Trojan Binary Asteroid Systems As Future Mission Targets

Trans. JSASS Aerospace Tech. Japan Vol. 8, No. ists27, pp. Pk_39-Pk_44, 2010 Original Paper

Trojan Binary Asteroid Systems as Future Mission Targets

By Julie BELLEROSE1) and Hajime YANO1),2)

1) JAXA Space Exploration Center (JSPEC), Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan 2) Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan

(Received July 17th, 2009)

To date, the Jupiter-Sun Lagrangian points are populated with almost 4500 asteroids, for which their formation and history are still debated. In the current work, we look at rationales for a mission to Jovian Trojan asteroids, and discuss the scientiﬁc beneﬁts to investigate binary systems and contact binary systems. We summarized the dynamics for a solar sail mission, which is currently thought to go along the Europa Jupiter System Mission (EJSM), and we show a case study of the contact binary Hektor, and its moon S/2006, which offer the most suitable conditions for spacecraft operations. Trojans asteroids offer many opportunities, and we list some of the targets in time.

KeyKey Words Words:: JovianJovian Trojan Trojan Asteroids, asteroids, Binary binary Systems, systems, C contactontact Binary, binary, solarSolar sailSail dynamics, Dynamics, Jupiter Jupiter system System

2 5) Nomenclature to date − . To give a few examples, (617) Patroclus and its companion Menoetius were found to be a low density EKBO : Kuiper Belt Objects asteroid system, while (624) Hektor is a fairly dense system EJSM : Europa Jupiter System Mission 3,4). These two systems have sizes between 140 km and 225 R3BP : Restricted Three Body Problem km, while Hektor is more than 300 km in diameter with a [x,y,z] : Position of S/C in R3BP satellite of 15 km. Mann et al. (2007) 2) have discussed the ΩJup : Orbit rate of Jupiter properties of suspected binary systems located at L4 and L5. µJup : Specific gravity Jupiter The Trojan asteroids formation and evolution are still rJA : Position w.r.t Jupiter debated, as they may be tied to the formation of the giant r : Position w.r.t. the Sun SA planets, or tied to capture of some of the Edgeworth-Kuiper SRP : Solar radiation Pressure [ , , ] Belt Objects (EKBO) in the process of possible migration gx gy gz : Acceleration due SRP 6) 7) [x˜,y˜,z˜] : Position S/C in Hill appr. . In their earlier work, Marzani et al. show that small 3 Ω = sqrtµsun/a : Orbit rate of the asteroid Trojans (with diameter < 1 km) are more stable at L5 due ast 8) µsun : Specific gravity Sun to gas drag. However, Gomes et al. have shown that aast : Asteroid distance to Sun planet migration tends to destabilize asteroids at this partic- U˜ : Asteroid potential ular region. Morbidelli has argued that their high inclina- [xˆ,yˆ,zˆ] : Position asteroid orbiter tions could only be explained from captures 9). Hence, it ωast : Asteroid spin rate is not clear if these asteroids were captured from outer re- aSRP : SRP, asteroid frame gions like the Kuiper Belt, or if they are remnants from the time of the giant planets formation. The work from Marzani 1. Introduction et al. 10), in Asteroids III, and more recently, Yano et al. 11) Trojan asteroids are orbiting the Sun in a 1:1 resonance also give a more complete description of these ques- with Jupiter, separated in two distinct regions, L4 and L5. tions and theories. Knowing more about the density, com- At the time of writing this paper, from the Minor Planet position, surface features such as impact history and space Center (MPC) (http://www.cfa.harvard.edu/iau/mpc.html), weathering of these objects can help validating these theo- we count 2798 at L4 and 1747 at L5. However, there are ries, and better complete our knowledge of the solar system only a fraction of them that have been more thoroughly formation. observed and have been given an estimated size. So far, Since Jovian Trojan asteroids are so remote, a solar pow- most of the spectrally observed Trojans have been classi- ered sail mission has now been proposed as part of the fied D-type, with a few being P-type 1). D-type asteroids coming international mission Europa Jupiter System Mis- are believed to be made of primordial, icy, and organic com- sion (EJSM) internationally worked on by NASA, ESA and 10,12) pounds. Among the Trojan asteroid population, sizes vary JAXA . A mission going to the L4 Trojan asteroid 13) from a few kilometers to 100’s of kilometers, and spin rate population would benefit from Jupiter’s gravity assist . may be only a few hours to 100’s of hours. They orbit with Hence, we look especially at suspected contact binary aster- an average inclination of 11 and 15 , respectively for oid systems located in this region and we discuss the benefit ∼ ◦ ∼ ◦ each L4 and L5 population, with some having inclinations of exploring these Jovian Trojan binary systems in more de- reaching 50 . tails. As the mission could integrate solar sail technology, ∼ ◦ Among this asteroid population, a few binary asteroid we give an overview of the basics on the dynamics of Tro- systems and contact binary systems have been discovered jans and on the dynamics of solar sail spacecraft at these

