A new class of long term stable lunar resonance orbits: Space weather applications and the Interstellar Boundary Explorer

Transcription

1 SPACE WEATHER, VOL. 9,, doi: /2011sw000704, 2011 A new class of long term stable lunar resonance orbits: Space weather applications and the Interstellar Boundary Explorer D. J. McComas, 1,2 J. P. Carrico, 3 B. Hautamaki, 4 M. Intelisano, 3 R. Lebois, 3 M. Loucks, 5 L. Policastri, 3 M. Reno, 1,6 J. Scherrer, 1 N. A. Schwadron, 1,7 M. Tapley, 1 and R. Tyler 4 Received 5 July 2011; revised 17 August 2011; accepted 18 August 2011; published 10 November [1] NASA s Interstellar Boundary Explorer (IBEX) mission was recently maneuvered into a unique long term stable Earth orbit, with apogee at 50 Earth radii (R E ). The Moon s ( 65 R E ) gravity disrupts most highly elliptical Earth orbits, leading to (1) chaotic orbital solutions, (2) the inability to predict orbital positions more than a few years into the future, and ultimately (3) mission ending possibilities of atmospheric reentry or escape from Earth orbit. By synchronizing the satellite s orbital period to integer fractions of the Moon s sidereal period, P M = 27.3 days (e.g., P M /2 = 13.6 days, P M /3 = 9.1 days), and phasing apogee to stay away from the Moon, very long term stability can be achieved. Our analysis indicates orbital stability for well over a decade, and these IBEX like orbits represent a new class of Earth orbits that are stable far longer than typical satellite lifetimes. These orbits provide cost effective and nearly ideal locations for long term space weather observations from spacecraft that can remotely image the Earth s magnetosphere from outside its boundaries while simultaneously providing external (solar wind or magnetosheath) observation over most of their orbits. Utilized with multiple spacecraft, such orbits would allow continuous and simultaneous monitoring of the magnetosphere in order to help predict and mitigate adverse space weather driven effects. Citation: McComas, D. J., et al. (2011), A new class of long term stable lunar resonance orbits: Space weather applications and the Interstellar Boundary Explorer, Space Weather, 9,, doi: /2011sw Space Science and Engineering, Southwest Research Institute, San Antonio, Texas, USA. 2 Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas, USA. 3 Space Systems, Applied Defense Solutions, Fulton, Maryland, USA. 4 Orbital Sciences Corporation, Dulles, Virginia, USA. 5 Space Exploration Engineering, Friday Harbor, Washington, USA. 6 Austin Mission Consulting, Austin, Texas, USA. 7 Department of Physics, University of New Hampshire, Durham, New Hampshire, USA. 1. Introduction [2] The Interstellar Boundary Explorer (IBEX) [McComas et al., 2004, 2009a] is a small NASA mission, demonstrating a unique high altitude ( 50 Earth radii (R E ) apogee), lunar resonance orbit for the first time. This orbit, and other lunar resonance orbits described here, would provide excellent locations for a variety of cost effective and very long term space weather monitoring satellites. [3] The IBEX mission is dedicated to making the first global observations of the interaction of our heliosphere with the local interstellar medium. These global observations are made by imaging individual energetic neutral atoms (ENAs) propagating in from the heliosphere s boundary region 100 AU from the Sun. However, in order to accomplish this, IBEX needed to be placed in a highly elliptical orbit with apogee 50 R E, well outside the Earth s magnetosphere. Most missions would simply use a larger launch vehicle (LV) to achieve this, but in order to stay within the cost constraints of a NASA Small Explorer mission, we had to use the smallest and least expensive LV available in NASA s arsenal an airplane launched Pegasus, which only places satellites into Low Earth Orbit (LEO). Therefore, the IBEX team needed to develop its own way to achieve a very high altitude Earth orbit starting from a Pegasus rocket drop off in LEO. [4] In order to achieve our orbit, we needed to add significant additional propulsion on top of the Pegasus rocket supplied by NASA. Therefore, the IBEX provided flight system included not just our spacecraft but also an adapter cone and a solid rocket motor (SRM) (Figure 1), which the IBEX team used to help boost the spacecraft into a highly elliptical, high altitude Earth orbit after separating from the Pegasus [McComas et al., 2006, 2009a; Scherrer et al., 2009]. IBEX was launched into LEO ( 200 km altitude) Copyright 2011 by the American Geophysical Union 1of9

