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#80
by
kfsorensen
on 16 Nov, 2006 00:58
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With the C3, right ascension, and declination of the hyperbolic departure asymptote essentially "chosen" by the interplanetary trajectory, the spacecraft mission planner then has to ascertain how to meet these goals in a launch campaign. At the risk of over-simplifying the problem, one has to meet three conditions, and one needs to be able to turn three "knobs" to meet this.
Let's consider the example of the Mars rover missions. Given their C3, RA, and DEC that they needed to get to Mars on June 10, 2003, they needed a launch vehicle with sufficient propulsive capability to meet the C3 (launch energy) requirement. They had chosen the Delta II as the launch vehicle even before they started designing the rovers, and they designed to the capability of the launch vehicle with their spacecraft. There wasn't any excess energy to waste on a non-planar injection. On launch day, they needed to be able to meet RA and DEC requirements. DEC was fairly easy--by launching out of Cape Canaveral, they exceeded the required DEC for hyperbolic injection--therefore they could actually have two hyperbolic launch asymptotes that would meet their purposes.
The final targeting variable was right ascension. Since the Earth sweeps through all the values of right ascension as it rotates each day, targeting RA came down to choosing the right time to launch. Launching at the right time, to the right inclination, would give them both the inclination and the ascending node position needed to then target the hyperbolic injection. And the hyperbolic injection did not come immediately--no, they coasted after launch until they reached the point where it was time to inject.
So, to summarize--they needed to target C3, RA, and DEC. They targeted declination by properly choosing the inclination of their parking orbit, which was done by choosing the launch azimuth of the rocket. (of course, there's a performance incentive to keeping the inclination as low as possible). They targeted DEC by choosing what time of day to launch, which then chose their ascending node of their orbit, which set them up for the right RA. And finally, they targeted C3 by the magnitude of the coplanar injection burn they did with the upper stage of the rocket.
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#81
by
kfsorensen
on 16 Nov, 2006 01:07
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Now what about a spacecraft already in low Earth orbit? Suppose you wanted to do an interplanetary departure from orbit?
You would run into this situation if you were departing from a space station, or even if you were assembling/docking a spacecraft together in orbit for eventual departure. Do you still have control over your departure?
Yes, and no. Once again, you want to target C3, RA, and DEC. You've got enough propellant in your departure stage to target C3, and you want to be in position for a coplanar launch. Let's assume that the inclination of your orbit is greater than the DEC of your injection asymptote--in that case, you'll have two injection opportunities. The problem is right ascension.
You see, the orbit that you're in is moving around the Earth in inertial space. This movement is called nodal regression, and it is caused by the oblateness of the Earth and its gravitational effects. The rate of nodal regression varies--it is maximum in a nearly equatorial orbit, and it goes to zero in a polar orbit. It also varies with altitude and eccentricity.
Moving the line-of-nodes of an orbit around on demand is extraordinarily difficult. It is nearly equivalent propulsively to a inclination-change maneuver. No, you really want to wait and let Mother Nature drift you into the right position. But the problem with that is that you may miss the best days of your launch window by not being in position. And this is a real issue for interplanetary injection from an inclined LEO.
Here's an image of what nodal regression "looks like" for an inclined, slightly elliptical orbit, showing the orbit successively displaced around the equator.
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#82
by
kfsorensen
on 16 Nov, 2006 02:16
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To the best of my knowledge, no interplanetary probe has ever been "assembled" in Earth orbit preparatory to hyperbolic injection, and so the "three knobs" of upper stage, launch azimuth, and launch time have been sufficient to allow interplanetary probes to target their departure asymptotes correctly over the years.
But as we imagine interplanetary vehicles that DO require on-orbit assembly/docking/preparation/etc it will become difficult to synchronize constraints on injection and orbital nodal regression such that successful launch occurs. One must seriously consider whether LEO represents the best "staging point" for future missions.
Compare and contrast these options:
1. The Earth's surface. The advantage is that the Earth, through its rotation, sweeps through all values of right ascension each day. Declination can be targeted, within reason, through choosing the right orbital inclination (although there will be a performance advantage to choosing the lowest one). But the entire payload must be launched on a single vehicle, and so the size of the payload will be constrained. Not really a problem for a Mars rover, but not really feasible for a human Mars mission.
2. Low Earth orbit. In LEO, a key mission event (launch) has already been accomplished. Assuming the inclination is sufficiently high, declination can be targeted. But the orbit sweeps slowly through the values of right ascension, with a rate of 2-4 degrees per day. At this slow rate, an unfortunate initial nodal orientation of the orbit could lead to a missed launch window, or a horrible propulsive penalty to try to reorient the orbit.
