Orbital Mechanics Tricksiness to Increase the Frequency of TLI Opportunities for LEO Depots

[Update 2/10/09 11pm: I’m actually pretty sure I made a mistake here, and my entire idea may be more or less worthless. Basically, the problem is that for any elliptical trajectory, you have a “line of apsides”, which basically is a line connecting the apogee and perigee. In order to have a good lunar transfer, you need that line of apsides to basically pass somewhere close to where your orbital plane and the lunar orbital plane intersect, with the moon being somewhere near that line. Unless I’m missing something, this may invalidate the whole idea, and you may really be stuck with a situation where a given depot only has a 2-4 narrow windows per month for a good lunar departure…until I can get verification from someone who knows more about orbital mechanics, you should probably ignore this idea.]

I’ve had an ongoing debate with a friend (“vanilla” from NASASpaceflight.com’s forums) about the utility of LEO propellant depots compared to doing a Lagrange Point Rendezvous architecture.  Vanilla is of the opinion that an architecture that launches crews, cargo, propellants etc directly to L2 (entirely bypassing LEO) is the way to go, while I favor having depots in LEO to aggregate propellants first.  Vanilla is a smart guy, and he raised a legitimate concern about using LEO stations and depots as departure points for cislunar missions–infrequent launch windows.  Mike Griffin also says the same in some of the presentations he gave before becoming a NASA admin, and various articles over the years about lunar transportation have also pointed out the issue in more detail.

The Issue with In-Plane Departure Opportunities
The basic challenge is that in order to keep delta-V requirements reasonable, you really want to depart for the moon when the moon is in the same plane as the orbit you’re departing from.  When you’re in LEO, say at a depot or staging station, you’re in a specific orbital plane, and that plane and the Moon’s orbit precess at  given rates resulting in the moon only crossing through a given orbit only a few times per month.  How frequent that is depends on a bunch of factors, but the typical frequency is every ~9 days.   Launching directly from the surface however doesn’t have this constraint, because you don’t establish your orbital plane until you’ve actually launched, and the plane you would enter from a given launch site will line up with the moon once every day.  If you’re trying to go to a station in LLO as opposed to a lagrange point, your windows get even more constrained compared with a ground launch to L1/L2.

Now, I’d love to be in a situation where two-three flights to the moon per month was considered a stifling constraint.  It’s a problem I’d really love to have.  But there are some additional considerations that make the constraints a drag even for early lunar development.  Infrequent launch windows means that scrubs are a bigger problem.  When your opportunities are rare, and scrubs can delay things significantly, it’s a lot easier to get “Go Fever” and end up taking more risks.  Also, earlier in our development of cislunar transportation systems (especially reusable ones), there will likely be a higher probability of scrubs as we work out the bugs in the system.

Multi-Burn Departure Options
So, for the last year or so since vanilla mentioned this constraint to me, I’ve had the problem in the back of my mind, trying to figure out if there was a way to give vehicles departing LEO stations more flexibility.  Saturday morning, I rediscovered a good idea from 40 years ago that looks like it can help retire this issue, and maybe even give LEO-based vehicles more launch flexibility than ground based systems.  All without adding very large performance or flight time penalties.

The idea I came up with is to move from a single-burn departure to a two or three-burn departure.  In case you don’t know what I mean by that, a traditional Trans Lunar Injection, the lunar stack in LEO does a single long engine burn that places the stack in a trajectory that passes near or tries to impact the moon.  Once you get close to the moon, you do a second burn (a Lunar Orbit Insertion burn or a Lagrange Point insertion burn) to deliver the stack to its destination orbit.  My idea was to instead go with a three-burn departure that uses an intermediate transfer orbit, and an apogee plane change.  For this concept the lunar injection process would take a form like this:

  1. Sometime after departing the LEO station, the stage would perform a burn into an elliptical orbit with a high apogee–possibly as high of an apogee as GEO (which would be ~2500m/s).
  2. At apogee a small plane change is performed (for GEO birds launched from Canaveral, the 23.8 change usually costs ~350m/s) that puts the stage into an orbital plane that will intersect with the moon at perigee.
  3. At perigee the remainder of the TLI burn is completed (~500m/s for a GEO apogee orbit in step 1), and the mission is continued as normal from there.

Now, there are plenty of subtle nuances involved with all of this (probably less than half of which I fully understand myself), but that’s the basic concept.  This is a complicated enough problem, that some enterprising PhD student could probably write a full dissertation on how best to balance the tradeoffs and timing issues for such trajectories.  However, it would appear pretty likely that such a solution would give at least daily low-cost opportunities for departure, and for some orbits you might even be able to get more frequent opportunities than that.