2 Figure 1. Shown is the Interstellar Boundary Explorer (IBEX) flight system beneath an exploded schematic including Pegasus third stage. After the Pegasus reached an altitude of 200 km, IBEX separated from it, released the adapter cone, and used the solid rocket motor (SRM) and internal hydrazine propulsion system to boost the IBEX spacecraft into an 50 R E apogee orbit. on 19 October 2008 from the Reagan Test Site at Kwajalein Atoll. This near equatorial launch allowed the Pegasus XL to carry maximum mass to LEO by making use of the Earth s rotational energy. [5] After completion of third stage burn out at 200 km altitude, Pegasus spun the entire flight system up to 60 RPM before separating from IBEX. We then sequentially ejected the adapter cone, ignited and burned the SRM, and released the burned out SRM, leaving the IBEX spacecraft in orbit with apogee at 35 R E and perigee still at 200 km. After this, we spun the spacecraft down to 23 RPM and performed a series of burns using our internal hydrazine propulsion system to raise both apogee and perigee. These maneuvers left IBEX in a highly elliptical, high altitude, 7.5 day orbit with initial perigee of 2 R E and apogee of 50 R E. Finally, we spun the spacecraft down to 4 RPM, pointed it toward the Sun, and, in January 2009, completed commissioning and began science operations. Because of the motion of the Earth around the Sun (360 rotation in 365 days), IBEX repoints back toward the Sun at each perigee in order to maintain the roughly Sun pointing attitude needed to power the spacecraft and make our science observations. [6] Figure 2 shows a typical IBEX orbit (orbit 51) in the middle of IBEX s 2 year prime science mission. In this particular case, IBEX was positioned not just to observe outer heliospheric ENAs over much of each spin, but also to have its field of view (FOV) scan through the magnetosphere, providing very high sensitivity ENA observations from a cut through the magnetosphere each spin. The IBEX orbit is roughly inertially fixed, so over the course of each year, the orbit appears to rotate once around the Earth. Because of IBEX s single pixel viewing perpendicular to the roughly Sun pointed spin axis, this geometry provided different sets of viewing slices through the magnetosphere over time. In addition, the low angular momentum associated with this high eccentricity orbit in combination with torques on the orbit arising from Earth s oblateness (acting in the equatorial plane) and Lunar and Solar tides (acting in the ecliptic) mean that the inclination of the orbit (angle about the apogee perigee vector) varies substantially over the course of the mission, providing still more perspectives for magnetospheric observations. [7] The first round of heliospheric observations from IBEX was published in a special issue of Science in These observations have already revolutionized our understanding of the heliosphere s interstellar interaction in multiple ways. First, IBEX discovered a ribbon of enhanced ENA emissions, several times larger than the globally distributed flux [McComas et al., 2009b; Fuselier et al., 2009; Funsten et al., 2009; Schwadron et al., 2009] that appears to be ordered by the draped and compressed interstellar magnetic field, just outside the heliopause in the outer heliosheath [McComas et al., 2009b; Schwadron et al., 2009]. These observations also show that the ribbon is narrow ( 20 full width at half maximum (FWHM)) at all energies [Fuselier et al., 2009], contains significant fine structure down to a few degrees in width [McComas et al., 2009b], and appears as almost a complete loop in the sky [Funsten et al., 2009]. IBEX also provided the first direct observations of the interstellar H and O (along with observations of He) penetrating in from the local interstellar medium [Möbius et al., 2009]. [8] Since the initial IBEX publications, there have been numerous theoretical studies examining one of the six possible explanations for the ribbon given by McComas Figure 2. Diagram of IBEX orbit 51 in the geocentric solar ecliptic (GSE) X Y plane, which extended from 27 October to 2 November 2009 (dots indicate 1 day intervals). IBEX s field of view (FOV) produces vertical cuts (gray FOV) through the magnetosphere and plasma sheet from the side. The thicker selected data portion of the orbit is used to generate the image on the righthand side of Figure 4. From McComas et al. [2011]. 2of9