3. An arbitrary highly-elliptical orbit. From a high-energy orbit of arbitrary orientation, even more of the departure energy has been invested in the orbit, which is attractive. Plane-change maneuvers at apogee could be used to alter orbital inclination and perhaps target declination. But the rate of nodal regression becomes VERY small (a fraction of a degree per day) meaning that an unfavorable nodal orientation can lead to a missed launch window. The CONTOUR mission used a highly-elliptical phasing orbit, but that orbit was entirely selected by the mission planners, and so could be optimum. An arbitrary orbit would not have that advantage.
4. Lunar orbit or the Lagrange points. From these locations, even more orbital energy has been invested, leading to a rather small "kick" required at perigee for injection. The Moon, via its orbit around the Earth, sweeps through all values of right ascension each month. That rate of movement (12 degrees per day) is faster than even the fastest nodal regression in low Earth orbit. By choosing departure time, the proper nodal orientation can be selected to target right ascension. Declination can be targeted with a minimum propulsive penalty by plane-change at apogee. But getting into that highly-elliptical Earth orbit is the real trick. From low lunar orbit, 900-1000 m/s of DV will be needed just to get back into a highly-elliptical Earth orbit. From L1 it will require 700 m/s. But from L2, using a powered lunar swingby, only 300 m/s of propulsion is needed to get back into an elliptical Earth orbit.
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#83
by
Bill White
on 16 Nov, 2006 02:26
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Vanilla, if a Mars mission (for example) were to utilize lunar LOX and depart from L1 or L2 it would still be necessary to reach those L points from the lunar surface, to deliver the oxygen.
Is there any difference in delta V and elapsed time to travel from the lunar surface to L1 versus L2?
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#84
by
kfsorensen
on 16 Nov, 2006 02:35
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Bill White - 15/11/2006 9:09 PM
Vanilla, if a Mars mission (for example) were to utilize lunar LOX and depart from L1 or L2 it would still be necessary to reach those L points from the lunar surface, to deliver the oxygen.
Is there any difference in delta V and elapsed time to travel from the lunar surface to L1 versus L2?
Bill, you're one step ahead of me. Lunar resources were the next factor in the consideration. No, there's no real difference in DV from the lunar surface to go to L1 or L2, or in travel time.
If you had no intention of ever going to the Moon, there would still be some interesting advantages that would make the lunar Lagrange points worth considering as staging locations. But if you really want to use lunar resources, that's when the story gets pretty compelling.
Let's assume we're going to use lunar-derived oxygen as part of the propellant to send a spacecraft to Mars. Launching it off the lunar surface is going to consume about 2000 m/s of DV. Injecting it back directly from LLO to a highly-elliptical Earth orbit is going to take another 900 m/s. If the staging point is LEO, then the LOX must be propulsively captured into low Earth orbit or aerobraked into low Earth orbit. Propulsive capture required a lot of propellant and aerobraking needs a heat shield. In either case, you are bleeding off much of the orbital energy that you will later use the LOX to generate in your Mars spacecraft. Pretty wasteful.
By collecting LOX in LLO, L1, or L2, and staging from that point into a trans-Mars injection, you preserve all of that wonderful orbital energy you have, and reduce the amount of propellant required for injection.
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#85
by
meiza
on 16 Nov, 2006 13:32
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What about earth-sun lagrange points?
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#86
by
kfsorensen
on 16 Nov, 2006 13:37
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meiza - 16/11/2006 8:15 AM
What about earth-sun lagrange points?
Transfer times to and from Sun-Earth Lagrange points range from 90-150 days vs. several days for the Earth-Moon Lagrange points. Energy-wise, there would still be benefit, but there's much more time spent in transit. Lunar swingbys also become more challenging, and it is the powered lunar swingby that makes getting into and out of L2 so propulsively efficient.
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#87
by
kfsorensen
on 17 Nov, 2006 00:40
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Here is a portion of a document written by JPL in the early 80s on the subject of interplanetary mission planning. The first section contains an excellent description of hyperbolic injection issues and a number of graphics that illustrate the geometries involved.
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#88
by
Bill White
on 19 Nov, 2006 04:40
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Thinking about routine human access to the Moon, I see a tradeoff between using EML-1 and EML-2 as a transfer point. Both offer perpetual 24/7 access to any point on the lunar surface (unlike low lunar orbit which appears to be a nightmare with regard to launch window calculations).