As is often the case in life, there are some drawbacks to this approach compared to the traditional method, such as:

  • Delta-V penalties–while the velocity expended to enter the transfer orbit wouldn’t be wasted, and would serve as the first part of the TLI burn, the plane change delta-V would be wasted.  So, there will be a tradeoff of performance vs. longer trip times.
  • Added mission complexity–while transfer orbits and apogee plane changes are actually quite common (all GEO missions launched from the US have to do this), it does add more things that can go wrong in a mission.  Depending on the reliability of your transfer system, and if you have engine-out capabilities, this could have a non-negligible impact on the probability of mission success
  • Van-Allen Belt Transits–you end up passing through the Van Allen belts two more times.  While this isn’t going to be a big issue for propellants or cargo, manned vessels might require a “storm shelter” to keep the radiation levels down–but such “storm shelters” are good ideas anyway for trips beyond the earth’s magnetosphere.
  • Trip Time Increases–this one’s pretty minor.  For a GEO altitude transfer orbit, you’re talking about adding ~10hrs to a 70-100 hr trip (ie less than 15% increase).

Of these concerns, the main two I’m worried about are the added complexity and the extra Van Allen crossings. But the added risks, with reliable engines like the RL-10 are not that great, and the complexity is on a level that seems to be acceptable for owners of billion dollar satellites, so it can’t be that bad of an added risk.

Other Benefits

One of the key benefits of this approach is that it allows you to get better utilization out of your cislunar transportation infrastructure.  Coming from a manufacturing background, its often easy to underestimate the value of being able to level the load, reduce lead times, allow for smaller more frequent deliveries and smaller move batches.   While turn-time isn’t as absolutely critical for interorbital reusable vehicles as it is for earth-to-orbit ones, it does make a difference.  The more flights per year you can get out of your vehicles and your people, the lower that portion of the mission cost gets.  And with more demand for propellant, that part of the cost equation can be driven down in time as well.

It is also worth mentioning that staging a transfer stage at the point where it’s at a GEO level apogee would make it a lot easier to reuse your cislunar transportation hardware.  I’ll have to run the numbers on that sometime.  But basically, without aerobraking, it’s a challenge to come up with a reusable cislunar architecture that closes easily.  But just like in terrestrial applications, breaking up the TLI/LOI/TEI/EOI delta-V into two stages can possibly make a big difference (round trip delta-V for a non-aerobraking stage is on the level of an SSTO).

Lastly, this is an option that can actually be used both coming and going from LEO and lunar orbit.  If you’re going to a lunar polar orbit station for instance, you can split your LOI into three burns.  One slows you enough to capture into a highly elliptical lunar polar orbit, followed by an appropriately timed plane change, and your final braking burn to bring you down tot he LLO station’s orbit.  You can do the reverse process to give you anytime return from an LLO outpost, and getting up to an altitude where the plane change is cheap is a lot quicker on the moon.

Basically, if I’m understanding this right, these tools can help take a lot of the orbita-mechanics-induced  pain out of moving goods between LEO and LLO transportation nodes.

What do you all think?

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Jonathan Goff

Jonathan Goff

President/CEO at Altius Space Machines
Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and is the founder and CEO of Altius Space Machines, a space robotics startup in Broomfield, CO. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.
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39 Responses to Orbital Mechanics Tricksiness to Increase the Frequency of TLI Opportunities for LEO Depots

  1. Eric Collins says:

    This is brilliant. Most of the expense that comes with plane changes is trying to change the momentum vector of the spacecraft to point in a new direction. At low altitudes, you have high velocity, and therefore high momentum. By boosting your altitude, you transfer you kinetic energy to potential, reducing your velocity, and making momentum changes much less drastic (and thus much less expensive). Excellent.

    Of course, there’s nothing special about GEO altitude for performing this maneuver. The actual apogee point could be selected in such a way as to minimize to total delta-v over all three burns. There is also nothing special about LLO as the final destination either. This same technique could be used to send your spacecraft to the Lagrange points, or even to properly phase a mission departing cislunar space. I guess it all depends upon the urgency of the departure and if it is worth the added expense.

    Now it would be very interesting if one could make up some of that delta-v lost to changing planes with a gravitational boost from a perigee slingshot maneuver. I’ve no idea if such a maneuver would be possible in this context, but it might be worth looking into.