3 Figure 3. Image of magnetospheric energetic neutral atom (ENA) emissions observed by IBEX during orbit 23. Observed, color coded ENA flux is superposed on model magnetic field lines. Comparatively strong emissions are evident from both the subsolar magnetopause and the northern and southern cusps. et al. [2009b] or proposing other, new possibilities (see summaries by McComas et al. [2010] and Schwadron et al. [2011]). Subsequent analyses of newer IBEX data have addressed a variety of topics. For example, McComas et al. [2010] examined the temporal stability of the ribbon and globally distributed ENA fluxes between the first two 6 month sky maps, and showed that while the heliosphere was largely stable over this timeframe, there was statistically significant evolution of some of the features, most significantly the bright knot in the ribbon. Subsequently, Schwadron et al. [2011] were able to separate the ribbon feature from the globally distributed flux in the timeaveraged sky maps and showed a slightly offset nose and substantially offset tail direction, confirming the importance of the external magnetic field on the heliosphere s global morphology. [9] In addition to exceeding all expectations for measurements of the interstellar interaction, IBEX has also made numerous ground breaking observations of other space phenomena. In particular, McComas et al. [2009c] published the first measurements of hydrogen atoms backscattered and neutralized by the lunar regolith. These observations provided the first space based measure of these processes from the Moon, revealing that 10% of all solar wind striking the Moon is reemitted as neutral H [McComas et al., 2009c]. This neutral backscatter value is especially important as it quantifies solar and stellar wind interactions with other small bodies and dust, which are important to planetary formation and interaction theories. [10] The benefits of the IBEX orbit for space weather applications are many fold. In particular, imaging may be a critical component of future space weather missions and IBEX has already proven to be an excellent platform for observing the Earth s magnetosphere from outside its boundaries. Figure 3 shows ENA observations from IBEX s orbit 23, integrated from 13:32 UT on 27 March 2009 to 21:52 UT on 28 March Over this relatively quiet interval, IBEX repeatedly scanned the dayside magnetosphere, moving slowly sunward in its orbit. IBEX observed significantly enhanced emissions from both the subsolar compression region ahead of the nose of the magnetopause [Fuselier et al., 2010] and from both the northern and southern cusp regions [Petrinec et al., 2011], where magnetic reconnection along the magnetopause allows solar wind ions to penetrate deeply into the Earth s magnetosphere where geocoronal neutral densities (and hence ENA emissions) are significantly enhanced. [11] ENA emissions from the nightside magnetosphere and plasma sheet are also readily observable by IBEX [McComas et al., 2011]. Figure 4 shows images from two IBEX orbits: orbit 52, which displays typical plasma sheet emissions that correlate reasonably well with a model magnetic field; and orbit 51, where a significant temporal intensification may indicate a near Earth disconnection event. IBEX energy spectra ( kev) from this latter orbit indicates the simultaneous addition of both hot (several kev) and colder ( 700 ev) ENAs (parent ions) during the mid tail intensification [McComas et al., 2011]. [12] In January 2011, IBEX finished its prime mission phase and formally passed into its extended mission. As planned from the start, IBEX required orbital maintenance maneuvers early in the extended mission in order to avoid eclipses longer than accommodated by IBEX s batteries and to avoid very low perigee orbits brought on by lunar gravitational perturbations to IBEX s very high altitude orbit. Roughly one year prior to these maneuvers, the IBEX team began studying various possible maneuver and orbit options in detail. In the process of this work, we explored a new class of orbits that, unlike our original orbit, are stable over decades, far longer than normal spacecraft and satellite lifetimes. Thus, instead of having to carry out orbit maintenance maneuvers every couple of years in the extended mission as originally planned, in June 2011, we maneuvered IBEX into its final, permanent orbit, which provides an orbital lifetime of at least several decades. This paper describes the new IBEX orbit and documents this new class of long term stable orbits. [13] For an ENA imager dedicated to magnetospheric observations for space weather purposes, global viewing from outside the Earth s magnetosphere at minimum cost in propellant and communications power could be accomplished from essentially any very high altitude, highly elliptic orbit, where the spacecraft essentially hangs 3of9