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systems. Finally, we look at Hektor as a case study, and a same line of thoughts, looking at differences in processes target opportunities in time. such as space weathering is primordial; the effects may be 2. Jovian Trojan Binary Asteroid System Exploration less in outer regions even if the composition is similar. It may even be different for each of the binary components. By exploring binary asteroid systems at Jovian Trojan lo- By exploring these systems, we can also make a direct cor- cations, we can directly verify their composition, and thus relation with data at 50 AU since, by the time of arrival to verify if they are both from common origins. Their forma- Lagrangian regions, the New Horizons mission to the Pluto- tion may also be tied to captures of EKBO, or may be a Charon system would have returned data from this remote 3,5) product of fission or dynamical friction . Binary may system 14). Having data from New Horizons, links may be also show a direct view of their internal composition if made between the two families of small bodies and minor formed through fission, and, of course, provide two target planets. This will greatly enhance our knowledge of the opportunities at once instead of only one. solar system evolution, on the scale from 1 AU to 50 AU. From current interest in sending a spacecraft to L4, Ta- Since Trojan asteroids are of large size, exploring the 2) ble 1 lists some of these suspected contact binaries at L4 , small satellites, which is still kilometers in size, may of- along with their nominal diameter (D), rotation period (P), fer better and safer conditions for orbiting or performing and asteroid spectral class, also including Hektor which is proximity operations compared to approaching the main believed to be a contact binary itself with a small moon dis- body. These rationales for exploring secondary satellites 3) covered in 2006 . From the list shown in Table 1, only have been discussed in Bellerose and Yano (2009) 15), also Hektor, Antilochus, and Neoptolemus have been classified discussing other binary system populations, and we give a D-type, while the other ones are yet to be determined. In more comprehensive approach with the Hektor case study addition, the rotation period which factor in the proximity presented next. We start by giving an overview of the dy- operations are only available for Hektor, 1999 YY2, Poly- namics related to Trojan asteroids, from far to near fields poites, Antilochus, Automedon, and Neoptolemus, being for close operations. 6.9 hrs, 7 hrs, 43 hrs, 31.5 hrs, 10.2 hrs, and 12 hrs. Al- though of similar type, fast rotation periods may indicate 3. Dynamics at Trojan Asteroids a higher strength body while slow rotating ones may be 3.13.1. SolarSolar Sailsail Explorationexploration loosely packed. There has been a few studies and mission proposals to Trojans in this last decade. Yano et al. (2004) 16) discussed Table 1. Ecliptic crossing timeline for Jovian Trojan suspected binary con- a solar powered sail flyby at the L4 Lagrangian point, and 2) tact asteroids at L4 (targets listed in Mann et al. (2007) ). Empty cells robotic exploration missions are currently being studied, indicate unresolved data to date. such as PARIS 17) (ESA) and SHOTPUT 18) (JPL) target- Trojans D (km) P (hrs) Class 19) 2146 Stentor 77 ing both Hektor, and ILion (NASA) to investigate Trojan 624 Hektor 360 6.9 D asteroids at L5. JAXA is now currently looking at the feasi- 9694 Lycomedes 78 bility of exploring Trojan asteroids at L4, as part of the next 4068 Menestheus 78 possible flagship mission to the Jovian system, in collabo- 1999 YY2 47 7 10,12) 3709 Polypoites 87 43 ration with NASA and ESA , as represented in Fig. 1. 9431 1996 PS1 59 1583 Antilochus 99 31.5 D 11668 Balios 47 2001 CE21 33 1868 Thersites 80 1999 XW261 44 2920 Automedon 111 10.2 1869 Philoctetes 34 1998 VA50 45 1647 Menelaus 37 1999 XJ55 38 2260 Neoptolemus 77 12 D 4834 Thoas 91 2002 EZ13 36 4833 Meges 95

If these Trojan asteroids are mostly composed of rocky material, and of similar composition to giant planets, they may indicate an outward migration of giants as the asteroids may have formed from rocky material inside the snow Fig. 1. Solar sail exploration of the Jovian system and the Jovian Trojan line. On the other hand, light density bodies may indicate asteroids. capture of outer objects such as the EKBO. In addition, by looking at the impact features on these bodies, we can directly correlate with the impact history, especially at 1 AU Since Trojans are small compared to planets, the low from the past and current Moon and NEO studies to date. In gravity pull makes ﬂyby and rendezvous achievable us-