  2. Eric,
    The main reasons I used GEO altitude was because I had the numbers for it. Not being a real orbital mechanics virtuoso, and not having access to something like STK Astrogator, or SEI’s Bullseye, I didn’t have a good way of running other numbers. And yes this is applicable to a lot of other spacecraft. Henry Spencer was telling me that the ill-fated “CONTOUR” spacecraft of about a decade back was using just such a trick to put itself on a trajectory that was impossible to reach otherwise from its launch site.

    Also running the performance numbers last night, using two Centaur stages, I was getting an available first stage velocity that would put the staging point a lot lower than a GTO transfer orbit…though admittedly, I don’t know with that low of an orbit if you could really get the plane change delta-V down low enough to do everything you’d want to…*sigh* I really wish I knew how to crunch the numbers better.

    As to your gravity slingshot maneuver…I don’t know. But what I do know is that you’ll be: a) doing a lot more of your burn lower in the gravity well, and b) doing a lot more of it with a shallow flight path angle, both of which should help reduce gravity losses for the mission a bit. Most upper stages and transfer stages end up having pretty crappy T/W ratios, which means their burns end up being less impulsive than would be preferrable. By splitting the burn into two main segments, both around perigee, that should help a bit. A little more Oberth effect, and a little less gravity losses. I doubt they would entirely pay for the change, but I’m not sure. Anyone with orbital mechanics skillz is invited to run the numbers.


  3. Martijn Meijering says:

    Hi Jon,

    Sounds like an interesting concept. But if you are planning to have a depot / gateway at L1, do the plane considerations still matter? As far as I know, delta-v to L1 doesn’t depend on inclination. Or at least not strongly. In fact going out to L1 and moving a constellation of satellites to LEO with different inclinations has been seriously proposed as an efficient mechanism. But you may still have the timing constraints. I’m still in the process of learning orbital mechanics, so I can’t say for sure.

    Another idea that I find very interesting is Belbruno trajectories. The idea is to go beyond two body dynamics and use three body trajectories. (Three celestial bodies + 1 satellite). On these trajectories you launch a satellite to SEL1, where its orbit undergoes serious influence from the sun and then ballistically (!) on to LLO. In other words, you do not need a lunar orbit insertion maneuver. The initial insertion maneuver to SEL1 is more expensive than a TLI, but that is more than made up for by not needing a LOI. I suppose you could devise Belbruno trajectories to the lunar L-points too.

    I’ve been thinking about a possible variant, but I’m not sure it would work economically. The idea is to launch the craft on a highly elliptical trajectory (with as little delta-v as you can get away with) so it will spend a lot of time away from the earth. After insertion into this orbit, you switch to ion propulsion and try to execute a continuous “maneuver” that will raise your perigee to above the van Allen belts. During this period, you are in a hurry, because you have to raise your perigee enough before you reach it, or you’ll cross the belts multiple times, which is exactly what you don’t want to do with SEP because it wears out your solar panels. If think that if you choose a sufficiently eccentric initial orbit, you can make this work, but I don’t know whether it will be cheap enough. You may end up spending more on your initial orbit than you save with SEP.

  4. Martijn Meijering says:

    It just occurred to me that it may not be necessary to avoid crossing the van Allen belts more than once, as long as you don’t stay there very long. If you only cross them around perigee, you will not be spending much time inside them, since angular velocity is so much higher then. So you may get away with a less eccentric and cheaper initial orbit than I had thought.

  5. Martijn Meijering says:

    I think this paper describes what I was thinking of in all its mathematical glory:


    This stuff is complicated…

  6. MG says:

    Why not inject directly toward the moon, and do a plane change near L1? That way, the mass of the stack is less than at the apogee of a high Earth transfer orbit.

    Also, one of the “tricks” is that the TLI can have a small (1-2 degree) inclination change with almost no dV cost… the inclination change dV goes with the sine of the angle between the existing orbital plane and the intended one, while the loss in angular momentum goes with 1- cosine of that angle.

    One can presumably do the same thing at the lunar insertion burn.

    For a patched conic analysis, this would be a spreadsheet analysis. For more precision… well, that’s outside my current level of knowledge.

