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Utilization of libration points for human exploration in the Sun–Earth–Moon system and beyond
Acta Astronautica 55 (2004) 687 – 700 www.elsevier.com/locate/actaastro
Utilization of libration points for human exploration in the Sun–Earth–Moon system and beyond Robert W. Farquhar∗ , David W. Dunham, Yanping Guo, James V. McAdams Applied Physics Laboratory, The Johns Hopkins University, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA
Abstract A plan to use the Sun–Earth L2 libration point as the primary hub for future human space activities in the Earth’s neighborhood is described. It is expected that the Sun–Earth L2 point will be the location of choice for a number of large astronomical observatories over the next 20 years. These observatories will probably require some level of servicing and/or repair by astronauts. To provide human access to the L2 point, the early development of a reusable vehicle called a Deep-Space Shuttle (DSS) is proposed. The DSS, based in low-Earth orbit, would be able to transport astronauts to and from the L2 point in about 35 days (including a 5-day stay time at L2). The Sun–Earth L2 point is also useful as a staging node for missions to near-Earth asteroids and Mars. For instance, a reusable interplanetary transfer vehicle (ITV) stationed at the L2 point could be used for the round-trip journey. The ITV would use lunar gravity-assists and a perigee :V maneuver to enter the desired interplanetary transfer trajectory. Just prior to the Earth-escape maneuver, a DSS “taxi” would transfer the crew to the ITV. A reverse procedure would be used to return the ITV to the libration point with the crew leaving the ITV just before the Earth-capture maneuver, and returning directly to Earth via an Apollo-style re-entry capsule. Using this technique, the L2-based ITV would save approximately 6:3 km=s in :V cost compared with an ITV stationed in low-Earth orbit. c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved.
1. Introduction In 1772, the French mathematician Joseph L. Lagrange (1736–1813) showed that there are @ve positions of equilibrium in a rotating two-body gravity @eld. Three of these “libration points” are situated on a line joining the two attracting bodies, and the other two form equilateral triangles with these bodies. As shown in Fig. 1, a total of seven libration points are located in the Earth’s neighborhood. Five of them are
∗ Corresponding author. Tel.: +1-240-228-5256; fax: +1-240228-3237. E-mail address: [email protected] (R.W. Farquhar).
members of the Earth–Moon system and two belong to the Sun–Earth system. In the reference frame used here, the Sun–Earth line is @xed and the Earth–Moon con@guration rotates around the Earth. Although the collinear points are unstable, very little propulsion is needed to keep a spacecraft at or near one of these points for an extended period of time [1,2]. The L1 and L2 points of the Sun–Earth system are noteworthy because their unique positions are advantageous for several important applications in astronautics. For instance, the Sun–Earth L1 point is an ideal location to continuously monitor the interplanetary environment upstream from the Earth. A suitably instrumented spacecraft placed in the vicinity of this point can provide data on the solar wind about
c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved. 0094-5765/$ - see front matter doi:10.1016/j.actaastro.2004.05.021
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an hour before it reaches the Earth’s magnetosphere. However, the spacecraft cannot be stationed too close to the L1 point because the Sun is directly behind this point when viewed from the Earth. This alignment is a problem because the intense solar noise background will severely degrade downlink telemetry. To avoid the zone of solar interference, a “halo orbit” is utilized [3]. This orbit has a period of approximately 6 months and passes slightly above and below the ecliptic plane, as shown in Fig. 2. It is inherently unstable,
Fig. 1. Libration points in the vicinity of the Earth.
and occasional stationkeeping maneuvers are required to keep the spacecraft close to the halo path. Fortunately, these maneuvers are only needed about once every three months and their associated :V costs are quite small (less than 5 m=s/year). On August 12, 1978, a spacecraft called the International Sun–Earth Explorer-3 (ISEE-3) was launched towards the Sun–Earth L1 libration point. One hundred days later, on November 20, 1978, ISEE-3 was inserted into a halo orbit around the L1 point, thus becoming the @rst libration-point satellite [4]. ISEE-3 remained in its L1 halo orbit until June 1982 when it used a propulsive maneuver of only 4:5 m=sec to transfer to the vicinity of the Sun–Earth L2 point. Subsequently, ISEE-3 used four lunar gravity-assist maneuvers to map the previously unexplored region of the Earth’s distant magnetotail [5]. Then, on December 22, 1983, a @fth lunar gravity-assist maneuver sent the spacecraft into a heliocentric trajectory that allowed ISEE-3 to carry out the @rst encounter
Fig. 2. Halo orbit around the Sun–Earth L1 libration point. Although the Sun’s disk as seen from the Earth subtends an angle of only 0:5◦ , the zone of solar interference for ground-based antennas is much larger.
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Table 1 Libration-point missions Missiona
Sun–Earth libration point
Date of orbit insertion
Mission purpose
ISEE-3 [NASA] WIND [NASA] SOHO [ESA/NASA] ACE [NASA] MAP [NASA] Genesis [NASA] Herschel [ESA] Planck [ESA] Eddington [ESA] JWST [NASA] Constellation-X [NASA] GAIA [ESA] DARWIN [ESA] TPF [NASA]
L1, L2 L1 L1 L1 L2 L1 L2 L2 L2 L2 L2 L2 L2 L2
1978,1983 1995,1997 1996 1997 2001 2001 2007 2007 2008 2011 2012 2012 2014 2015
Solar wind, cosmic rays, plasma studies Solar-wind monitor Solar observatory Solar wind, energetic particles Cosmic microwave background Solar-wind composition Far infrared telescope Cosmic microwave background Stellar observations Deep space observatory X-Ray astronomy Galactic structure, astrometry Detection of Earth-like planets Detection of distant planets
a Acronyms:
ISEE (International Sun–Earth Explorer); SOHO (Solar & Heliospheric Observatory); ACE (Advanced Composition Explorer); MAP (Microwave Anistropy Probe); GAIA (Global Astrometric Interferometer for Astrophysics); JWST (James Webb Space Telescope); TPF (Terrestrial Planet Finder).
with a comet (P/Giacobini-Zinner) on September 11, 1985 [6]. The highly successful Pight of ISEE-3 dramatically demonstrated the utility of libration-point orbits and lunar gravity-assist trajectories in accomplishing a variety of space exploration objectives in the Sun– Earth–Moon system and beyond. Although a second libration-point mission did not occur until 1995, the pace has recently accelerated with four additional missions taking place between 1996 and 2001 (see Table 1). Beginning in 2007, orbits in the vicinity of the Sun–Earth L2 point will be the locations of choice for a number of large astronomical facilities. There are several advantages for the L2 site. Viewing constraints are minimized because the Sun, Earth, and Moon all lie in the same direction providing a space telescope with an unhindered view of over half of the sky at all times. Other advantages include simpli@ed thermal control and pointing requirements for high-gain antennas. Earth eclipses can be avoided, ensuring a continuous source of solar power [7]. NASA’s highest-priority big-astronomy mission at L2 will be the James Webb Space Telescope (JWST). Current plans call for a 6-meter telescope behind a tennis-court-size Sun shield. JWST will operate mainly in the infrared at wavelengths of
approximately 0.6–28 m. Two more NASA observatories, Constellation-X and the Terrestrial Planet Finder (TPF), will be located around L2 sometime after JWST becomes operational. The European Space Agency (ESA) is also planning to station large observatory-class spacecraft near the L2 point. Three of these missions, Herschel, Planck, and Eddington, should be on station by 2008. The early astronomy missions to L2 have not been designed for human servicing and repair, but this situation will surely change as L2 telescopes become more complex and expensive. As a matter of fact, the construction and maintenance of large astronomical facilities at L2 could provide a compelling rationale for the initial step in a program of human exploration beyond low-Earth orbit [8,9]. Of course, telescope servicing by itself is not suRcient justi@cation for a human spacePight program that could cost billions and take at least a decade to complete. However, by extending humankind’s reach to the Sun–Earth L2 libration point, we would develop some of the capability that will be needed to provide human access to the Moon, near-Earth asteroids, Mars, and beyond. For the past three years, a group of about 100 NASA scientists and engineers known as the NASA Exploration Team (NEXT) has devised an ambitious plan for future human exploration [10,11]. The basic ideas
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Fig. 3. Architecture for Earth–Moon L1 “Gateway” mission scenario [10].