EML-2 offers lower delta V numbers but longer elapsed time to/fromLEO. More time for astronauts in transit to soak up radiation.
If the lunar architecture contemplates a re-useable lunar lander (a single stage LSAM that shuttles between the surface and EML-1 and/or EML-2) and a some sort of LEO to EML 1&2 transfer taxi together with an L-point transfer station, over time the L-point stations can stockpile water which is a superb radiation shield.
Make the dash from LEO to EML-1 in a less shielded vessel, dock and hunker down behind a large water shield. Then change trains to the lunar lander and well shielded bases on the lunar surface.
Use EML-1 and lunar LOX for routine crew access to the lunar surface and use EML-2 and lunar LOX for routine automated cargo deliveries to the lunar surface. [Edit: For this visualize an unpressurized LSAM that can accept modular cargo cannisters at EML-2 along with fuel (CH4 or H2 or whatever) brought from Earth. LOX is from Luna. This way a LEO to EML-2 tug does not need a lander.]
= = =
Of course, lunar LOX extraction and a single stage fully re-useable LSAM are prerequisites for this architecture.
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#89
by
TyMoore
on 19 Nov, 2006 14:43
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Thank you Vanilla for your excellent, detailed description of trajectory analysis! There are enough subtleties that I often shake my head in wonder at the accuracy of various 'long shots' like Voyagers 1 and 2, Galileo, Cassini and many others.
As far as Lunar Oxygen is concerned, it seems to me that it makes more sense to establish enough infrastructure on the moon to shoot regolith up to a catcher/processor station for materials extraction. Otherwise you end up loosing a lot of reaction mass because you end up burning about 'half' of it on the ride up from the lunar surface. It's even worse at the lunar poles (where the water ice may be) because then you have to not only orbit the moon, but do a plane change, unless the depot station is located at the L1 point about 61,500 Km from the moon in the direction of Earth.
Even then, using something like RL-10B2's and assuming of course you've got hydrogen to 'burn' you still are assuming a big penalty by transporting LUNOX this way...delta-V of about 2.5km/s or so...
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#90
by
kfsorensen
on 19 Nov, 2006 21:05
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Bill White - 18/11/2006 11:23 PM
Thinking about routine human access to the Moon, I see a tradeoff between using EML-1 and EML-2 as a transfer point. Both offer perpetual 24/7 access to any point on the lunar surface (unlike low lunar orbit which appears to be a nightmare with regard to launch window calculations).
Hi Bill, that idea is interesting, and I hadn't thought of a "split" approach much previously. Unfortunately, it would negate one of the big advantages I would hope NASA would pursue if they adopted an L2-architecture approach for the lunar mission.
Right now, the CEV configured for lunar expeditions requires 900 m/s of DV capability for trans-Earth injection (TEI) and whatever plane-change DV that they have bookkept for LOR operations (on the order of 1000 m/s the last time I checked). This plane change DV can be reduced through combinations of longer pre-landing loiters, surface loiters, post-launch loiters, or any combination. But NASA seems to be expressing a desire to keep the LSAM ascent stage running on batteries and so would probably want to keep any post-ascent loiters to a minimum.
So the CEV carries (900 + x) m/s of DV capability, where x is the plane-change DV they mean to carry. This means it has far more DV capability than is needed for LEO missions like ISS rendezvous (200-300 m/s of post-insertion DV).
For a trip to and from L1, the CEV will need about 700 m/s to get in and out of L1: 1400 m/s.
For a trip to and from L2 using lunar powered swingbys, the CEV would only need about 330 m/s each time: ~700 m/s.
Thus a CEV designed for L2 rendezvous would be much more similar in size to the LEO-only variant--more so than a CEV intended for LOR or L1 rendezvous. Beyond that, if Mars missions (high-thrust or low-thrust) originated from L2, the CEV would already have the correct DV budget to accommodate crew transfers to and from the Mars vehicle.
The DV savings from using L2 rendezvous can also buy a lot of mass savings, some of which could be invested in better radiation shielding.
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#91
by
Bill White
on 19 Nov, 2006 22:17
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TyMoore - 19/11/2006 9:26 AM
As far as Lunar Oxygen is concerned, it seems to me that it makes more sense to establish enough infrastructure on the moon to shoot regolith up to a catcher/processor station for materials extraction. Otherwise you end up loosing a lot of reaction mass because you end up burning about 'half' of it on the ride up from the lunar surface. It's even worse at the lunar poles (where the water ice may be) because then you have to not only orbit the moon, but do a plane change, unless the depot station is located at the L1 point about 61,500 Km from the moon in the direction of Earth.