  7. Jonathan Goff Jonathan Goff says:

    The problem is that in order to get anywhere near L1/L2, you pretty much want to have your departure plane fairly close to lined up with the Moon anyway, I think. If you depart at a time when the the moon was say at the furthest point from intersecting your plane (like it is in the bottom of pg 112 of the second link I provided), your orbital plane would take you way “above” the moon. I guess you could do a plane change out there, along with a maneuver to rotate your semi-major axis down (ie a burn either before apogee, or at apogee with a substantial radial component)….but I don’t think it would really end up actually saving you anything. Of course, without good tools, I have no way of knowing for sure. But my intuition says it looks like it would be a longer trip, with more delta-V involved.


  8. Dennis Wingo says:


    By far very few launches are to the traditional GTO orbit anymore. The Atlas goes out as far as 141,000 km to do its GEO plane change and I strongly suspect that your suggestion here would benefit from that change.

    There is another consideration here. If the plane in which you are leaving from is at a high inclination, oh lets say 51.6 degrees, and you are looking to go into a 90 degree lunar orbit, the delta V is less than a similar lunar orbit from 28.5 degrees. Since 90 degree polar is by far the desired orbit for any serious development, the high altitude plane change makes even more sense.

  9. Dennis Wingo says:

    Oh, the goal here is at least a bi weekly transfer between LEO and LLO or L1/L2. This is where the Reusable Space Vehicle (RSV) makes a lot of sense.

  10. Ken Murphy says:


    You might want to check out ‘The Lunar Base Handbook’, which has a section in Chapter 6 on Earth-Moon transportation that addresses a lot of these issues (like the 6-11 day window for Moon orbital declinations).

    You should have a copy…

  11. Jonathan Goff Jonathan Goff says:

    Yeah, I actually had that out on Saturday when the idea first popped up. The Lunar Base Handbook you gave me wasn’t as clear as some of the other sources. But I can take a look at it again.


  12. Jonathan Goff Jonathan Goff says:

    I didn’t realize Atlas went up that high to do the plane change. That’s good to know.

    As for “the Reusable Space Vehicle”, I agree that reusable space vehicles are what I’m driving at (that’s one of the big benefits of propellant depots).


  13. Dennis Wingo says:


    Propellant depots are a somewhat later spiral in the total cislunar infrastructure development process. As this is one of my hobby horses, here is how it would unfold.

    An RSV is built at ISS from components brought up by the Shuttle, Falcon 9 and possibly EELV. Here are some of the aerocapture numbers from papers located on ntrs.nasa.gov
    The mass is about 15,000 kg fully loaded and an upper stage brought up by the Shuttle C.

    A waiting fully fueled Altair is in orbit around the Moon, also brought up by a Shuttle C directly.
    The RSV has enough propulsive capability for the Trans earth injection and to null the errors of the aerobraking maneuver.

    After a while, and ISRU production ramp up, The Altairs are refueled on the surface, eliminating the need for the Second Shuttle C flight.

    The Altairs, operating as a cargo SSTO (Lunar), brings up 25 tons of fuel to refuel the RSV in LLO, eliminating the need for that fuel to be brought all the way from the Earth. There is enough extra fuel to take care of the aerobrake errors.

    Fuel packs, manufactured on the Moon, are brought up with the Altair cargo vehicles to provide enough fuel for the RSV to return to lunar orbit without any additional Shuttle C flights.

    Shuttle C is eventually retired in favor of an RLV. The Shuttle C upper stages are recovered and reused for future missions.

    This way you don’t need any LEO fuel depots, only in lunar orbit. The benefit is huge. The only caveat is how much hydrogen there is at the Moon. If it is hydrogen poor the the Shuttle C upper stage goes away, replaced with a hydrogen payload that completes the fuel loop.

    Far more efficient than this moronic ESAS or its younger brother DIRECT.

  14. Bob Steinke says:


    I want to make sure I understand your architecture.

    First, get an RSV into space (possible in-space construction).

    Then there is an initial phase where each mission looks like this:
    1) Shuttle C launches an expendable upper stage.
    2) This upper stage attaches to the RSV and does the TLI burn.
    3) The RSV goes to LLO. What does the LOI burn? Is it the upper stage or the RSV?
    4) Separately, an Altair lander is placed in LLO by a Shutle C.
    5) The RSV meets up with the Altair.
    6) Altair lands on moon
    7) Altair takes off again and goes back to LLO to meet up with RSV.
    8) RSV does the TEI burn.
    9) RSV does aerobraking with propulsive correction.

    At this point, you are almost back where you started. You have an RSV in LEO and an Altair in LLO, but they have expended their propellants. How do they get refueled in this initial phase before ISRU ramps up, or are they expendable during this phase?