for the mission architecture advocated by NEXT are shown schematically in Fig. 3. In this scenario, the Earth–Moon L1 libration point is the primary staging node for missions to the Moon, Mars, and the Sun–Earth L2 point. Of particular interest is the strategy for the construction and repair of the telescopes that reside at the Sun–Earth L2 point. It is assumed that large aperture telescopes are constructed at the Earth–Moon L1 point and then sent to the Sun–Earth L2 location via a low-energy transfer (:V ∼ 50 m=s; :T ∼ 50 days). If repairs or upgrades are needed for an operational telescope at the Sun–Earth L2 point, it is @rst transferred to the Earth–Moon L1 point for human servicing and then returned to its original location. There are no requirements for human missions to the Sun–Earth L2 point in the NEXT concept. In the present study, an alternative approach has been employed. As shown in Fig. 4, the “Gateway” is now located at the Sun–Earth L2 point 1 instead of the Earth–Moon L1 point. This major change leads to a number of diSerent vehicle and operational requirements. Key features of the new plan include the 1 A “Gateway” at the Sun–Earth L1 point is essentially equivalent to one at the Sun–Earth L2 point. Either location could serve as a staging node for the ITV or ICS. The L2 point was baselined because this point is envisioned as the primary location for space telescopes in the foreseeable future. In any case, transfers between the two libration points can be carried out with virtually zero :V expenditure.
following: • Telescopes that reside in the vicinity of the Sun–Earth L2 point will be serviced on site. • The Deep–Space Shuttle (DSS) that is based in low-Earth orbit is not required to interact with the International Space Station (ISS). • Separate vehicles are used for crew and cargo Pights. This should reduce overall mass requirements, shorten Pight times for piloted missions, and provide some assurance that key elements are in place and working at the destination before a crew leaves Earth orbit. • Stationkeeping operations are greatly simpli@ed at the Sun–Earth L2 point. As noted earlier, :V costs for stationkeeping maneuvers are relatively low at all collinear libration points (Sun–Earth or Earth –Moon). However, while maneuvers every 3–4 months are adequate for orbit maintenance at the Sun–Earth L2 point, maneuvers are needed every week at the Earth–Moon collinear points. • The interplanetary transfer vehicle (ITV) can also serve as a habitat for extended crew operations in the vicinity of the Sun–Earth L2 point. • The primary long-term goal of the mission strategy advocated in this plan is human access to Mars on a regular basis. Missions to the Sun–Earth L2 libration point, near-Earth asteroids, and Phobos/Deimos are viewed as “stepping stones” in an evolutionary process to achieve this goal. In this regard, it is
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Fig. 4. Architecture for Sun–Earth L2 “Gateway” mission scenario.
important to note that lunar missions are not on the critical path to Mars. Further details of the mission scenario outlined in Fig. 4 are presented in the following sections. Fundamental facts on trajectories to collinear libration points including their :V requirements are summarized. The rationale for the baseline scenario is described, and in some cases, compared with alternative plans (e.g., the NEXT proposal). Basic requirements for primary hardware elements such as the DSS and ITV are also given. 2. Trajectories to the Sun–Earth and Earth–Moon collinear libration points
Fig. 5. Trajectories to the Sun–Earth L1 libration point (trajectories shown with respect of @xed Sun–Earth line).
Optimized trajectories for the two principal classes of ballistic transfers between a low-Earth orbit and a collinear Sun–Earth collinear libration point are illustrated in Fig. 5. Although Fig. 5 shows trajectories to the L1 point, the general characteristics and :V costs are virtually identical for the L2 point. Optimality has been determined on the basis of the :V cost for the terminal maneuver at L1 because, for the Pight times considered here, the :V for the injection maneuver in low-Earth orbit is always around 3200 m=s. Lower :V costs can be obtained by using much longer Pight times and/or lunar gravity-assist maneuvers,
but a more eSective way to lower the terminal :V maneuver is to place a spacecraft into a periodic orbit around the libration point instead of at the point. This technique was used by the ISEE-3 spacecraft to enter its halo orbit around the Sun–Earth L1 point (see Fig. 6). The semi-major axis of the ISEE-3 halo orbit was about 670; 000 km. By increasing the orbit amplitude to roughly 770; 000 km, the insertion :V cost actually goes to zero (see Fig. 7). Another type of slow transfer to an orbit around a Sun–Earth collinear libration point is shown in Fig. 8. This
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transfer uses phasing orbits and a single lunar gravity-assist maneuver to place a spacecraft into a small-amplitude orbit around the Sun–Earth L2 point without any insertion :V maneuver [12–14].
Fig. 6. ISEE-3 transfer trajectory to halo orbit.
Fig. 7. :V cost for slow transfers to periodic orbits around the Sun–Earth collinear libration points.
Originally developed for the now-defunct Russian Relikt-2 mission proposal in 1990, the innovative trajectory concept was eventually utilized by NASA’s MAP mission in 2001. The trajectories described above are quite suitable for cargo missions to the Sun–Earth L2 region. However, because shorter Pight times are required for piloted missions, :V costs for fast transfers to the Sun– Earth L2 point are given in Fig. 9. From this @gure, it is evident that :V costs increase rapidly for one-way Pight times under 2 weeks. Nevertheless, for a 30-day round-trip Pight, the :V cost at L2 is approximately 1800 m=s, which is not unreasonable. The situation for fast transfers to the Earth–Moon collinear libration points is somewhat diSerent than the Sun–Earth case. There are basically two types of transfers to the Earth–Moon points, the direct and
Fig. 9. One-way fast transfers from low-Earth orbit (altitude ∼ 188 km) to the Sun–Earth L2 point. The :V cost to enter an orbit around the L1 point is approximately the same.
Fig. 8. Relikt-2 trajectory using lunar gravity-assist for transfer to Sun–Earth L2 point.
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Fig. 10. Trajectories to the vicinity of the Earth–Moon collinear libration points.
the indirect [15,16]. Optimized transfers to the Earth –Moon L2 point are shown in Fig. 10 for both types. Corresponding results for the L1 point are also given in Fig. 10. Notice that the retro-:V cost for an indirect transfer to L2 is about 900 m=s lower than the cost for a direct transfer. However, for the L1 point, the diSerence between the direct and indirect transfers is not signi@cant. Finally, it should be mentioned that transfer trajectories to either L1 or L2 with retro-:V ’s under 50 m=s are possible, but transfer times are more than 100 days [17,18]. Due to the lengthy transfer times, these trajectories are only of interest for cargo missions. 3. A logical rst step: The deep-space shuttle As mentioned earlier, human servicing of L2 telescopes would be a relatively inexpensive way to begin a program of human exploration beyond low-Earth orbit. One way to achieve this goal would be to develop a reusable crew-transfer vehicle called a Deep-Space Shuttle (DSS). As shown in Fig. 11, the DSS could be used to transport astronauts between a low-Earth orbit and a Sun–Earth L2 orbit. The DSS is envisioned as a one and a half-stage vehicle (i.e., a core stage with drop tanks) that uses storable propellants [e.g.,
Fig. 11. Mission scenario for telescope servicing in the vicinity of the Sun–Earth L2 libration point. Nominal round-trip transfer time ∼ 35 days.
liquid oxygen/methane (LOX=CH4 ) with a speci@c impulse of about 365 s]. The mission pro@le outlined in Fig. 11 requires a deterministic :V capability of
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Table 2 Telescope servicing alternatives Servicing location
Sun–Earth L2 Earth–Moon L1 Earth–Moon L2 High-Earth orbit • Perigee ∼ 2 RE • Apogee ∼ 60 RE
Requirements for deep-space shuttle
Comments
:V at LEO departure (m/s)
:V to enter and Round-trip Pight time exit servicing with 5-day stay location (m/s) at location (days)
3230 3100 3150 3150
1800 1500 700 ¡ 500
35 12 23 10
about 5 km=s, and at least 35 days of consumables (oxygen, water, food, etc.) for the crew. It is assumed that the crew returns directly to Earth in an Apollo-style re-entry capsule. The DSS (sans crew) then uses multiple aerobraking maneuvers to return to a desired low-Earth orbit. Multiple aerobraking passes are preferred to a single aerocapture maneuver because this method eases the requirements on the thermal protection system for the DSS. To summarize, the top-level requirements for the DSS are: • Crew size: 3–4 people. • Consumables for Pights of 35–50 days. • :V capability ∼ 6 km=s (includes navigation and margin). • Storable propellants (I sp ∼ 365 s). • Apollo-style re-entry capsule for crew. • Aerobraking capability. There are several alternative proposals for servicing the L2 telescopes (see Table 2), but they all have the major disadvantage of requiring the L2 telescope to transfer to a new location. Although it is possible to use a low-energy transfer trajectory between the Sun–Earth L2 point and the other proposed servicing locations, an impaired telescope might not be able to carry out this transfer. In any event, assuming that an L2 telescope could be safely transported to one of the alternative locations listed in Table 2, which location should it be? As noted earlier, the Earth– Moon L1 location was recommended by NEXT. However, Table 2 shows that a high-Earth orbit location is preferable to the Earth–Moon L1 point because the :V cost is lower by at least 950 m=s, and the roundtrip
On-site servicing Must transfer telescope to servicinglocation [17,18] Must transfer telescope to servicing location [17,18] Lunar gravity-assist maneuvers used to transfer telescope to and from servicing location (see Fig. 12)
Fig. 12. Simpli@ed version of a double lunar-swingby trajectory that could be used to transfer an L2 telescope to and from a high-Earth orbit [19,20].
