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 3rd-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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