    Then, once you have ISRU producing propellant on the moon, each mission has an additional step:

    The Altair refuels on the moon, and there are multiple Altair flights per mission taking propellant to a LLO propellant depot. When the RSV is in LLO it loads enough propellant at the depot for it to do the TEI burn, the propulsive corrections to aerobraking, the TLI burn, and the LOI burn so it can get back to LLO to be refueled and doesn’t ever need any more fuel from Earth.

  15. Dennis Wingo says:

    3) The RSV goes to LLO. What does the LOI burn? Is it the upper stage or the RSV?

    LOI by RSV

    At this point, you are almost back where you started. You have an RSV in LEO and an Altair in LLO, but they have expended their propellants. How do they get refueled in this initial phase before ISRU ramps up, or are they expendable during this phase?

    Would be expendable or stored in orbit for later use until ISRU is up and running. A trade would need to be done whether it makes more sense for the Altair to be two stage or SSTO. The current Altair descent stage makes a great SSTO for 25 tons to LLO and return to the surface.

    We also have to use the real Shuttle C numbers, not the ones made up by the Direct crowd.

    With the improvements that the SRB gets already under the Ares program that can be moved back over to the STS stack and the superlightweight ET the Shuttle C will have the same performance as the Shuttle C/ASRM. Here are the numbers

    156,600 to 220 nautical miles 28.5 degrees (-6.3% for 51.6 degrees)
    (146,734 lbs)

    This does not include any materials improvements to the Shuttle C structure which should get about another 5-10,000 lbs of performance.

  16. john hare says:

    Unless I’m missing something, this may invalidate the whole idea, and you may really be stuck with a situation where a given depot only has a 2-4 narrow windows per month for a good lunar departure…until I can get verification from someone who knows more about orbital mechanics, you should probably ignore this idea. And yes, I do feel retarded–why do you ask?]

    Would you please retract that retarded statement. You have one post in a bunch that may not work, and I have one in a whole bunch that might work. If that makes you retarded, then I must aspire to the heights of becoming a drooling idiot.

  17. John,
    Fair enough.


  18. Andrew Swallow says:

    An architecture that uses a Shuttle C means that we have to wait for a Shuttle C to be developed. NASA tends to add lots of extras to big projects so that could take a long time. Any chance of getting the equipment lifted on smaller launch vehicles?

  19. tom says:

    Yes, the perils of 2-D orbital mechanics in a 3-D planetary system. I’m not sure what you mean by the line of apsides comment though. If you’re in an equatorial orbit, the LEO orbit will cross the moon’s plane twice a day.
    If you do your first burn (TLI1) in LEO, your perigee will be 3 days out at the equator. At perigee or near it, you do a second burn (TLI 2) which can place you into a second, larger elliptical orbit that intersects the moon’s path, anywhere from 0 days (for when the moon crosses the equator) up to 14 days (for when the moon is far from the equator.) At intersection the difference between an in-plane and out-of plane LO circ burn is negligible.
    So it’s not your launch windows that shrink, it’s your 3 day transfer windows. As long as you’re willing to extend to a week or 10 day transfer, you will get between 30-40 windows per month, with about a 1 week- 10 day period where it’s prohibitive.
    Even if you insist on a less than 7 day transfer, I think you still get 14-20 opportunities per month.

  20. tom says:

    edit ** that should say “will cross the moon’s plane twice an orbit, not a day”

  21. Eric Collins says:

    Let’s see if I understand the problem correctly (just thinking out loud here). You propose to accomplish an efficient plane change by making the plane change burn as far out of the gravity well as possible (at apogee). The most efficient plane changes also involve thrusting in a direction that is perpendicular to your current orbital plane and this is done at the ascending or descending nodes (the point where your current orbit passes through the plane of your desired orbit).

    Assuming you start out in a near circular orbit in LEO, then you will want to do your first burn at the ascending/descending node when your current orbit intersects the plane of the desired orbit (i.e. the plane of the moon’s orbit). That position then becomes the perigee, and the point on the opposite side becomes the apogee. This establishes the line of apsides through the ascending and descending nodes which makes it possible to do the plane change burn at apogee.

    After the plane change burn, the perigee and apogee are still in the same locations. If I understand you correctly, you want to do your TLI burn as close to perigee as possible, but the timing has to be just right so that the moon arrives at the opposite side of the orbit at the same time as your spacecraft. This is what you meant when you said the line of apsides must line up close to the moon.