Pight time is also reduced. Finally, it should be pointed out that the DSS could be used to transport astronauts to other interesting destinations in the Earth’s neighborhood. As a matter of fact, a DSS with a :V capability of 6 km=s would provide access to almost any place in the Earth’s neighborhood including either of the Earth–Moon collinear libration points, geosynchronous orbit, or even lunar orbit (see Table 3). 4. L2 “Gateway” to near-Earth asteroids, Mars, and beyond Although the DSS will allow humans to reach destinations well beyond the Moon’s orbit, a larger and more capable transfer stage will be needed for missions to near-Earth asteroids and Mars. To satisfy this requirement, the baseline architecture of Fig. 4 calls for a reusable stage based at the Sun– Earth L2 “Gateway.” This reusable stage termed the
R.W. Farquhar et al. / Acta Astronautica 55 (2004) 687 – 700 Table 3 Approximate round-trip :V requirements for transfers between a low-Earth orbit (LEO) and various destinations Destinations Sun–Earth Low-lunar Geosynchronous L1 or L2 orbit orbit (without point plane change) Round-trip Pight time (does not include stay time at destination)
30 days
7 days
:V requirements (m/s) LEO exit 3230 Destination entry 900 Destination exit 900 LEO entry (aerobrake) —
3150 850 850 —
2430 1470 1470 —
4850
5370
Total
5030
∼ 11 h
interplanetary transfer vehicle (ITV) will be used to transfer astronaut crews to and from their interplanetary destinations. The basic mission scenario is shown in Fig. 13. The scenario begins with the ITV (sans crew) departure from its L2 base. The ITV then uses a series of small propulsive maneuvers (total :V ¡ 50 m=s) and lunar gravity-assists to target its @nal Earth escape maneuver (usually a propulsive :V maneuver at perigee). Just prior to this escape maneuver, a DSS “taxi” is used to transfer the crew to the outward-bound ITV. 2 The :V requirement of roughly 3:7 km=s for the rendezvous and crew transfer is well within the capability of the DSS. The ITV (with its crew) then proceeds towards its interplanetary destination. After completing the interplanetary mission, the ITV returns the crew to the vicinity of the Earth where the crew returns directly to Earth in an Apollo-style re-entry capsule. The ITV (sans crew) uses a perigee :V maneuver for Earth capture followed by lunar gravity-assists and small propulsive maneuvers to return to the L2 “Gateway.” As an example of the eRciency of using the Sun–Earth L2 point as a staging node for interplanetary destinations, it is useful to compare :V requirements for diSerent staging locations. Fig. 14 illustrates 2 This tactic will give the crew an opportunity to abort the perigee maneuver before leaving Earth orbit.
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a one-year mission pro@le to a near-Earth asteroid and lists round-trip :V costs for several potential staging nodes. Notice that an ITV located at the Sun– Earth L2 point can perform this mission with a deterministic :V cost of only 5:3 km=s, which is less than one-half the cost for an ITV based in LEO. It is also important to observe that the Earth–Moon L1 “Gateway” location favored by NEXT and others [10,11,16, 21–23] is 1:5 km=s more costly than the Sun–Earth L2 node. Therefore, a Sun–Earth collinear libration point (L1 or L2) is a very attractive staging node for an ITV. The use of the Sun–Earth collinear libration points as staging nodes for human missions to Mars is not a new idea. This mission concept was fully described in a widely distributed article by Farquhar in 1969 [24]. A key graphic from this article is reproduced here (see Fig. 15). In the concept shown in Fig. 15, the ITV operates between the Sun–Earth and Sun–Mars collinear points which leads to further reductions in the :V cost for the ITV. With this plan, the crew could use an aerocapture vehicle to proceed directly to Mars’ surface just before the ITV executes a braking maneuver at B. Of course, when the crew is ready to return, they would need another vehicle to travel from Mars surface and/or Mars orbit to the ITV at the libration point. Fig. 16 gives :V costs for fast transfers between a low-Mars circular orbit and a collinear Sun–Mars libration point. It is diRcult to provide a de@nitive list of requirements for the ITV because there are several viable alternative solutions that will require further study before making a @nal selection. However, for the mission scenario outlined in Fig. 13, a few general observations indicate that: • Round-trip Pight times could be as long as 3 years or, in some cases, even longer. Trip times less than 6 months are not likely. • The ITV will not require an aerocapture or aerobraking capability. • An Apollo-style crew re-entry capsule will be required. • The ITV could use either chemical propulsion (I sp ∼ 365 s) or a nuclear thermal rocket (I sp ∼ 900 s). A hybrid nuclear system that integrates high thrust and low thrust in a single reactor would be even more desirable [25].
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Fig. 13. Mission scenario for interplanetary transfer vehicle (ITV) that is based at the Sun–Earth L2 “Gateway.”
Fig. 14. Mission to near-Earth asteroid 1999 A010 with a launch in 2025.
A nuclear ITV based at a distant location such as one of the Sun–Earth collinear libration points would not cause as much concern as a nuclear system operating in low-Earth orbit. However, in the
scenario of Fig. 13, perigee :V maneuvers are used for Earth escape and capture. Clearly, these maneuvers must be done at a high altitude to minimize the risk of Earth impact. Current mission studies have
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A low-thrust vehicle is ideally suited to this location because the L2 point is at the edge of the Earth’s energy well, and will not require time-consuming spiral trajectories for Earth escape and capture. Detailed descriptions of various low-thrust trajectories to and from the Sun–Earth L2 point are given by Kawaguchi and Yoshimura in [26,27]. 5. Future human expeditions to the Moon
Fig. 15. Interplanetary transport system using the Sun–Earth and Sun–Mars libration points [24]. Periapsis :V maneuvers are executed at A and B in the diagram.
Fig. 16. One-way fast transfers from a low-Mars orbit (altitude ∼ 500 km) to the Sun–Mars L1 point. The :V cost to enter an orbit around the L2 point is approximately the same.
speci@ed a minimum altitude of 2500 km for nuclear operations. The architecture of Fig. 4 also includes a reusable interplanetary cargo stage (ICS) that is based at the Sun–Earth L2 “Gateway.” It is anticipated that the ICS will use some form of low-thrust propulsion such as solar-electric, nuclear-electric, or even a solar sail.
The fact that the Moon always presents the same face towards the Earth both aids and hinders lunar exploration. Near-side lunar missions are simpli@ed because they have direct access to Earth-based control centers. However, farside lunar operations will require some kind of satellite communications link with the Earth. In 1966, Farquhar showed that it would be possible to establish a continuous farside communications link using a single comsat in a halo orbit around the translunar libration point, L2 [28,29]. The basic idea is illustrated in Fig. 17. A halo orbit with a radius of only 3500 km will always maintain line-of-sight contact with the Earth and the Moon’s farside. When viewed from the lunar surface, the entire halo orbit subtends an angle of 6:2◦ . In the Fall of 1971, NASA considered the use of a halo comsat to support a farside landing by Apollo-17. Unfortunately, a reluctance to try anything new at the end of a very successful program resulted in NASA losing a tremendous opportunity to end the Apollo Program on a high note. A brief account of this episode is given in [6]. In addition to its potential use for farside communications, the L2 halo orbit has also been proposed as an ideal staging node for a future lunar shuttle transportation system [15]. However, current studies of the lunar
Fig. 17. Lunar farside communications link.