4 Figure 4. ENA fluxes projected onto the GSE X Z plane. These images show time averaged ENA fluxes from 2.0 to 3.8 kev full width at half maximum (FWHM) from orbit 52 (10:48 UT on 5 November 2009 to 02:23 UT on 7 November 2009) and orbit 51 (21:21 UT on 27 October 2009 to 13:40 UT on 29 October 2009). Note that the instantaneous FOV of IBEX is 5.5 R E wide (lower right corner), so the image was built up as IBEX s viewing moved slowly down the tail (Figure 2). Field lines were generated with the CCMC Tsyganenko model for the central time of the data interval. From McComas et al. [2011]. near apogee for most of its orbit period. IBEX has already demonstrated the utility of this sort of orbit for magnetospheric ENA imaging, and optimized magnetospheric instrumentation could easily view and image the entire magnetosphere simultaneously at high (less than one minute) cadence, combining information on (1) the location of the magnetopause from enhanced emission from the stagnation region [Fuselier et al., 2010], (2) the openness of the dayside magnetopause from cusp emissions [Petrinec et al., 2011], and (3) the size, shape, and variations of the magnetotail plasma sheet [McComas et al., 2011]. With additional ENA measurements at somewhat higher energies, the ring current could be imaged and EUV, FUV, and other potential imaging techniques would also be greatly enhanced by an orbit with such long, high altitude observations. [14] Because spacecraft in such high altitude orbits spend the vast majority of their time in either the unperturbed solar wind or magnetosheath, it could simultaneously provide direct in situ observations of the external plasma and energetic particle conditions interacting with the magnetosphere. Furthermore, while a single spacecraft in any highly elliptical Earth orbit cannot continually reside in the external environment, one can envisage a mission with two to three spacecraft providing the excellent combination of continuous coverage of external conditions, ENA remote observations from outside the magnetosphere, and local, in situ measurements within it. Thus, the long term stable, very high altitude orbit being demonstrated by IBEX and described in this paper would provide excellent platforms for remote sensing of the time evolution of magnetospheric conditions and measuring solar driven changes that can drive geomagnetic activity and deleteriously impact critical infrastructure such as space systems and the electric grid, as well as supporting numerous other non space weather applications. 2. The New IBEX Orbit [15] Since the completion of initial orbit raising in late 2008, the IBEX team had not carried out any other propulsion except for routine attitude control to rotate the spin axis back toward the Sun each orbit. These rotations are accomplished with very small and nearly balanced 5N radial thruster firings once each 7.5 day orbit, so the IBEX orbit is nearly inertially fixed except for gravitational perturbations. Figure 5 shows the IBEX orbit around the Earth from the end of initial orbit raising up to June 2011 in inertial coordinates (Figure 5a) and in the Earth Moon rotating frame such that the Moon remains fixed at the top of its orbit (Figure 5b). In this latter plot it is easy to see that while most of the orbits have apogee far from the Earth Moon line, phasing between the orbital and lunar periods causes a small fraction of the orbits to pass much closer to the Moon. For these nearer passes, the lunar gravitational perturbations on the orbit can be quite large and significantly affect the orbit. [16] The orbits nearly centered on the vertical Earth Moon line in Figure 5b show particularly pathological cases. If such an orbit has its apogee just behind the Earth Moon line, then the spacecraft velocity is increased by the Moon s gravity, increasing IBEX s orbital energy. In contrast, if apogee is just ahead of the Earth Moon line, then the Moon decelerates the spacecraft velocity, decreasing 4of9