    Therefore, the time limiting factor in all of this is that the line connecting the ascending and descending nodes must be properly aligned with the moon at the time the first burn is initiated. Unless I am mistaken, this would happen roughly twice a month, with maybe a few orbits (in LEO) worth of launch window at each opportunity. Of course, you could accomplish the transfers at other times, but they would cost you more propellant.

    Did I miss anything?

  22. Eric,
    Exactly. The problem is though that in situations where those apsidal lines line up in that manner, you don’t need to do a plane change in the first place. For an in-plane transfer orbit, all you need is for your line of apsides of your departure trajectory to intersect the moon’s orbital plane at a point about 3 days ahead of the moon, so that when you reach apogee, the moon was there.

    If you are using plane changes just at apogee, and TLI burns just at perigee, you can only slightly widen the launch windows using my original idea, not make it so you have unlimited windows like I had originally thought. There may be some tricks that Henry Spencer has mentioned offline about doing a plane change/apsidal shift burn at a point other than apogee, but I don’t know how much more that buys you–and that’s getting to orbital mechanics at a level beyond my comfort zone. I’m trying to study-up on the stuff, but having a user friendly orbital mechanics program that I could try out different things to intuitively see what happens would be *super* helpful.

    The reality seems to be (at least for now) that if you want frequent LEO to Lunar vicinity departure dates, you’ll need to have multiple departing stations. Not a heartbreaker or a dealbreaker, it just means that early lunar commercial transportation may be limited to 3 windows per month.


  23. Eric Collins says:

    I’ve probably mentioned it before, or you’ve probably already heard of it, but Orbiter is a very good spaceflight simulator. I knew a little bit about orbital mechanics from my undergraduate days, but this program really brought the concepts home for me in a much more visceral context.

    There is also a quite active development community focused on adding additional space crafts, space stations, and planetary bases to the program. You could probably get the XA-* series up and flying in Orbiter without too much difficulty. I see that someone has already done a module for Armadillo’s quad vehicle.

  24. Martijn Meijering says:

    Eric: excellent recommendation!

    Jon: My understanding is that you have daily launch opportunities to L1 (don’t know about L2, I suppose the situation is similar), both from the surface and from LEO. At least that’s what the Jupiter documents say. Also, a plane change at L1 is supposed to be cheap, so whichever inclination you start from is OK. So for an architecture that does L1 rendez-vous and is prepared to pay the delta-v penalty for that, we don’t have a problem.

    So as far as I know, you could easily start from say the ISS, provided it has the capacity to accommodate a small number of extra crew for a couple of days. Eventually that means you could launch crew purely commercially, say on a Falcon + Dragon.

    Can anyone who’s knowledgeable on orbital mechanics confirm if this will work?

  25. Martijn,
    I don’t think you get daily opportunities to go to L1 from LEO. At least as far as I understand things (which has been demonstrated to be somewhat deficient), I don’t see how you could get to L1 any more frequently than to any other lunar orbit. You still have to have the line of apsides of your departure trajectory intersect L1 by the time your spacecraft gets out to L1.


  26. Martijn Meijering says:


    I don’t understand it either, I’m still working on the basics. But I found another link that agrees with the DIRECT documentation. It may not be an independent source, maybe the DIRECT people got it from here:

    Strategic Considerations for Cislunar Space Infrastructure

    L1 lunar surface
    “A number of orbits are possible in the volume about L1. […] Transportation to and from any point on the lunar surface can take place at any time; launch windows are unconstrained by orbit phasing relationships.”

    L1 earth’s surface
    “There are two launch windows associated with the L1 station that must be considered: launch from the Earth’s surface and departure from the L1 station for an interplanetary trajectory. For the first situation there is roughly a once-per-day launch opportunity to the L1 point from any launch site on the Earth, if no other constraints are placed on the trajectory.”

    I guess it’s high time to write some code to see how it all works…

  27. Martijn,
    Yeah, there’s a big difference between launch window frequency from the earth’s surface to L1 and from an LEO station to L1. The LEO station constrains your starting plane in a way that you get less frequent opportunities, but with a departure from the earth’s surface, your launch plane hasn’t been constrained until you launch into your parking orbit.

    Unfortunately, in order to make propellant depots really work, you’ll have to live with the constraints that places on you–a tradeoff that I think is entirely worth it.