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Table 4 Comparison of diSerent transportation modes between LEO (altitude ∼ 185 km) and lunar orbit (altitude ∼ 100 km) • DSS operates between LEO and L1, L2, or lunar orbit. • Lunar tug operates between L1,L2 and lunar orbit (one-way :V ∼ 750 m=s). • DSS uses aerobraking to return to LEO. Round-trip :V for deep-space shuttle (m/s)
Round-trip :V (m=s)
Round-trip time (days)
Staging node
:V at LEO
:V at node
Tug :V
Total :V
DSS
Tug
Total
Direct to L0 Earth–Moon L1 Earth–Moon L2
3150 3100 3150
1700 1500 700
— 1500 1500
4850 6100 5350
9 7 18
— 5 6
9 12 24
transportation problem have concentrated on the use of the Earth–Moon L1 point as the staging node for further human expeditions to the Moon [10,11,16,21,22]. Both of the Earth–Moon collinear points have important operational advantages over the standard lunar orbit rendezvous (LOR) mission mode, such as
back. Previous studies of a lunar shuttle system using the aforementioned assumptions have shown that the payload delivered to lunar orbit is signi@cantly higher with L2 staging when compared with a direct transfer [15,30]. To sum up the lunar transport trades, it appears that:
• The launch window for transfers between the libration point and any point on the lunar surface is essentially unconstrained (i.e., any site, anytime). • An increased Pexibility for transfers between the libration point and the Earth. • A DSS located in an L2 halo orbit would have complete farside communications coverage.
• For infrequent human Pights to the Moon (i.e., one or two missions per year), the standard LOR mode using a DSS would be a sensible approach. • If a permanent lunar base were established requiring frequent missions to the Moon, a lunar shuttle system using the L2 staging concept might provide an eRcient and Pexible way to maintain this base. • It is unlikely that L1 staging will oSer any performance advantage regardless of the Pight frequency.
To have a better understanding of the advantages and disadvantages of the libration-point staging concepts, it is useful to compare the :V costs and transfer times for a round-trip mission between a low-Earth orbit and a low lunar orbit. Approximate results for the two libration-point modes and a direct transfer to lunar orbit are given in Table 4. For the libration-point modes, it is assumed that a second vehicle called a “lunar tug” would be used to transport the crew to and from lunar orbit. As Table 4 clearly shows, a direct Pight to lunar orbit provides the shortest round-trip Pight time and the smallest :V cost. The comparison between the libration-point modes is mixed, with the shortest Pight time for L1 and the smallest :V cost for L2. However, the situation is quite diSerent if we assume a reusable shuttle system where the lunar tug is already based at the libration point (i.e., transported there by an earlier cargo Pight). For this case, it is also assumed that the DSS would be required to replenish the fuel for the tug’s transfer to lunar orbit and
6. Conclusions and recommendations Although a de@nitive strategy for the next steps in deep-space exploration is still evolving, it is clear that the collinear libration points in the Earth’s vicinity will play an important role in this plan. Some key @ndings of this study can be summarized as follows: • The Sun–Earth collinear libration points, L1 and L2, are increasingly popular locations for a variety of scienti@c spacecraft. This situation is especially true for the Sun–Earth L2 point which is an ideal site for astronomical observations. • Human servicing of large astronomical facilities at the Sun–Earth L2 point is highly desirable. This study calls for the development of a DSS that would transport astronauts to the L2 telescopes where they could be repaired on station. Round-trip Pight times for these servicing missions would be about 30–35
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•
•
days which is considered excessive by critics of this plan. However, if 35-day missions are considered to be too long, humans will never get to near-Earth asteroids or Mars where Pight times are typically 6 –24 months! Another way to service the L2 telescopes would be to require the telescope to use a low-energy trajectory to transfer to a location that is more accessible to astronauts. This technique has a number of obvious drawbacks, but if required for some reason, the best location would be a highly-elliptical Earth orbit. Several staging nodes were examined for human missions to near-Earth asteroids and Mars. It was found that a node at either of the Sun–Earth collinear points would yield the best result. For a sample round-trip mission to a near-Earth asteroid, it was shown that the mission could be performed with a deterministic :V of about 5:3 km=s when using a node at the Sun–Earth L2 point. The corresponding cost for a node at the Earth–Moon L1 point was roughly 6:8 km=s. It is clear that a comsat stationed in a halo orbit around the Earth–Moon L2 point, where it would provide continuous farside communications coverage, will be an important element for future human expeditions to the Moon. The preferred mission mode for future human expeditions to the Moon is somewhat dependent on the Pight rate. For one or two missions/year, the familiar lunar–orbit rendezvous (LOR) mode is probably the best choice. However, for support of a lunar base that could require a Pight rate of 12 or more missions per year, the trades are a little murky. Even so, it appears that the leading contenders would be LOR and a staging node at the Earth–Moon L2 point.
In addition to the @ndings listed above, a number of important trade studies have been identi@ed. A few of these studies are briePy noted below. • Comprehensive studies of alternative mission modes that would involve the Sun–Earth L2 “Gateway” concept. These studies would include telescope servicing as well as missions to near-Earth asteroids and Mars. In addition to mission design trades, a variety of vehicle designs and propulsion
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options should be examined. Baseline designs for the principal vehicles mentioned in this study (i.e., DSS, ITV, and ICS) should be de@ned at least to a conceptual level. • A focused study of Mars transportation scenarios that utilize both the Sun–Earth and Sun–Mars collinear libration points. The advantages and disadvantages of this intriguing technique require an in-depth analysis to be fully understood. • Realistic trade studies of a variety of mission modes for a lunar shuttle system that could support a lunar base at various locations on the Moon (e.g., farside, north or south polar regions). This type of comparative study has not been investigated in detail since the early 1970s. References [1] R.W. Farquhar, The control and use of libration-point satellites, NASA TR R-346, September 1970. [2] D.W. Dunham, C.E. Roberts, Stationkeeping techniques for libration-point satellites, Journal of the Astronautical Sciences 49 (1) (2001) 127–144. [3] R.W. Farquhar, D.P. Muhonen, D.L. Richardson, Mission design for a halo orbiter of the earth, Journal of Spacecraft and Rockets 14 (3) (1977) 170–177. [4] R.W. Farquhar, et al., Trajectories and orbital maneuvers for the @rst libration-point satellite, Journal of Guidance and Control 3 (6) (1980) 549–554. [5] R. Farquhar, D. Muhonen, L.C. Church, Trajectories and orbital maneuvers for the ISEE-3/ICE comet mission, Journal of the Astronautical Sciences 33 (3) (1985) 235–254. [6] R.W. Farquhar, The Pight of ISEE-3/ICE: origins, mission history, and a legacy, Journal of the Astronautical Sciences 49 (1) (2001) 23–73. [7] R.W. Farquhar, D.W. Dunhan, Use of libration-point orbits for space observatories, in: Y. Kondo (Ed.), Observatories in Earth Orbit and Beyond, Kluwer Academic Publishers, Dordrecht, 1990, pp. 391–395. [8] Do we still need astronauts? Nature 419 (2002) 653. [9] T. Reichhardt, A million-mile service, Nature 419 (2002) 666. [10] B.G. Drake, et al., Technologies for human space exploration: earth’s neighborhood and beyond, AIAA Paper 2001-4634, August 2001. [11] D.R. Cooke, et al., Innovations in mission architectures for exploration beyond low-Earth orbit, IAC Paper 02-Q.6.04, October 2002. [12] R.W. Farquhar, Halo-orbit and lunar-swingby missions of the 1990’s, Acta Astronautica 24 (1991) 227–234. [13] N. Eismont, et al., Lunar swingby as a tool for halo-orbit optimization in Relikt-2 project, ESA SP-326, December 1991, pp. 435–439.
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[14] M.L. Lidov, et al., Earth–Moon halo-orbit Pight paths in the vicinity of the Earth–Sun libration point L2, Cosmic Research 30 (4) (1992) 607–621. [15] R.W. Farquhar, The utilization of halo orbits in advanced lunar operations, NASA TN D-6365, July 1971. [16] G.L. Condon, D.J. Pearson, The role of humans in libration-point missions with speci@c application to an Earth –Moon libration-point gateway station, Advances in the Astronautical Sciences: Astrodynamics 109 (2001) 95–110. [17] E. Belbruno, Ballistic lunar capture transfers using the fuzzy boundary and solar perturbations: a survey, Journal of the British Interplanetary Society 47 (1994) 73–80. [18] D.C. Folta, et al., Servicing and deployment of national resources in Sun–Earth libration-point orbits, IAC Paper 02-Q.6.08, October 2002. [19] R.W. Farquhar, D.W. Dunham, A new trajectory concept for exploring the earth’s geomagnetic tail, Journal of Guidance and Control 4 (2) (1981) 192–196. [20] D.W. Dunham, S.A. Davis, Catalog of double lunar-swingby orbits for exploring the earth’s geomagnetic tail, NASA CR-160066, December 4, 1980. [21] B.K. Joosten, Human space exploration in earth’s neighborhood-strategy and architectural approach, AIAA Paper 2001-4561, August 2001. [22] M. Lo, S. Ross, The lunar L1 gateway: portal to the stars and beyond, AIAA Paper 2001-4768, August 2001.