5 IBEX s orbital energy. Orbits such as these produce bifurcations in the orbital solutions, which create increasingly variable predictions for the future orbit and ultimately lead to chaotic solutions where the spacecraft can either be driven down into the atmosphere or escape from Earth orbit, ending the mission in either case. The inability to predict the future relationship of the apogees with respect to the Moon, because of uncertainties from orbit estimation and maneuver execution, is the primary cause of the chaotic behavior which prevents the long term prediction of the orbit evolution. [17] Figure 6 shows the Monte Carlo simulation for the predicted perigee radius. These simulations varied the initial orbit state using a Gaussian probability distribution up to ±3s from the orbit state error covariance from orbit Figure 6. Monte Carlo simulation of the predicted perigee radius as a function of time. The black line indicates the actual orbit up through 5 June 2011 when the IBEX maneuver began and the nominal predicted solution after that time. determination, which included both the position and velocity components. The initial state for this simulation was taken near apogee. The 1s uncertainty in the position was less than 2 km, and the 1s uncertainty in velocity was less than 5 mm s 1. The magnitude of each attitude re pointing maneuver was nominally 41 mm s 1 also varied by 2% (±3s), based on operational trending. Each Monte Carlo run is a high fidelity numerically integrated trajectory propagation. [18] As the predictions extend further into the future, very small perturbations produce increasingly larger uncertainties, with apogees near the Earth Moon line Figure 5. IBEX orbit displayed in the lunar orbital plane in two Earth centered coordinate systems. (a) IBEX orbital progression in inertial coordinates for the 2.5 years between the end of initial orbit raising and our recent maneuvers (January 2009 to June 2011). (b) Same orbits in a rotating system where the Moon remains at the top of its orbit. In this system, IBEX s inertially fixed orbit appears to rotate around the Earth with a few petals passing close to the Moon; lunar gravitational perturbations can be quite large for these orbits, leading to chaotic orbital solutions. All orbital dynamics analyses carried out to design the IBEX orbit were done with STK/Astrogator [Carrico and Fletcher, 2002]. We configured Astrogator to use a dual order, variable step size Runge Kutta integrator to numerically integrate the trajectories. The force model included gravitational effects of the Sun, Moon, and nonspherical Earth; solar radiation pressure; and atmospheric drag (when applicable). During orbit maneuvers the equations of motion also included the accelerations due to thrust computed from propulsion system and engine models. 5of9

6 Figure 7. The predicted perigee radius from a Monte Carlo simulation run after spacecraft commissioning (blue line) showing negligible spread after 1.5 years. The actual perigee radius from orbit estimation is overlaid (dashed black line). The Monte Carlo simulation varied the initial orbit position and velocity vectors according to the 6 6 orbit state error covariance matrix and included the uncertainty of the magnitude of the attitude repointing maneuvers performed every orbit (see section 2). [20] The maneuvers that were carried out in June 2011 comprised three 600 s burns from IBEX s 22 N aft axial thruster on two successive orbits near apogee. These burns produced an overall Dv of 263 m s 1. Collectively, these three burns raised IBEX s perigee from 2.5 to 8 R E, both moving perigee above the outer radiation belts (minimizing radiation fluence throughout the rest of the mission) and putting IBEX on a new and far more stable lunar resonance orbit. This orbit also fulfilled IBEX s requirements for low rate communications at apogee and high rate around perigee, taking into account IBEX s nonspherical antenna pattern, ground station capabilities, and accumulated data each orbit. [21] Figure 8 shows a plot in the same Earth Moon rotating frame as used in Figure 5b with the last 20 orbits before IBEX was moved to its present orbit (green), transfer orbit (red), and IBEX s new predicted orbit (blue) for the 10 years. Clearly, this new 3 petal orbit avoids near Moon encounters by always having spacecraft apogee ±60 or 180 away from the Earth Moon line. The period for this orbit is 9.1 days, which is roughly one third of the sidereal lunar orbit (P M = days); we designate this as a P M /3 lunar resonance orbit. [22] Additional Dv could have been used to move IBEX into such an orbit at any time, but in order to minimize the hydrazine required (and maintain enough for repointing creating the largest uncertainties and bifurcations as described