved in the design.  There is an unaddressed optimization lurking behind that question.

Explanation Of How These Stages Operate

Just to make these concepts perfectly clear,  see Figure 10.  The ferry stage never leaves the moon.  It waits in LLO,  after launching with the full transfer stage,  until the transfer stage arrives in LLO,  now empty.  The ferry stage rendezvouses and docks,  then carries the transfer stage back to the lunar landing site,  where both are refilled with propellants made on the moon. 

The transfer stage is full for its departure burn from LLO.  It does make a course correction burn,  then an arrival burn into LEO.  In LEO,  500 metric tons of propellant are off-loaded for eventual loading into the “big ship”.  The transfer stage then burns to depart LEO,  makes a small course correction,  and then an arrival burn into LLO,  which depletes its propellant.  The ferry stage then docks with it,  and takes it to the lunar surface for refill of both stages.

The transfer stage has the larger dV requirement,  but the lower burnout mass,  by far.  The ferry stage has a substantially lower dV requirement,  but has the much higher burnout mass,  carrying the transfer stage as payload,  particularly at launch,  when the transfer stage is full. 

Figure 10 – Illustration of How These Stages Operate

Some Notions of the Engine Thrust Requirements

I did take a rough shot at sizing actual engines for these stages.  The transfer stage never goes anywhere but out in space,  in orbits about Earth and the moon,  and the transfer orbit between them.  I used a time limit on the burn to ensure it is impulsive.  The 6 minute figure I used is more-or-less arbitrary,  but falls in the range of 5-7% of the orbital period about the Earth or the moon. 

The dV divided by that time is an acceleration needed,  which worked out to be between 80-90% of a standard gee.  That and the max mass,  sized the max engine thrust.  The same acceleration applied to the min mass provided an estimate of min thrust.  I chose an engine thrust and a number of engines such that max thrust occurs with all engines running near 100% throttle,  and the min thrust with one engine running at roughly 50% thrust.

The ferry stage sizes more by the kinematics of the takeoff fully loaded.  To get good kinematics,  the thrust to local weight ratio should equal or exceed 1.5,  as a really good rule of thumb.  I used 2 for this.  And again,  I sized the max thrust per engine and number of engines at 100% setting,  and the min thrust near 50% setting on only one engine,  in turn acting upon an unfactored weight,  which allows it to settle for landing.

One can always argue with my exact numbers,  but that is what I did.  See Figure 11 for the results.  

Figure 11 – Rough Estimates of Engine Thrust Requirements for These Stages

Misc. Remarks

An unaddressed issue remains,  one which I chose not to address here.  The transfer stage is going to need to execute a rendezvous and dock procedure with either the “big ship” or an on-orbit propellant depot.  It needs to do this,  in order to offload the 500 tons of propellant usefully. 

I did not include a rendezvous-and-dock allowance on the dV value I used to size this stage.  However,  the course correction budgets are probably overkill,  so in that sense,  I have it “sort-of” covered.  That is why I chose not to go back and change all these numbers,  just to include that allowance.

Conclusions

#1. Lunar-made propellant shipped to LEO would seem to make many of the orbit-to-orbit “big ship” transport scenarios far more favorable in terms of propellant quantities and rates.  This is a mission nuance every bit as important as the space tug concepts explored in Ref. 1.   

#2. To do this lunar-made propellant thing requires emplacing significant propellant-manufacturing infrastructure on the moon (and also on Mars).  Any such facility,  at either location,  will need to produce a few hundred to several hundred tons of propellant each month.

#3. It seems quite unlikely that LCH4 can be produced on the moon,  because of a lack of easily-recoverable carbon;  LH2 and LOX seem very likely,  provided that real ground truth reveals easily-recoverable ice resources are available. “Easily recoverable” does not mean 1-or-2% moisture content in regolith,  it means more-or-less massive buried ice deposits.  That’s a few hundred kilograms per day,  or several kilograms per hour,  guys!  The grams-per-hour demonstrator hardware items are simply several orders of magnitude outside the ballpark we need to be playing in. 

#4. LH2 has a much higher boiloff risk compared to LCH4.  LOX-LH2 chemical is not very attractive for the “big ship” to Mars,  precisely because of that risk,  and the months-long flight times.  If that issue had a ready-to-fly solution,  the outcome would be different:  LOX-LH2 chemical would be feasible,  and would fall in between the LOX-LCH4 chemical and the LH2 NERVA options evaluated in Ref. 1.

#5. LH2 would support NERVA or any of the gas core concepts for the “big ship” propulsion;  it might even support electric,  if a hydrogen-fueled variant can be developed and scaled up.  But,  for any of these options,  it is simply required that the LH2 boiloff risk can be handled acceptably-well!  We need a ready-to-fly solution to this problem!  We do not yet have one!

#6. This analysis presumed an equatorial location for the propellant station on the moon.  Things look less favorable,  but very likely still attractive,  if a polar location is really required,  driving-up the dV required surface-to-LLO,  and thereby raising the ratio of launch-and-transfer propellant to the propellant deliverable on-orbit in LEO.  

References

#1.  G. W. Johnson,  “Earth-Mars Orbit-to-Orbit Transport Propulsion Studies”,  posted 2 April 2022,  on http://exrocketman.blogspot.com.  (There is an associated PowerPoint presentation.)

#2.  G. W. Johnson,  “A Concept For an On-Orbit Propellant Depot”,  posted 1 February 2022,  on http://exrocketman.blogspot.com.

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