[23] F. Morring, Stepping-stone path to anywhere, Aviation Week & Space Technology (2002) 48–49. [24] R.W. Farquhar, Future missions for libration-point satellites, Astronautics & Aeronautics (1969) 52–56. [25] S.K. Borowksi, L.A. Dudzinski, M.L. McGuire, Vehicle and mission design options for the human exploration of mars/phobos using bimodal NTR and LANTR Propulsion, AIAA Paper 98-3883, July 1998. [26] J. Kawaguchi, M. Yoshimura, Deep space quay at L2 and low thrust departure/return Pight strategy, 16th International Symposium on Space Flight Dynamics, Pasadena, California, December 2001. [27] J. Kawaguchi, M. Yoshimura, On a representative solar sail deep space Pight based at the quay around L2 point, IAC Paper 02-A.7.03, October 2002. [28] R.W. Farquhar, Station-keeping in the vicinity of collinear libration points with an application to a lunar communications problem, AAS Science and Technology Series: Space Flight Mechanics Specialist Symposium 11 (1966) 519–535. [29] R.W. Farquhar, Lunar communications with libration-point satellites, Journal of Spacecraft and Rockets 4 (10) (1967) 1383–1384. [30] R.W. Farquhar, A halo-orbit lunar station, Astronautics & Aeronautics 10 (6) (1972) 59–63.
Utilization of libration points for human exploration in the Sun–Earth–Moon system and beyond Robert W. Farquhar∗ , David W. Dunham, Yanping Guo, James V. McAdams Applied Physics Laboratory, The Johns Hopkins University, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA
Abstract A plan to use the Sun–Earth L2 libration point as the primary hub for future human space activities in the Earth’s neighborhood is described. It is expected that the Sun–Earth L2 point will be the location of choice for a number of large astronomical observatories over the next 20 years. These observatories will probably require some level of servicing and/or repair by astronauts. To provide human access to the L2 point, the early development of a reusable vehicle called a Deep-Space Shuttle (DSS) is proposed. The DSS, based in low-Earth orbit, would be able to transport astronauts to and from the L2 point in about 35 days (including a 5-day stay time at L2). The Sun–Earth L2 point is also useful as a staging node for missions to near-Earth asteroids and Mars. For instance, a reusable interplanetary transfer vehicle (ITV) stationed at the L2 point could be used for the round-trip journey. The ITV would use lunar gravity-assists and a perigee :V maneuver to enter the desired interplanetary transfer trajectory. Just prior to the Earth-escape maneuver, a DSS “taxi” would transfer the crew to the ITV. A reverse procedure would be used to return the ITV to the libration point with the crew leaving the ITV just before the Earth-capture maneuver, and returning directly to Earth via an Apollo-style re-entry capsule. Using this technique, the L2-based ITV would save approximately 6:3 km=s in :V cost compared with an ITV stationed in low-Earth orbit. c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved.
1. Introduction In 1772, the French mathematician Joseph L. Lagrange (1736–1813) showed that there are @ve positions of equilibrium in a rotating two-body gravity @eld. Three of these “libration points” are situated on a line joining the two attracting bodies, and the other two form equilateral triangles with these bodies. As shown in Fig. 1, a total of seven libration points are located in the Earth’s neighborhood. Five of them are
∗ Corresponding author. Tel.: +1-240-228-5256; fax: +1-240228-3237. E-mail address: [email protected] (R.W. Farquhar).
members of the Earth–Moon system and two belong to the Sun–Earth system. In the reference frame used here, the Sun–Earth line is @xed and the Earth–Moon con@guration rotates around the Earth. Although the collinear points are unstable, very little propulsion is needed to keep a spacecraft at or near one of these points for an extended period of time [1,2]. The L1 and L2 points of the Sun–Earth system are noteworthy because their unique positions are advantageous for several important applications in astronautics. For instance, the Sun–Earth L1 point is an ideal location to continuously monitor the interplanetary environment upstream from the Earth. A suitably instrumented spacecraft placed in the vicinity of this point can provide data on the solar wind about
c 2003 International Astronautical Federation. Published by Elsevier Ltd. All rights reserved. 0094-5765/$ - see front matter doi:10.1016/j.actaastro.2004.05.021
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an hour before it reaches the Earth’s magnetosphere. However, the spacecraft cannot be stationed too close to the L1 point because the Sun is directly behind this point when viewed from the Earth. This alignment is a problem because the intense solar noise background will severely degrade downlink telemetry. To avoid the zone of solar interference, a “halo orbit” is utilized [3]. This orbit has a period of approximately 6 months and passes slightly above and below the ecliptic plane, as shown in Fig. 2. It is inherently unstable,
Fig. 1. Libration points in the vicinity of the Earth.
and occasional stationkeeping maneuvers are required to keep the spacecraft close to the halo path. Fortunately, these maneuvers are only needed about once every three months and their associated :V costs are quite small (less than 5 m=s/year). On August 12, 1978, a spacecraft called the International Sun–Earth Explorer-3 (ISEE-3) was launched towards the Sun–Earth L1 libration point. One hundred days later, on November 20, 1978, ISEE-3 was inserted into a halo orbit around the L1 point, thus becoming the @rst libration-point satellite [4]. ISEE-3 remained in its L1 halo orbit until June 1982 when it used a propulsive maneuver of only 4:5 m=sec to transfer to the vicinity of the Sun–Earth L2 point. Subsequently, ISEE-3 used four lunar gravity-assist maneuvers to map the previously unexplored region of the Earth’s distant magnetotail [5]. Then, on December 22, 1983, a @fth lunar gravity-assist maneuver sent the spacecraft into a heliocentric trajectory that allowed ISEE-3 to carry out the @rst encounter
Fig. 2. Halo orbit around the Sun–Earth L1 libration point. Although the Sun’s disk as seen from the Earth subtends an angle of only 0:5◦ , the zone of solar interference for ground-based antennas is much larger.
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Table 1 Libration-point missions Missiona
Sun–Earth libration point
Date of orbit insertion
Mission purpose
ISEE-3 [NASA] WIND [NASA] SOHO [ESA/NASA] ACE [NASA] MAP [NASA] Genesis [NASA] Herschel [ESA] Planck [ESA] Eddington [ESA] JWST [NASA] Constellation-X [NASA] GAIA [ESA] DARWIN [ESA] TPF [NASA]
L1, L2 L1 L1 L1 L2 L1 L2 L2 L2 L2 L2 L2 L2 L2
1978,1983 1995,1997 1996 1997 2001 2001 2007 2007 2008 2011 2012 2012 2014 2015
Solar wind, cosmic rays, plasma studies Solar-wind monitor Solar observatory Solar wind, energetic particles Cosmic microwave background Solar-wind composition Far infrared telescope Cosmic microwave background Stellar observations Deep space observatory X-Ray astronomy Galactic structure, astrometry Detection of Earth-like planets Detection of distant planets
a Acronyms:
ISEE (International Sun–Earth Explorer); SOHO (Solar & Heliospheric Observatory); ACE (Advanced Composition Explorer); MAP (Microwave Anistropy Probe); GAIA (Global Astrometric Interferometer for Astrophysics); JWST (James Webb Space Telescope); TPF (Terrestrial Planet Finder).
with a comet (P/Giacobini-Zinner) on September 11, 1985 [6]. The highly successful Pight of ISEE-3 dramatically demonstrated the utility of libration-point orbits and lunar gravity-assist trajectories in accomplishing a variety of space exploration objectives in the Sun– Earth–Moon system and beyond. Although a second libration-point mission did not occur until 1995, the pace has recently accelerated with four additional missions taking place between 1996 and 2001 (see Table 1). Beginning in 2007, orbits in the vicinity of the Sun–Earth L2 point will be the locations of choice for a number of large astronomical facilities. There are several advantages for the L2 site. Viewing constraints are minimized because the Sun, Earth, and Moon all lie in the same direction providing a space telescope with an unhindered view of over half of the sky at all times. Other advantages include simpli@ed thermal control and pointing requirements for high-gain antennas. Earth eclipses can be avoided, ensuring a continuous source of solar power [7]. NASA’s highest-priority big-astronomy mission at L2 will be the James Webb Space Telescope (JWST). Current plans call for a 6-meter telescope behind a tennis-court-size Sun shield. JWST will operate mainly in the infrared at wavelengths of
approximately 0.6–28 m. Two more NASA observatories, Constellation-X and the Terrestrial Planet Finder (TPF), will be located around L2 sometime after JWST becomes operational. The European Space Agency (ESA) is also planning to station large observatory-class spacecraft near the L2 point. Three of these missions, Herschel, Planck, and Eddington, should be on station by 2008. The early astronomy missions to L2 have not been designed for human servicing and repair, but this situation will surely change as L2 telescopes become more complex and expensive. As a matter of fact, the construction and maintenance of large astronomical facilities at L2 could provide a compelling rationale for the initial step in a program of human exploration beyond low-Earth orbit [8,9]. Of course, telescope servicing by itself is not suRcient justi@cation for a human spacePight program that could cost billions and take at least a decade to complete. However, by extending humankind’s reach to the Sun–Earth L2 libration point, we would develop some of the capability that will be needed to provide human access to the Moon, near-Earth asteroids, Mars, and beyond. For the past three years, a group of about 100 NASA scientists and engineers known as the NASA Exploration Team (NEXT) has devised an ambitious plan for future human exploration [10,11]. The basic ideas
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Fig. 3. Architecture for Earth–Moon L1 “Gateway” mission scenario [10].