above. By the time the solutions are propagated 3 years, the predictions break down into a chaotic set with both very high and very low perigees possible. Figure 6 also illustrates why IBEX s initial orbital maintenance maneuver was scheduled for June 2011, prior to the low perigees in July September 2011 when IBEX s perigee was predicted to drop down into the very high radiation environment of the inner radiation belt. [19] The validity of the orbit propagation and these Monte Carlo simulations for the IBEX orbit was described by Carrico et al. [2010]. One method of validation is shown in Figure 7, which displays the actual orbit perigee radius overlaid on the results of a Monte Carlo simulation. This is the exact simulation that the IBEX operations team used to verify that the spacecraft was on the correct orbit after commissioning in November The actual orbit evolution estimated from tracking data through May 2010 matches the prediction extremely well. The software and algorithms used for this orbit propagation, STK/ Astrogator, have also been verified though operational use on many other missions, including several with strong multibody gravitational sources. These multibody missions include the Wilkinson Microwave Anisotropy Probe (WMAP) libration point mission, the Lunar Crater Observation and Sensing Satellite (LCROSS), The Lunar Reconnaissance Orbiter (LRO), The New Horizons mission to Pluto, and the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission. Figure 8. Plot of IBEX s newp M /3 ( 9.1 day) orbit (blue),the last 20 cycles of the old orbit (green), and the transfer orbit between these (red) in the same Earth Moon rotating system used for Figure 5. With the Moon at the top in this system, this lunar synchronous orbit avoids any close encounters with the Moon, minimizing orbital perturbations for such a high altitude orbit. 6of9

7 Figure 9. Orbital period prediction showing oscillation about the effectively stable 9.1 day P M /3 period. maneuvers for decades to come) we waited until IBEX s pre maneuver orbit approached very close to one of the three petals in this plot. By doing this, the minimum energy input was achieved and only burns to raise perigee were needed to place IBEX into the P M /3 orbit. [23] Figure 9 shows the predicted orbital period for the new orbit over the course of 10 years. As expected, the period is near to the predicted P M /3 of 9.1 days, but instead of locking in at precisely this value, the orbit oscillates about the 9.1 day period. This oscillation produces the range of apogee locations seen in Figure 8. In addition, the fact that the orbital solution oscillates around the stable P M /3 value, and insertion into this orbit can be accomplished far ( 0.2 days) from the optimum period and still be pulled in, suggests that there is a restoring force pushing the orbit back toward the theoretical orbit period. Although a formal stability analysis of the orbit has not been conducted, it is clear from the information presented that such orbits can be stable far longer than most satellite mission lifetimes. Thus, this lunar resonant orbit is Figure 11. Two other lunar synchronous, periodic orbits: (a) P M /2 (13.65 days) and (b) P M /4 (6.825 days) shown in the Earth Moon rotating frame. Figure 10. Predicted perigee radius from the Monte Carlo simulations over 10 years in the new IBEX orbit; extended Monte Carlo runs indicate stability out to functionally stable for typical duration space weather and other space missions. [24] In contrast to the rapidly developing chaotic perigee predictions for the original IBEX orbit shown in Figure 6, Figure 10 shows 10 years of Monte Carlo predictions in the new P M /3 orbit. This Monte Carlo plot includes all of the same disruptive forces as in Figure 6, and includes two spin axis repointing maneuvers per orbit instead of one, but the variation in the solutions is barely visible as all solutions lie essentially on top of each other. Finally, while the orbit perigee rises over this interval, analysis of the nominal orbit indicates that the perigee radius slowly oscillates from 6 16 R E out to [25] Other solutions exist at other integer fractions of the lunar period: P M = days. In addition to the 9.1 day P M /3 orbits, other resonance orbits exist around 13.7 days (P M /2, Figure 11a) and 6.8 days (P M /4, Figure 11b). At increasingly shorter resonant periods less than P M /3, the 7of9