  28. Martijn Meijering says:

    I would suspect (but what do I know) that opportunities to L1 would be at least a bit better than those to the moon. The delta-v is smaller and I’d think the variation in delta-v would be too. But even if orbital launch opportunities to L1 aren’t much better than to the moon, what if we threw L4 and L5 and maybe even L3 into the mix? I’m assuming without much evidence that L2 opportunities would be similar to those to L1. L4 and L5 are 60 degrees away from the moon, so that might help.

    High time to learn more about orbital mechanics!

  29. Martin,
    Your point about L4/L5 is interesting. It might be possible to go to L4/L5, then go from there to LLO…the extra cost would be a little less than 1km/s, and you would get much more frequent windows…but with the added time of flight, I’m not positive it’s worth it. You’re probably talking about 3 days extra, so you have to balance that against just waiting 3 days later to start. But it is an interesting idea.

    I’m starting to read up on orbital mechanics some more, but I really need to find some cheap software where I can experiment a bit with different trajectories to see if I can get a better intuition.


  30. Martijn Meijering says:

    As always, it depends on what goal you are trying to achieve. If it is having a new market that is accessible to new, relatively small players (a worthy goal imo), then you’re ok for Earth to LEO. Small players can launch to LEO. Other players can transport stuff or people from LEO to Lagrange points.

    For transport beyond LEO, small players would need to refuel at a depot. For cargo the resulting delay should not be a problem. For passengers it might be. But assuming that most of the traffic would be tourism, a delay might not be a problem, as long as you can stay a relatively comfortable space station. Think of it as a cruise. After the initial excitement of a launch, you get to enjoy the view from LEO for a couple of days. Then you move on to a Lagrange station, then you fly around the moon a couple of times before heading back to a Lagrange point and then back to Earth, possibly via the LEO station. All of these destinations have different touristic qualities. Sounds exciting!

  31. Martijn,
    I think we’re talking past each other a bit. What I’m saying is that for a given depot, you have cheap, no-trickiness departure opportunities every ~9 days (plus or minus some depending on inclination and altitude of your station). Say you’re at the worst position, 4.5 days out from your next in-plane launch opportunity. Your choices are either a) launch right away and do something tricky that will take extra time and delta-V, or b) wait another 4.5 days, and launch then with the non-tricky, lower delta-V orbit.

    If the added time is only 12-24 hrs, then it really buys you something to be able to leave whenever you want. But if it adds 4 days to your trip, you haven’t gained anything. Your payload arrives at the moon at about the same time both ways, but in one way you have a simple two-burn trajectory, and in the other you have a complex trajectory with more delta-V requirements…

    So my point is any “launch any time from an LEO station” approach has to not only cost little extra delta-V, but it also needs to not take so long that you’d be better off just waiting a few days for another launch window.


  32. Martijn Meijering says:


    “but it also needs to not take so long that you’d be better off just waiting a few days for another launch window.”

    I can see why that would be so if you had to go to the moon in a hurry. What application are you thinking of?


  33. Martijn,
    I still think we’re talking past each other. What I mean, is if you have to choose between waiting 4 days, then doing a 3 day transfer that costs ~4200m/s to get from LEO to LLO, vs leaving right away for a 7 day transfer that costs ~5000-6000m/s of delta-V to go from LEO to L4/L5 to LLO…there wouldn’t really be much point of taking the more roundabout route. Now, if the second one took more time, but cost a lot less propellant, that would be one thing. But slower (or just as slow), but a lot more propellant, and it isn’t actually gaining you anything.


  34. Joey says:

    Maybe I missed the conversation but here goes. As I skimmed over most of the comments I didn’t see this mentioned: why isn’t the LEO depot just in the same orbital plane as the moon, or at least near it? As far as I know the Moon has an orbital inclination of 5.145° to the ecliptic (Earth’s orbital plane around the sun as you probably know) which means it varies between 18.295° and 28.585° relative to the Earth’s axial tilt of 23.44°. So if you have a launch site at less than 18.295° latitude you should have 2 opportunities per day to launch into the same orbital plane as the Moon. Once in this orbit you basically get a launch window to the Moon/L1/L2 every orbit. The stability of the orbit over the long term is something that seems doable, as the precession of the lunar nodes is on a 18.6 year cycle and it seems like if your going to build a propellant station you could afford to have an electric propulsion system to slowly precess the orbit over that long period. But even if you didn’t want to do have a correction system, you could just place your LEO depot exactly on the ecliptic (with a constant 23.4° inclination to the equator). Slowly the Lunar plane would precess with the inclination for each launch from your LEO depot changing between a min of 0° and max of 5.145°. Even with the really high delta-v you need to do plane changes in LEO, 5.145° means you only need about 700 m/s max. And it seems like 5.145° is low enough that you could do some kind of mid course correction anyways, but I don’t know enough to say that with confidence. So to summarize, as far as I can tell as long as you put your LEO depot near the ecliptic plane you’re orbit is never inclined more than 5.145° from the Moon’s orbit, and if you have active control it could probably be synced.