for the mission architecture advocated by NEXT are shown schematically in Fig. 3. In this scenario, the Earth–Moon L1 libration point is the primary staging node for missions to the Moon, Mars, and the Sun–Earth L2 point. Of particular interest is the strategy for the construction and repair of the telescopes that reside at the Sun–Earth L2 point. It is assumed that large aperture telescopes are constructed at the Earth–Moon L1 point and then sent to the Sun–Earth L2 location via a low-energy transfer (:V ∼ 50 m=s; :T ∼ 50 days). If repairs or upgrades are needed for an operational telescope at the Sun–Earth L2 point, it is @rst transferred to the Earth–Moon L1 point for human servicing and then returned to its original location. There are no requirements for human missions to the Sun–Earth L2 point in the NEXT concept. In the present study, an alternative approach has been employed. As shown in Fig. 4, the “Gateway” is now located at the Sun–Earth L2 point 1 instead of the Earth–Moon L1 point. This major change leads to a number of diSerent vehicle and operational requirements. Key features of the new plan include the 1 A “Gateway” at the Sun–Earth L1 point is essentially equivalent to one at the Sun–Earth L2 point. Either location could serve as a staging node for the ITV or ICS. The L2 point was baselined because this point is envisioned as the primary location for space telescopes in the foreseeable future. In any case, transfers between the two libration points can be carried out with virtually zero :V expenditure.
following: • Telescopes that reside in the vicinity of the Sun–Earth L2 point will be serviced on site. • The Deep–Space Shuttle (DSS) that is based in low-Earth orbit is not required to interact with the International Space Station (ISS). • Separate vehicles are used for crew and cargo Pights. This should reduce overall mass requirements, shorten Pight times for piloted missions, and provide some assurance that key elements are in place and working at the destination before a crew leaves Earth orbit. • Stationkeeping operations are greatly simpli@ed at the Sun–Earth L2 point. As noted earlier, :V costs for stationkeeping maneuvers are relatively low at all collinear libration points (Sun–Earth or Earth –Moon). However, while maneuvers every 3–4 months are adequate for orbit maintenance at the Sun–Earth L2 point, maneuvers are needed every week at the Earth–Moon collinear points. • The interplanetary transfer vehicle (ITV) can also serve as a habitat for extended crew operations in the vicinity of the Sun–Earth L2 point. • The primary long-term goal of the mission strategy advocated in this plan is human access to Mars on a regular basis. Missions to the Sun–Earth L2 libration point, near-Earth asteroids, and Phobos/Deimos are viewed as “stepping stones” in an evolutionary process to achieve this goal. In this regard, it is
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Fig. 4. Architecture for Sun–Earth L2 “Gateway” mission scenario.
important to note that lunar missions are not on the critical path to Mars. Further details of the mission scenario outlined in Fig. 4 are presented in the following sections. Fundamental facts on trajectories to collinear libration points including their :V requirements are summarized. The rationale for the baseline scenario is described, and in some cases, compared with alternative plans (e.g., the NEXT proposal). Basic requirements for primary hardware elements such as the DSS and ITV are also given. 2. Trajectories to the Sun–Earth and Earth–Moon collinear libration points
Fig. 5. Trajectories to the Sun–Earth L1 libration point (trajectories shown with respect of @xed Sun–Earth line).
Optimized trajectories for the two principal classes of ballistic transfers between a low-Earth orbit and a collinear Sun–Earth collinear libration point are illustrated in Fig. 5. Although Fig. 5 shows trajectories to the L1 point, the general characteristics and :V costs are virtually identical for the L2 point. Optimality has been determined on the basis of the :V cost for the terminal maneuver at L1 because, for the Pight times considered here, the :V for the injection maneuver in low-Earth orbit is always around 3200 m=s. Lower :V costs can be obtained by using much longer Pight times and/or lunar gravity-assist maneuvers,
but a more eSective way to lower the terminal :V maneuver is to place a spacecraft into a periodic orbit around the libration point instead of at the point. This technique was used by the ISEE-3 spacecraft to enter its halo orbit around the Sun–Earth L1 point (see Fig. 6). The semi-major axis of the ISEE-3 halo orbit was about 670; 000 km. By increasing the orbit amplitude to roughly 770; 000 km, the insertion :V cost actually goes to zero (see Fig. 7). Another type of slow transfer to an orbit around a Sun–Earth collinear libration point is shown in Fig. 8. This
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transfer uses phasing orbits and a single lunar gravity-assist maneuver to place a spacecraft into a small-amplitude orbit around the Sun–Earth L2 point without any insertion :V maneuver [12–14].
Fig. 6. ISEE-3 transfer trajectory to halo orbit.
Fig. 7. :V cost for slow transfers to periodic orbits around the Sun–Earth collinear libration points.
Originally developed for the now-defunct Russian Relikt-2 mission proposal in 1990, the innovative trajectory concept was eventually utilized by NASA’s MAP mission in 2001. The trajectories described above are quite suitable for cargo missions to the Sun–Earth L2 region. However, because shorter Pight times are required for piloted missions, :V costs for fast transfers to the Sun– Earth L2 point are given in Fig. 9. From this @gure, it is evident that :V costs increase rapidly for one-way Pight times under 2 weeks. Nevertheless, for a 30-day round-trip Pight, the :V cost at L2 is approximately 1800 m=s, which is not unreasonable. The situation for fast transfers to the Earth–Moon collinear libration points is somewhat diSerent than the Sun–Earth case. There are basically two types of transfers to the Earth–Moon points, the direct and
Fig. 9. One-way fast transfers from low-Earth orbit (altitude ∼ 188 km) to the Sun–Earth L2 point. The :V cost to enter an orbit around the L1 point is approximately the same.
Fig. 8. Relikt-2 trajectory using lunar gravity-assist for transfer to Sun–Earth L2 point.
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693
Fig. 10. Trajectories to the vicinity of the Earth–Moon collinear libration points.
the indirect [15,16]. Optimized transfers to the Earth –Moon L2 point are shown in Fig. 10 for both types. Corresponding results for the L1 point are also given in Fig. 10. Notice that the retro-:V cost for an indirect transfer to L2 is about 900 m=s lower than the cost for a direct transfer. However, for the L1 point, the diSerence between the direct and indirect transfers is not signi@cant. Finally, it should be mentioned that transfer trajectories to either L1 or L2 with retro-:V ’s under 50 m=s are possible, but transfer times are more than 100 days [17,18]. Due to the lengthy transfer times, these trajectories are only of interest for cargo missions. 3. A logical rst step: The deep-space shuttle As mentioned earlier, human servicing of L2 telescopes would be a relatively inexpensive way to begin a program of human exploration beyond low-Earth orbit. One way to achieve this goal would be to develop a reusable crew-transfer vehicle called a Deep-Space Shuttle (DSS). As shown in Fig. 11, the DSS could be used to transport astronauts between a low-Earth orbit and a Sun–Earth L2 orbit. The DSS is envisioned as a one and a half-stage vehicle (i.e., a core stage with drop tanks) that uses storable propellants [e.g.,
Fig. 11. Mission scenario for telescope servicing in the vicinity of the Sun–Earth L2 libration point. Nominal round-trip transfer time ∼ 35 days.