8 apogee becomes even lower inside the Moon s orbit, the effects of lunar gravitational perturbations smaller, and the importance of lunar avoidance less. Both the P M /2 and P M /4 orbits were achievable as transfers from IBEX s original orbit at about the same time as our P M /3 transfer and had target perigee radii of 7 R E, but neither served the overall mission requirements as well as the 9.1 day (P M /3) orbit. [26] The P M /2 orbit shown in Figure 11 is oriented in the Earth Moon rotating frame such that the apogees are as far as possible from the Earth Moon line. A. Kogan proposed using a different P M /2 orbit with the apogees aligned directly on the Earth Moon line for the Regatta D mission [Farquhar, 1991]. The perigee radius of the Regatta D orbit was designed to be 22.5 R E so that the apogee radius was inside the Moon s orbit, about 50 to 53 R E. 3. Discussion [27] The IBEX spacecraft is the first ever to fly in a very high apogee (tens of R E ) long term stable lunar resonance orbit. The space weather applications for these new orbits are clear. Because spacecraft in the P M /2 4 orbits hang for long times at apogees of many tens of R E, they make ideal platforms for some space weather missions, especially those that seek to combine remote viewing from outside the magnetosphere with direct in situ observations of the external solar wind and magnetosheath environments. This unique combination provides for the global study and monitoring of the magnetosphere from a single platform. [28] Because these orbits can be reached with very low energy launch vehicles, they also enable highly cost effective, very high altitude missions. In particular, in addition to the NASA provided Pegasus LV, the full IBEX mission cost only $100 million (IBEX actually under ran our mission budget). Thus, for IBEX and IBEX like launches, spacecraft of just over 100 kg can be fielded to any of these orbits cheaply and efficiently. Similarly, larger spacecraft could achieve these orbits with somewhat larger LVs. Because of the cost factor, very affordable missions flying a pair or triad of spacecraft phased for observations from different petals could provide essentially continuous coverage with significant simultaneous magnetospheric observations, in some ways analogous to Two Wide angle Imaging Neutral atom Spectrometers [McComas et al., 2009d], but with far longer apogee residence times and from completely outside the magnetosphere, where penetrating particle backgrounds are much lower. [29] Another advantage of these lunar resonant orbits is that they can be reached from almost any launch window. Once a spacecraft is placed in any orbit with an appropriate apogee, it will drift in lunar phase, and eventually the orbit will cross very close to a resonance orbit petal. At that time, the minimum energy opportunity for transfer exists and the spacecraft can be readily moved onto the stable orbit. In the case of IBEX, we drifted around with respect to the Earth Moon line for over two years in order to avoid any maneuvers during the mission s prime phase. However, over this interval, there were several very good orbital matches that provided other opportunities for capture into the P M /3 and the other lunar resonance orbits. [30] Multiple spacecraft could also be released into lunar resonant orbits to provide near continuous coverage of the supersonic solar wind and the magnetosphere from different vantage points. For example a 3 spacecraft mission in which each spacecraft occupies a different lobe of the 3 lobe resonant orbits (see Figure 8) would provide simultaneous access to spatially separated regions both inside and outside the magnetosphere. While we have not fully explored the benefits and trades of a multiple spacecraft scenarios, it is clear that the resonant orbits provide a new capability to simultaneously explore spatially separated regions of geospace. Multiple spacecraft in these orbits would not be difficult to control and could sample different parts of the magnetosphere and/or radiation belts yielding simultaneous observations of dynamic activity. Additionally, IBEX demonstrates the ability for remote sensing missions to have perigee above the radiation belts, dramatically reducing instrument backgrounds even near perigee and extending mission lifetime. [31] Other objectives besides those of space weather missions could also be accomplished from these lunar resonance orbits. Some of these include Earth remote sensing, astrophysical, and national security missions. While the orbits described here were specifically intended for Earth orbiting missions, obviously, they