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What’s the better choice: the Lagrange point between the Earth and Moon (L1), or the one just beyond the Moon (L2)? (credit: D. Lester)

Picking sides in cislunar space

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In debates about human space policy, the question of destinations looms over all the others. If human spaceflight is about going somewhere, where one goes determines the plan, the architecture, and the investment strategy. Destinations for exploration are historically defined as places where one can leave footprints or collect samples. Big rocks, like the Moon and Mars, and even smaller rocks like asteroids seem to fit that bill. But attached to this list of destinations for federal space policy are some very different places, the L1 and L2 Earth-Moon Lagrange (or libration) points (see “Making the path for human spaceflight less rocky”, The Space Review, June 21, 2010).

The Earth-Moon Lagrange points have been understood to be unambiguously opportunistic locations for space exploration efforts. For these venues, the opportunities may be on the Moon or farther away.

Those “destinations” are defined not by rocks but dynamically, as saddle points in the potential energy of cislunar space where one can stay without too much trouble. These saddle points are about 84% of the way from the Earth to the Moon (L1), and symmetrically beyond the Moon (L2). In fact, spacecraft wouldn’t really even stay at these points, but would orbit around them with periods of roughly half a month. The fact that one cannot plant a flag at a Lagrange point or even leave iconic footprints has led for years to some exasperation to those advocating trips there; plans to send people to those venues have been dismissed as “missions to nowhere”.

They aren’t. To the extent that going to venues in space that aren’t occupied by rocks isn’t justified, one has to wonder about the hundreds of billions of investment dollars, both commercial and defense-related, on facilities in somewhat closer Earth orbit (LEO, GEO, etc.) Just as for these more nearby rockless locations, the Earth-Moon Lagrange points have been understood to be unambiguously opportunistic locations for space exploration efforts. For these venues, the opportunities may be on the Moon or farther away. As a solar system “Gateway” for human trips down to the lunar surface, for low-latency and uninterrupted telerobotic control of facilities on the lunar surface, for depoting in situ resource utilization (ISRU) products, as a job site for servicing cislunar science missions in free space and development of future solar system expedition vehicles, these Lagrange points are truly enabling.

Our leaders are coming to the realization that human visits to Mars are not going to happen soon, and return of humans to the Moon is highly desirable but not affordable on a short time scale either. The idea of sending people to a near Earth asteroid has been floated, even by the president, but although a sophisticated landing craft is not needed for such a trip, finding an accessible target and establishing compelling and sustainable rationale has continued to be a challenge. It is fair to say that going to a rock is not likely to be humanity’s next step beyond LEO. It is in this policy arena that L1 and L2 have become increasingly attractive as the first stepping stones (that would be stones without rocks, I guess) for human travels beyond low Earth orbit (see “First stop for Flexible Path?”, The Space Review, November 30, 2009). They have been featured in long range agency planning and in Congressional authorization views of our space future. They may well define our space future.

The ARTEMIS mission, created with two spacecraft from the retired THEMIS constellation of heliophysics satellites, has exercised our abilities to go into orbit at both Earth-Moon L1 and L2, and stay in those orbits for extended periods of time. Earth-Moon Lagrange point orbits are not just theory. We’ve been there! NASA has begun to develop concepts for habitation facilities that could support humans for long periods at these locations (see “Human operations beyond LEO by the end of the decade: an affordable near-term stepping stone”, The Space Review, January 10, 2011).

Of course, the big difference between L1 and L2 is which side of the Moon one is looking at.

As we look ahead to a near-term future for human travel beyond LEO, the question of destinations is ceasing to be the Moon, or Mars, or asteroids, but rather L1 versus L2. Which side of the Moon should we first aim for? The idea of using Earth-Moon Lagrange points for future human space operations was developed by Bob Farquhar about forty years ago in an inspired series of papers. In his early calculations, Farquhar found that L2, over the lunar farside, was a slightly longer trip from the Earth, but somewhat less expensive propulsion-wise compared to L1 over the lunar nearside. He figured the total delta-V for a roundtrip L2 visit was about 20% lower than for L1, and he presumed that L2 would thus be the best site for a human occupied outpost. This difference may be lowered by making compromises on travel time. For slow cargo transport, there need be no difference at all. So propulsion budget is an important, but not necessarily decisive factor in determining which side is optimal. In fact, Earth-return time is substantially shorter for L1, which may be relevant with regard to safety and risk for human missions. Orbits around L1 and L2 are not entirely stable, and stationkeeping propulsion is required to maintain them. But the propulsion needs to do so are very manageable and economical at levels of 10–50 meters per second per year, depending on the orbit, navigation accuracy, and thruster stationkeeping precision, with proper accounting for solar wind and radiation pressure. The stationkeeping budgets for L1 and L2 are roughly the same.