liquid oxygen/methane (LOX=CH4 ) with a speci@c impulse of about 365 s]. The mission pro@le outlined in Fig. 11 requires a deterministic :V capability of
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Table 2 Telescope servicing alternatives Servicing location
Sun–Earth L2 Earth–Moon L1 Earth–Moon L2 High-Earth orbit • Perigee ∼ 2 RE • Apogee ∼ 60 RE
Requirements for deep-space shuttle
Comments
:V at LEO departure (m/s)
:V to enter and Round-trip Pight time exit servicing with 5-day stay location (m/s) at location (days)
3230 3100 3150 3150
1800 1500 700 ¡ 500
35 12 23 10
about 5 km=s, and at least 35 days of consumables (oxygen, water, food, etc.) for the crew. It is assumed that the crew returns directly to Earth in an Apollo-style re-entry capsule. The DSS (sans crew) then uses multiple aerobraking maneuvers to return to a desired low-Earth orbit. Multiple aerobraking passes are preferred to a single aerocapture maneuver because this method eases the requirements on the thermal protection system for the DSS. To summarize, the top-level requirements for the DSS are: • Crew size: 3–4 people. • Consumables for Pights of 35–50 days. • :V capability ∼ 6 km=s (includes navigation and margin). • Storable propellants (I sp ∼ 365 s). • Apollo-style re-entry capsule for crew. • Aerobraking capability. There are several alternative proposals for servicing the L2 telescopes (see Table 2), but they all have the major disadvantage of requiring the L2 telescope to transfer to a new location. Although it is possible to use a low-energy transfer trajectory between the Sun–Earth L2 point and the other proposed servicing locations, an impaired telescope might not be able to carry out this transfer. In any event, assuming that an L2 telescope could be safely transported to one of the alternative locations listed in Table 2, which location should it be? As noted earlier, the Earth– Moon L1 location was recommended by NEXT. However, Table 2 shows that a high-Earth orbit location is preferable to the Earth–Moon L1 point because the :V cost is lower by at least 950 m=s, and the roundtrip
On-site servicing Must transfer telescope to servicinglocation [17,18] Must transfer telescope to servicing location [17,18] Lunar gravity-assist maneuvers used to transfer telescope to and from servicing location (see Fig. 12)
Fig. 12. Simpli@ed version of a double lunar-swingby trajectory that could be used to transfer an L2 telescope to and from a high-Earth orbit [19,20].
Pight time is also reduced. Finally, it should be pointed out that the DSS could be used to transport astronauts to other interesting destinations in the Earth’s neighborhood. As a matter of fact, a DSS with a :V capability of 6 km=s would provide access to almost any place in the Earth’s neighborhood including either of the Earth–Moon collinear libration points, geosynchronous orbit, or even lunar orbit (see Table 3). 4. L2 “Gateway” to near-Earth asteroids, Mars, and beyond Although the DSS will allow humans to reach destinations well beyond the Moon’s orbit, a larger and more capable transfer stage will be needed for missions to near-Earth asteroids and Mars. To satisfy this requirement, the baseline architecture of Fig. 4 calls for a reusable stage based at the Sun– Earth L2 “Gateway.” This reusable stage termed the
R.W. Farquhar et al. / Acta Astronautica 55 (2004) 687 – 700 Table 3 Approximate round-trip :V requirements for transfers between a low-Earth orbit (LEO) and various destinations Destinations Sun–Earth Low-lunar Geosynchronous L1 or L2 orbit orbit (without point plane change) Round-trip Pight time (does not include stay time at destination)
30 days
7 days
:V requirements (m/s) LEO exit 3230 Destination entry 900 Destination exit 900 LEO entry (aerobrake) —
3150 850 850 —
2430 1470 1470 —
4850
5370
Total
5030
∼ 11 h
interplanetary transfer vehicle (ITV) will be used to transfer astronaut crews to and from their interplanetary destinations. The basic mission scenario is shown in Fig. 13. The scenario begins with the ITV (sans crew) departure from its L2 base. The ITV then uses a series of small propulsive maneuvers (total :V ¡ 50 m=s) and lunar gravity-assists to target its @nal Earth escape maneuver (usually a propulsive :V maneuver at perigee). Just prior to this escape maneuver, a DSS “taxi” is used to transfer the crew to the outward-bound ITV. 2 The :V requirement of roughly 3:7 km=s for the rendezvous and crew transfer is well within the capability of the DSS. The ITV (with its crew) then proceeds towards its interplanetary destination. After completing the interplanetary mission, the ITV returns the crew to the vicinity of the Earth where the crew returns directly to Earth in an Apollo-style re-entry capsule. The ITV (sans crew) uses a perigee :V maneuver for Earth capture followed by lunar gravity-assists and small propulsive maneuvers to return to the L2 “Gateway.” As an example of the eRciency of using the Sun–Earth L2 point as a staging node for interplanetary destinations, it is useful to compare :V requirements for diSerent staging locations. Fig. 14 illustrates 2 This tactic will give the crew an opportunity to abort the perigee maneuver before leaving Earth orbit.
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a one-year mission pro@le to a near-Earth asteroid and lists round-trip :V costs for several potential staging nodes. Notice that an ITV located at the Sun– Earth L2 point can perform this mission with a deterministic :V cost of only 5:3 km=s, which is less than one-half the cost for an ITV based in LEO. It is also important to observe that the Earth–Moon L1 “Gateway” location favored by NEXT and others [10,11,16, 21–23] is 1:5 km=s more costly than the Sun–Earth L2 node. Therefore, a Sun–Earth collinear libration point (L1 or L2) is a very attractive staging node for an ITV. The use of the Sun–Earth collinear libration points as staging nodes for human missions to Mars is not a new idea. This mission concept was fully described in a widely distributed article by Farquhar in 1969 [24]. A key graphic from this article is reproduced here (see Fig. 15). In the concept shown in Fig. 15, the ITV operates between the Sun–Earth and Sun–Mars collinear points which leads to further reductions in the :V cost for the ITV. With this plan, the crew could use an aerocapture vehicle to proceed directly to Mars’ surface just before the ITV executes a braking maneuver at B. Of course, when the crew is ready to return, they would need another vehicle to travel from Mars surface and/or Mars orbit to the ITV at the libration point. Fig. 16 gives :V costs for fast transfers between a low-Mars circular orbit and a collinear Sun–Mars libration point. It is diRcult to provide a de@nitive list of requirements for the ITV because there are several viable alternative solutions that will require further study before making a @nal selection. However, for the mission scenario outlined in Fig. 13, a few general observations indicate that: • Round-trip Pight times could be as long as 3 years or, in some cases, even longer. Trip times less than 6 months are not likely. • The ITV will not require an aerocapture or aerobraking capability. • An Apollo-style crew re-entry capsule will be required. • The ITV could use either chemical propulsion (I sp ∼ 365 s) or a nuclear thermal rocket (I sp ∼ 900 s). A hybrid nuclear system that integrates high thrust and low thrust in a single reactor would be even more desirable [25].
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Fig. 13. Mission scenario for interplanetary transfer vehicle (ITV) that is based at the Sun–Earth L2 “Gateway.”
Fig. 14. Mission to near-Earth asteroid 1999 A010 with a launch in 2025.
A nuclear ITV based at a distant location such as one of the Sun–Earth collinear libration points would not cause as much concern as a nuclear system operating in low-Earth orbit. However, in the
scenario of Fig. 13, perigee :V maneuvers are used for Earth escape and capture. Clearly, these maneuvers must be done at a high altitude to minimize the risk of Earth impact. Current mission studies have
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A low-thrust vehicle is ideally suited to this location because the L2 point is at the edge of the Earth’s energy well, and will not require time-consuming spiral trajectories for Earth escape and capture. Detailed descriptions of various low-thrust trajectories to and from the Sun–Earth L2 point are given by Kawaguchi and Yoshimura in [26,27]. 5. Future human expeditions to the Moon
Fig. 15. Interplanetary transport system using the Sun–Earth and Sun–Mars libration points [24]. Periapsis :V maneuvers are executed at A and B in the diagram.
Fig. 16. One-way fast transfers from a low-Mars orbit (altitude ∼ 500 km) to the Sun–Mars L1 point. The :V cost to enter an orbit around the L2 point is approximately the same.
speci@ed a minimum altitude of 2500 km for nuclear operations. The architecture of Fig. 4 also includes a reusable interplanetary cargo stage (ICS) that is based at the Sun–Earth L2 “Gateway.” It is anticipated that the ICS will use some form of low-thrust propulsion such as solar-electric, nuclear-electric, or even a solar sail.