  35. Martijn Meijering says:

    Bump. Can anyone comment on Joey’s suggestion?

  36. Eric Collins says:

    That sounds good. For lunar missions, you would like to get into an orbit as close to the lunar plane as possible as soon as possible. Ideally, we’d like to have a LEO station in an orbit coplanar with the moon or the ecliptic, from which lunar or planetary missions could be staged.

    Unfortunately, we don’t have any launch facilities far enough south to take advantage of these low inclination orbits. Cape Canaveral is at about 28.6 degrees north latitude and this is currently the only launch site from which the US can launch crewed missions. SpaceX has been able to launch from the Kwajalein atoll at about 9.1 degrees north latitude, but as far as I can tell, they are currently not able to handle anything larger than a Falcon 1. Probably the most favorable site is the ESA’s launch site in French Guiana at about 5 degrees north latitude. This site can launch the Arianne 5 and is supposed to be able to handle Soyuz vehicles sometime in the near future.

    Getting into orbits with an inclination higher than the launch latitude is fairly trivial. The only penalty you pay is for how much of the Earth’s rotational velocity you ignore by not launching due east. To get into a lower inclination orbit, however, you still have to do a plane change. Hence the discussion above.

    With our present rocket technology, we can just barely get crews into orbit. Once the inclination of that orbit is established (at the launch latitude or higher) it is fairly expensive to make any significant plane changes. Thus if the depots are established in a LEO that can be easily reached from the surface, then perhaps there would be sufficient fuel reserves to make the required plane changes, however, you are now restricted by the phasing (timing) constraints dictated by orbital mechanics.

  37. Joey :-( says:

    Looking up more info about orbital dynamics and its pretty apparent what I first thought doesn’t work. Two words: nodal precession. Launching into the ecliptic at 23.5° and everyday your whole orbital plane spins around the equator 0-9° (depending on altitude and inclination, 100nmi at 0° inclination is 9°/day). So, it wouldn’t take long for nothing to line up. Honestly it makes me mad, too much stuff rotating/orbiting/regressing/ascending/precessing that there’s little you can do to sync it all. 🙁

  38. Martijn Meijering says:

    Some additional thoughts now that I’ve learned a bit more about orbital mechanics.

    Most of the time you cannot launch straight into the moon’s orbital plane from KSC anyway. There’s something called the Saros cycle which causes the inclination of the moon’s orbit to vary with a ~18 year period. For a lot of that time the inclination is below 28deg.

    The competitors to depot centric architectures (aka SDLV architectures) suffer from the same problem because they have to do rendez-vous with an EDS that is launched first and whose orbit precesses too. Launching straight to L1/L2 would obviate that problem, but our SDLV loving friends won’t go there. I think it is for two reasons: 1) L1/L2 are too easy to reach for competitors and 2) AVUS/JUS are so damned heavy that you’d be hauling a bunch of useless metal to L1/L2, which hurts performance a lot. You could avoid this by using a Delta upper stage, but they won’t do this because this invites EELV Phase 1 which will prove their launcher superfluous. Not that they will ever admit any of this of course.

  39. Martijn Meijering says:

    Some more thoughts. The above essentially says that issues with nodal regression aren’t unique to depot architectures, but have to do with LEO rendez-vous which the competition has to do anyway. It can be eliminated as an argument against depots.

    Another consideration is that using the ISS as a gateway station, as it was originally intended, actually helps with these issues. If you launch your crew first and your EDS second, you mitigate boil-off issues (pre-depot) and launch window issues (depot). The crew can stay safely inside the ISS while it awaits the EDS and its launch window.

    ISS also helps commercial space by providing an anchor customer for manned flights and perhaps by sharing costs if tourists are allowed on the ISS, say in an attached Bigelow module.

    Thirdly, having the ISS around hurts SDLV because it eats up money. This cuts both ways of course. We will probably lose the battle to kill SDLV now, but that doesn’t mean we can’t stop it from ever entering service. It also means that even though ISS may be safe for now, it isn’t safe beyond 2020 and it may require action soon if we want to do something about that.

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