Even then, using something like RL-10B2's and assuming of course you've got hydrogen to 'burn' you still are assuming a big penalty by transporting LUNOX this way...delta-V of about 2.5km/s or so...
"Down the road" I would agree that mass drivers are a terrific idea. But that is a lot of infrastructure and if we start extracting lunar LOX ASAP we can use that lunar LOX to power cargo only LSAMs that shuttle back and forth from Luna to EML-2 and that would lower the cost of establishing the infrastructure you suggest.
I visualize it like this: a cargo only single stage LSAM lands with enough fuel (LH2, CH4,
) to reach EML-2 but without substantial LOX reserves. Tank up on LOX from lunar supplies, enough to travel to & from EML-2 with reserves. Travel to EML-2 (with platinum bearing asteroid fragments? LOX for export if there is a demand?) off load the PGMs and load up with materials to establish greater lunar infratructure AND fuel (LH2, CH4,
) sufficient for a round trip to Luna and back to EML-2.
Even if there is little market for lunar LOX in the short term, lunar LOX will lower the cost of delivering the cargo needed to build infrastructure.
= = =
Vanilla, IMHO, the best reasons for using EML-1 and/or EML-2 right now is to pave the way for permanent transfer stations which are merely enough shelter to protect against radiation and allow passengers to change trains.
A bare-bones station could be built today with Russia's spare FGB-2, a Bigelow inflatable habitat and a multi-bay docking module. Add a genuine resuable single stage LSAM and a Soyuz or Shenzou would be sufficient to handle the Earth to EML-1 and/or EML-2 legs of the journey. Its the thought of 8 days in a Soyuz outside Earth's magnetic fields (radiation protection) that made me think 4 days to EML-1 would be safer from a radiation perspective.
As far as a single stage re-useable LSAM, the NewSpace mantra has long been that its "dumb" to litter the Atlantic with hardware dropped from an expendable rocket. If that is true, then it it "double dumb" to leave a single use non-reuseable LSAM on the Moon.
= = =
Add: I do not oppose EML-2. Its just that whenever I sense an either/or question (L1 or L2?) I immediately attempt to consider whether we can answer: BOTH!
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#92
by
kfsorensen
on 20 Nov, 2006 00:27
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Bill White - 19/11/2006 5:00 PM
A bare-bones station could be built today with Russia's spare FGB-2, a Bigelow inflatable habitat and a multi-bay docking module. Add a genuine resuable single stage LSAM and a Soyuz or Shenzou would be sufficient to handle the Earth to EML-1 and/or EML-2 legs of the journey. Its the thought of 8 days in a Soyuz outside Earth's magnetic fields (radiation protection) that made me think 4 days to EML-1 would be safer from a radiation perspective.
The mass savings of using L2 would let you carry more shielding and reduce radiation exposure of an 8-day journey to L2 to less than that of a 4-day journey to L1. You'll come out way ahead, even with the extra shielding. In either case, an lunar lander makes a 3-day journey to the lunar surface and a 3-day journey back to the L-points.
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#93
by
Bill White
on 20 Nov, 2006 03:51
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vanilla - 19/11/2006 7:10 PM
Bill White - 19/11/2006 5:00 PM
A bare-bones station could be built today with Russia's spare FGB-2, a Bigelow inflatable habitat and a multi-bay docking module. Add a genuine resuable single stage LSAM and a Soyuz or Shenzou would be sufficient to handle the Earth to EML-1 and/or EML-2 legs of the journey. Its the thought of 8 days in a Soyuz outside Earth's magnetic fields (radiation protection) that made me think 4 days to EML-1 would be safer from a radiation perspective.
The mass savings of using L2 would let you carry more shielding and reduce radiation exposure of an 8-day journey to L2 to less than that of a 4-day journey to L1. You'll come out way ahead, even with the extra shielding. In either case, an lunar lander makes a 3-day journey to the lunar surface and a 3-day journey back to the L-points.
Very interesting. So tell me, is EML-1 good for anything?
In either case, an lunar lander makes a 3-day journey to the lunar surface and a 3-day journey back to the L-points.
Is there a curve that allows trade-offs between delta V and elapsed time or is 3 days pretty much optimal without a sharp increase in the required delta V?
= = =
I hope someone at NASA is looking at this with the objective to moving quickly to an architecture that permits routine access to the Moon. After thinking about L point rendevouz and reuseable landers, a return to the Moon using lunar orbit rendevouz and a disposable LSAM seems so, well, primitive.