For both L1 and L2, power generation is straightforward, unlike on the surfaces of, or in low orbit around, large rocks, which can shadow the Sun. With the exception of occasional eclipses of the Sun by the Earth or Moon, spacecraft in L1 or L2 orbits are illuminated continuously. For L1, on the Earthward side of the Moon, communication with the Earth is continuous. For L2, a wide enough orbit with a “halo” topology, in which the spacecraft circles the Earth-Moon line, can allow continuous line-of-sight to the Earth over the lunar limb.

One of the hallmarks of the Earth-Moon Lagrange points is the dynamical advantageousness for traveling to more distant locations. As pointed out by Martin Lo and Shane Ross a decade ago, an “interplanetary superhighway” connects Lagrange points in the solar system, such that going from one to the other requires only tiny amounts of propellant. While the speeds on the superhighway can be pretty slow, such that trips with humans on board do not necessarily benefit from these low-propulsion options, advantages for cargo transport can be enormous. Using an Earth-Moon Lagrange point as a depot for lunar ISRU products is highly relevant in this regard. Many of our prime science spacecraft operate at the Earth-Sun Lagrange points, about four lunar distances away. These spacecraft could easily be moved to and from a “jobsite” at an Earth-Moon Lagrange point where they could be serviced much more easily than by sending people or servicing robots to their operational locales. Both Earth-Moon L1 and L2 could offer these dynamical advantages.

Of course, the big difference between L1 and L2 is which side of the Moon one is looking at. Observers at L1 are looking down at the near side, and L2 at the far side. Only one hemisphere is visible from each venue, and there is line-of-site communication just with that side. To the extent that future plans for humans on the lunar surface feature one side, that decision would bear on which Lagrange point is chosen for a habitat/depot that would support it. Such a habitat could even be used to telerobotically develop a site in advance of human surface presence. While ambitious plans for a farside lunar radio telescope have been proposed, the far side is not generally featured in future lunar plans by the science community. With the notable exception of the South Pole Aitken basin, most identified high priority science targets are on the nearside. For ISRU production, there is no evidence that one side is any better than the other, and one must presume that the nearside, with communication sightline to the Earth, is preferable for control and monitoring of mining and refining operations.

The main obstacle for planning trips to the Earth-Moon Lagrange points is, “there ain’t nothin’ there”. This is an artificial obstacle, however, that just highlights what might be a somewhat primitive—and constraining—perspective of human space exploration by the public.

Of relevance is the recent “Stepping Stones” strategic plan developed by Lockheed-Martin (see “Early Human L2-Farside Missions”, Lockheed Martin, 2010). This creative plan is a series of increasingly challenging human spaceflight missions that build incrementally toward putting humans on Mars. A key early step in this plan is a mission to Earth-Moon L2, in order to explore the lunar farside. This step might follow an Apollo 8-type lunar flyby, and be followed by a trip to a near-Earth asteroid. The choice of L2 over L1 was an interesting one, though in their view, either Lagrange point would exercise our human spaceflight capabilities in deep space for more ambitious later exploration. For an early trip, with limited propulsion capabilities, the smaller propellant cost into L2 was a significant factor in the decision. To some extent, a habitat at L2 offers lunar surface farside telerobotic control that would not be possible directly from the Earth. One major advantage of L2 over L1 in the public spirit of exploration is that “far” is always better than “near”, and the Apollo missions have already travelled through, if not stayed at, the L1 venue.

The purpose of this essay is not to recommend L1 versus L2 as the next destination for our travels beyond low-Earth orbit. In many respects, they offer identical advantages. Rather, we have laid out some of the differences between the two. In fact, L1 and L2 are not dynamically that far apart. As demonstrated by NASA’s ARTEMIS mission, moving between L1 and L2 is a low delta-V operation, such that a habitat deployed at one location could be moved, without much trouble, to the other.

All voyages beyond Earth orbit have to contend with radiation exposure, especially when it is for an extended period of time, and where there are no rocks to hide under. While the importance of this issue should not be minimized, experts have pointed out that with foreseeable habitat shielding, radiation exposure at L1 and L2 to galactic cosmic rays (which are most difficult to shield) can be kept below what are currently adopted dose limits for astronauts at ISS. Whether those limits, which are substantially higher than for the Earth-bound public, are too risky, is yet to be established.

The main obstacle for planning trips to the Earth-Moon Lagrange points is, as noted above, “there ain’t nothin’ there”. This is an artificial obstacle, however, that just highlights what might be a somewhat primitive—and constraining—perspective of human space exploration by the public. No one is proposing to “explore” L1 or L2, but to use those locations as steps to exploring other destinations. That an orbit can be a “place”, and can offer enabling value to major goals (which include eventually getting toes onto big rocks), is something that has to be understood more widely, and marks progress not just in exploration, but in understanding what space exploration really means.