would also apply to other planets with single major moons. Finally, because these orbits are stable for very long times, it is possible that material could be caught in these orbits, just as they are in other long term stable locations, such as the Sun planet L4/L5 points. [32] Acknowledgments. We are deeply indebted to all of the outstanding men and women who have made IBEX such an outstanding success. We also thank Don Dichmann for helpful comments on stability, Steve Petrinec for producing Figure 3, Wendy Mills for helping with the editing, and Lou Lanzerotti, the Editor of Space Weather, for encouraging us to submit our paper to this journal. This work was supported by the IBEX mission as a part of NASA s Explorer Program. References Carrico, J., and E. Fletcher (2002), Software architecture and use of Satellite Tool Kit s Astrogator module for libration point orbit missions, in Libration Point Orbits and Applications: Proceedings of the Conference, Aiguablava, Spain, June 2002, edited by G. Gómez, M. W. Lo, and J. J. Masdemont, pp , World Sci., River Edge, N. J. Carrico, J., L. Policastri, R. Lebois, and M. Loucks (2010), Covariance analysis and operational results for the Interstellar Boundary Explorer (IBEX), paper presented at the AAS/AIAA Astrodynamics Specialist Conference, Toronto, Ont., Canada, 2 5 Aug. Farquhar, R. (1991), Halo orbit and lunar swingby missions of the 1990s, Acta Astronaut., 24, , doi: / (91)90170-a. Funsten, H. O., et al. (2009), Structures and spectral variations of the outer heliosphere in IBEX energetic neutral atom maps, Science, 326, , doi: /science of9

9 Fuselier, S. A., et al. (2009), Width and variation of the ENA flux ribbon observed by the Interstellar Boundary Explorer, Science, 326, , doi: /science Fuselier, S. A., et al. (2010), Energetic neutral atoms from the Earth s subsolar magnetopause, Geophys. Res. Lett., 37, L13101, doi: / 2010GL McComas, D. J., et al. (2004), The Interstellar Boundary Explorer (IBEX), AIP Conf. Proc., 719, , doi: / McComas, D. J., et al. (2006), The Interstellar Boundary Explorer (IBEX): Update at the end of Phase B, AIP Conf. Proc., 858, , doi: / McComas, D. J., et al. (2009a), IBEX Interstellar Boundary Explorer, Space Sci. Rev., 146, 11 33, doi: /s McComas, D. J., et al. (2009b), Global observations of the interstellar interaction from the Interstellar Boundary Explorer (IBEX), Science, 326, , doi: /science McComas, D. J., et al. (2009c), Lunar backscatter and neutralization of the solar wind: First observations of neutral atoms from the Moon, Geophys. Res. Lett., 36, L12104, doi: /2009gl McComas, D. J., et al. (2009d), The Two Wide angle Imaging Neutralatom Spectrometers (TWINS) NASA Mission of Opportunity, Space Sci. Rev., 142, , doi: /s McComas, D. J., et al. (2010), Evolving outer heliosphere: Large scale stability and time variations observed by the Interstellar Boundary Explorer, J. Geophys. Res., 115, A09113, doi: /2010ja McComas, D. J., et al. (2011), First IBEX observations of the terrestrial plasma sheet and a possible disconnection event, J. Geophys. Res., 116, A02211, doi: /2010ja Möbius, E., et al. (2009), Direct observations of interstellar H, He, and O by the Interstellar Boundary Explorer, Science, 326, , doi: /science Petrinec, S. M., et al. (2011), Neutral atom imaging of the magnetospheric cusps, J. Geophys. Res., 116, A07203, doi: / 2010JA Scherrer, J., et al. (2009), The IBEX flight segment, Space Sci. Rev., 146, 35 73, doi: /s Schwadron, N. A., et al. (2009), Comparison of Interstellar Boundary Explorer observations with 3D global heliospheric models, Science, 326, , doi: /science Schwadron, N. A., et al. (2011), Separation of the IBEX ribbon from globally distributed energetic neutral atom flux, Astrophys. J., 731 (1), 56, doi: / x/731/1/56. J. P. Carrico, M. Intelisano, R. Lebois, and L. Policastri, Space Systems, Applied Defense Solutions, 8171 Maple Lawn Blvd., Ste. 210, Fulton, MD 20759, USA. B. Hautamaki and R. Tyler, Orbital Sciences Corporation, Atlantic Blvd., Dulles, VA 20166, USA. M. Loucks, Space Exploration Engineering, 640 Mullis St., Friday Harbor, WA 98250, USA. D. J. McComas, J. Scherrer, and M. Tapley, Space Science and Engineering, Southwest Research Institute, P.O. Drawer 28510, San Antonio, TX 78228, USA. (dmccomas@swri.edu) M. Reno, Austin Mission Consulting, 4301 W. William Cannon Dr., Ste. B 150, Austin, TX 78749, USA. N. A. Schwadron, Department of Physics, University of New Hampshire, 8 College Rd., Morse Hall, Rm. 354, Durham, NH 03824, USA. 9of9