The fact that the Moon always presents the same face towards the Earth both aids and hinders lunar exploration. Near-side lunar missions are simpli@ed because they have direct access to Earth-based control centers. However, farside lunar operations will require some kind of satellite communications link with the Earth. In 1966, Farquhar showed that it would be possible to establish a continuous farside communications link using a single comsat in a halo orbit around the translunar libration point, L2 [28,29]. The basic idea is illustrated in Fig. 17. A halo orbit with a radius of only 3500 km will always maintain line-of-sight contact with the Earth and the Moon’s farside. When viewed from the lunar surface, the entire halo orbit subtends an angle of 6:2◦ . In the Fall of 1971, NASA considered the use of a halo comsat to support a farside landing by Apollo-17. Unfortunately, a reluctance to try anything new at the end of a very successful program resulted in NASA losing a tremendous opportunity to end the Apollo Program on a high note. A brief account of this episode is given in [6]. In addition to its potential use for farside communications, the L2 halo orbit has also been proposed as an ideal staging node for a future lunar shuttle transportation system [15]. However, current studies of the lunar
Fig. 17. Lunar farside communications link.
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Table 4 Comparison of diSerent transportation modes between LEO (altitude ∼ 185 km) and lunar orbit (altitude ∼ 100 km) • DSS operates between LEO and L1, L2, or lunar orbit. • Lunar tug operates between L1,L2 and lunar orbit (one-way :V ∼ 750 m=s). • DSS uses aerobraking to return to LEO. Round-trip :V for deep-space shuttle (m/s)
Round-trip :V (m=s)
Round-trip time (days)
Staging node
:V at LEO
:V at node
Tug :V
Total :V
DSS
Tug
Total
Direct to L0 Earth–Moon L1 Earth–Moon L2
3150 3100 3150
1700 1500 700
— 1500 1500
4850 6100 5350
9 7 18
— 5 6
9 12 24
transportation problem have concentrated on the use of the Earth–Moon L1 point as the staging node for further human expeditions to the Moon [10,11,16,21,22]. Both of the Earth–Moon collinear points have important operational advantages over the standard lunar orbit rendezvous (LOR) mission mode, such as
back. Previous studies of a lunar shuttle system using the aforementioned assumptions have shown that the payload delivered to lunar orbit is signi@cantly higher with L2 staging when compared with a direct transfer [15,30]. To sum up the lunar transport trades, it appears that:
• The launch window for transfers between the libration point and any point on the lunar surface is essentially unconstrained (i.e., any site, anytime). • An increased Pexibility for transfers between the libration point and the Earth. • A DSS located in an L2 halo orbit would have complete farside communications coverage.
• For infrequent human Pights to the Moon (i.e., one or two missions per year), the standard LOR mode using a DSS would be a sensible approach. • If a permanent lunar base were established requiring frequent missions to the Moon, a lunar shuttle system using the L2 staging concept might provide an eRcient and Pexible way to maintain this base. • It is unlikely that L1 staging will oSer any performance advantage regardless of the Pight frequency.
To have a better understanding of the advantages and disadvantages of the libration-point staging concepts, it is useful to compare the :V costs and transfer times for a round-trip mission between a low-Earth orbit and a low lunar orbit. Approximate results for the two libration-point modes and a direct transfer to lunar orbit are given in Table 4. For the libration-point modes, it is assumed that a second vehicle called a “lunar tug” would be used to transport the crew to and from lunar orbit. As Table 4 clearly shows, a direct Pight to lunar orbit provides the shortest round-trip Pight time and the smallest :V cost. The comparison between the libration-point modes is mixed, with the shortest Pight time for L1 and the smallest :V cost for L2. However, the situation is quite diSerent if we assume a reusable shuttle system where the lunar tug is already based at the libration point (i.e., transported there by an earlier cargo Pight). For this case, it is also assumed that the DSS would be required to replenish the fuel for the tug’s transfer to lunar orbit and
6. Conclusions and recommendations Although a de@nitive strategy for the next steps in deep-space exploration is still evolving, it is clear that the collinear libration points in the Earth’s vicinity will play an important role in this plan. Some key @ndings of this study can be summarized as follows: • The Sun–Earth collinear libration points, L1 and L2, are increasingly popular locations for a variety of scienti@c spacecraft. This situation is especially true for the Sun–Earth L2 point which is an ideal site for astronomical observations. • Human servicing of large astronomical facilities at the Sun–Earth L2 point is highly desirable. This study calls for the development of a DSS that would transport astronauts to the L2 telescopes where they could be repaired on station. Round-trip Pight times for these servicing missions would be about 30–35
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•
•
•
•
days which is considered excessive by critics of this plan. However, if 35-day missions are considered to be too long, humans will never get to near-Earth asteroids or Mars where Pight times are typically 6 –24 months! Another way to service the L2 telescopes would be to require the telescope to use a low-energy trajectory to transfer to a location that is more accessible to astronauts. This technique has a number of obvious drawbacks, but if required for some reason, the best location would be a highly-elliptical Earth orbit. Several staging nodes were examined for human missions to near-Earth asteroids and Mars. It was found that a node at either of the Sun–Earth collinear points would yield the best result. For a sample round-trip mission to a near-Earth asteroid, it was shown that the mission could be performed with a deterministic :V of about 5:3 km=s when using a node at the Sun–Earth L2 point. The corresponding cost for a node at the Earth–Moon L1 point was roughly 6:8 km=s. It is clear that a comsat stationed in a halo orbit around the Earth–Moon L2 point, where it would provide continuous farside communications coverage, will be an important element for future human expeditions to the Moon. The preferred mission mode for future human expeditions to the Moon is somewhat dependent on the Pight rate. For one or two missions/year, the familiar lunar–orbit rendezvous (LOR) mode is probably the best choice. However, for support of a lunar base that could require a Pight rate of 12 or more missions per year, the trades are a little murky. Even so, it appears that the leading contenders would be LOR and a staging node at the Earth–Moon L2 point.
In addition to the @ndings listed above, a number of important trade studies have been identi@ed. A few of these studies are briePy noted below. • Comprehensive studies of alternative mission modes that would involve the Sun–Earth L2 “Gateway” concept. These studies would include telescope servicing as well as missions to near-Earth asteroids and Mars. In addition to mission design trades, a variety of vehicle designs and propulsion
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options should be examined. Baseline designs for the principal vehicles mentioned in this study (i.e., DSS, ITV, and ICS) should be de@ned at least to a conceptual level. • A focused study of Mars transportation scenarios that utilize both the Sun–Earth and Sun–Mars collinear libration points. The advantages and disadvantages of this intriguing technique require an in-depth analysis to be fully understood. • Realistic trade studies of a variety of mission modes for a lunar shuttle system that could support a lunar base at various locations on the Moon (e.g., farside, north or south polar regions). This type of comparative study has not been investigated in detail since the early 1970s. References [1] R.W. Farquhar, The control and use of libration-point satellites, NASA TR R-346, September 1970. [2] D.W. Dunham, C.E. Roberts, Stationkeeping techniques for libration-point satellites, Journal of the Astronautical Sciences 49 (1) (2001) 127–144. [3] R.W. Farquhar, D.P. Muhonen, D.L. Richardson, Mission design for a halo orbiter of the earth, Journal of Spacecraft and Rockets 14 (3) (1977) 170–177. [4] R.W. Farquhar, et al., Trajectories and orbital maneuvers for the @rst libration-point satellite, Journal of Guidance and Control 3 (6) (1980) 549–554. [5] R. Farquhar, D. Muhonen, L.C. Church, Trajectories and orbital maneuvers for the ISEE-3/ICE comet mission, Journal of the Astronautical Sciences 33 (3) (1985) 235–254. [6] R.W. Farquhar, The Pight of ISEE-3/ICE: origins, mission history, and a legacy, Journal of the Astronautical Sciences 49 (1) (2001) 23–73. [7] R.W. Farquhar, D.W. Dunhan, Use of libration-point orbits for space observatories, in: Y. Kondo (Ed.), Observatories in Earth Orbit and Beyond, Kluwer Academic Publishers, Dordrecht, 1990, pp. 391–395. [8] Do we still need astronauts? Nature 419 (2002) 653. [9] T. Reichhardt, A million-mile service, Nature 419 (2002) 666. [10] B.G. Drake, et al., Technologies for human space exploration: earth’s neighborhood and beyond, AIAA Paper 2001-4634, August 2001. [11] D.R. Cooke, et al., Innovations in mission architectures for exploration beyond low-Earth orbit, IAC Paper 02-Q.6.04, October 2002. [12] R.W. Farquhar, Halo-orbit and lunar-swingby missions of the 1990’s, Acta Astronautica 24 (1991) 227–234. [13] N. Eismont, et al., Lunar swingby as a tool for halo-orbit optimization in Relikt-2 project, ESA SP-326, December 1991, pp. 435–439.
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