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#94
by
kfsorensen
on 20 Nov, 2006 12:25
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Bill White - 19/11/2006 10:34 PM
Very interesting. So tell me, is EML-1 good for anything?
Is there a curve that allows trade-offs between delta V and elapsed time or is 3 days pretty much optimal without a sharp increase in the required delta V?
I hope someone at NASA is looking at this with the objective to moving quickly to an architecture that permits routine access to the Moon. After thinking about L point rendevouz and reuseable landers, a return to the Moon using lunar orbit rendevouz and a disposable LSAM seems so, well, primitive.
The curve of transfer time vs. DV was given earlier in the thread. I don't know if anyone at NASA is looking at this...
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#95
by
publiusr
on 19 Dec, 2006 22:18
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L-points are fine for large structures in the far future. For now--it sounds like just one more way to get an astronaut killed.
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#96
by
kfsorensen
on 19 Dec, 2006 23:26
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publiusr - 19/12/2006 5:01 PM
L-points are fine for large structures in the far future. For now--it sounds like just one more way to get an astronaut killed.
You might want to actually take the time to read the material in the future, rather than doing your standard "drive-by commenting"...
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#97
by
Smatcha
on 20 Dec, 2006 01:05
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Vanilla, thanks for referring me to this discussion. In our AIAA Space 2006 paper we had some of the same references for the same issues covered in this thread. I have also been in communications with engineers at JPL concerning Lagrange Points.
We choose EML1 for the Space Station largely due to quicker access times to and from Earth. For cargo to the Space Station an Earth to EML2 to EML1 might make sense as well. EML2-Halo Orbit was used for the communications satellite. Since our baseline architecture doesn’t require a Lunar Orbit rendezvous we didn’t look at better locations than LLO as ESAS recommended.
As for the best point to stockpile Lunar LOX for Mars mission fueling, EML1 also made sense do the presence of the Space Station. We can also transfer back and forth from EML1 to EML2 at any time with very little DV.
I would be interested in any information you have concerning Mars transfer trajectories, DV, and limitations from EML1 and/or EML2. Everything we can find is understandably Earth centric for departure. For the Mars mass estimate we just winged it based on C3. The biggest benefit of Lunar LOX for Mars is reducing the IMLEO for the fuel needed at Mars and to a lesser extent Earth Departure. The fuel needed at Mars is driven by the aero-braking assumptions which I believe are very optimistic. We haven’t had time to refine this either. I suspect that there could be an optimal balance of propulsive and multi-pass aero-braking if Lunar LOX was available. Propulsive followed by direct descent re-entry with final powered descent might also work. The variability of the Martian atmosphere is a big issue here along with the no abort scenario. Maybe this method would be best for Mars ISRU/Equipment followed by a more traditional/precise orbit insertion, plane change, and descent approach for the Mars crew. There are a large number of important issues to be worked on in the future.
At present though we are still dealing with the obvious improvements needed in ESAS in order to achieve VSE within our lifetimes.
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#98
by
kfsorensen
on 20 Dec, 2006 01:14
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Earlier posts in the thread detail the delta-V advantages of L2 basing, and there is also an extensive sequence on how to use L2 as a Mars departure node, both for low-thrust and high-thrust vehicles. Although it takes little delta-V to go from L1 to L2 and vice versa, the trip times are measured in weeks and are not practical for crew. Better to begin with an L2 base, which can be both serviced for less DV, and which represents less of a DV penalty for a departing Mars vehicle.
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#99
by
Smatcha
on 20 Dec, 2006 21:02
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vanilla - 19/12/2006 5:57 PM
Earlier posts in the thread detail the delta-V advantages of L2 basing, and there is also an extensive sequence on how to use L2 as a Mars departure node, both for low-thrust and high-thrust vehicles. Although it takes little delta-V to go from L1 to L2 and vice versa, the trip times are measured in weeks and are not practical for crew. Better to begin with an L2 base, which can be both serviced for less DV, and which represents less of a DV penalty for a departing Mars vehicle.
I'm not seeing a lot of benfit for EML2 for Lunar Surface missions. See attached
) to reach EML-2 but without substantial LOX reserves. Tank up on LOX from lunar supplies, enough to travel to & from EML-2 with reserves. Travel to EML-2 (with platinum bearing asteroid fragments? LOX for export if there is a demand?) off load the PGMs and load up with materials to establish greater lunar infratructure AND fuel (LH2, CH4, 