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ing a solar sail combined with ion propulsion. In over- The Hill approximation can also be used for studying the all, a solar powered sail would allow reducing the over- dynamics close to the asteroid, in particular for transition all mass, and thus cost. There is still uncertainty in with the asteroid sphere of influence, how to navigate such a sail, however, the coming so- x˜¨ 2Ωy˜˙ 3Ω2x˜ = U + g , (4) lar sail technology demonstration mission, Ikaros, to be − − x x launched in 2010 to Venus, will provide important know- how regarding material, handling, and control operations y˜¨+ 2Ωx˜˙ = Uy + gy, (5) (www.jaxa.jp/projects/sat/ikaros/index e.html). 3.23.2. FromFrom Farfar to to near Near fields Fields using using solar Solar sail Sail and Studying solar sail missions is not a new subject. The 2 research groups of McInnes, Scheeres and Jorba indepen- z˜˙+ Ω z˜ = Uz + gz, (6) dently studied solar sail applications, which goes from within the Restricted Three Body Problem (R3BP) and for wherer ˜ =[x˜,y˜,z˜] is the spacecraft position with respect to 20 22) 3 asteroid orbiters − . Scheeres and Rios-Reyes then stud- the asteroid, Ω = µsun/aast is the non-dimensional orbit 23) rate of the asteroid, µ is the specific gravitational con- ied the mathematical modeling for navigation . There are  sun only a few studies of solar sail missions in a populated en- stant of the Sun, aast is the distance of the asteroid from vironment such as the Lagrangian points of the Sun-Jupiter the Sun, and U is the asteroid potential. Solving for equi- system. librium points, we can map the Hill radius for such large The problem can be stated in a few different frames de- and distant objects, shown in Fig. 2, accounting for solar pending on the spacecraft-asteroid relative distance. For in- radiation pressure on a sail (g). stance, being outside of the asteroid sphere of influence, the Sun-Jupiter R3BP would become the ruling dynamics. As the asteroid comes closer to the target, the Hill approximation may be best to take into account the influence from the Sun. Then, as the spacecraft approaches near the asteroid, the asteroid orbiter and binary asteroid system orbiter problem would be best to evaluate the proximity operations, including a refined solar sail model. In the R3BP, we can approximate a spacecraft/point mass equations of motion as the following,

x¨ 2Ω y˙ Ω 2x = − Jup − Jup (1 µ )(x µ )/r 3 − − Jup − Jup JA µ (x µ + 1)/r3 + g , (1) − Jup − Jup SA x Fig. 2. Hill radius for Jovian Trojan asteroid targets.

2 (1 µJup) y¨+ 2ΩJupx˙ ΩJup y = − 3 y − − rJA Now, considering the asteroid orbiter, in the rotating y frame of the target, µJup 3 + gy, (2) − rSA xˆ¨ 2ω yˆ˙ ω 2xˆ = Uˆ + a , (7) and − ast − ast x SRP,x (1 µ ) µ Jup Jup y¨+ x˙ 2y = Uˆ + a , z˙ = − 3 z 3 z + gz, (3) ˆ 2ωast ˆ ωast ˆ y SRP,y (8) − rJA − rSA − and where r =[x,y,z] is the position of the spacecraft, ΩJup is the orbit rate of Jupiter, µJup is the Jupiter specific gravity zˆ˙ = Uˆz + aSRP,z, (9) constant, rJA and rSA are the position vectors of the spacecraft with respect to the Jupiter and the Sun, respectively, wherex ˆ,ˆy, andz ˆ are the position coordinates of the or- and g =[gx,gy,gz] is the acceleration due to the solar radia- biter in the asteroid frame, ωast is the asteroid spin rate, tion pressure. The location of the Trojan asteroids is found and aSRP is the solar radiation pressure in the asteroid rotat- from solving the equilateral equilibrium points of Eq. 1- 3, ing frame. Morrow et al. (2001) 22) have also solved for the although the trajectory of a solar sail spacecraft uses low out of plane equilibria and sail configurations as function of thrust tools, as discussed in Kawaguchi et al (2009) 10). the spacecraft position with respect to the target, which can Trivailo (2007) 24) studied the dynamics and effects of a also be applied for the current targets investigated. For pre- spacecraft in a Trojan asteroid population, and confirmed cise solar sail modeling, the geometry represented in Fig. that other Trojans don’t have a significant effect hence, they 3 needs to be taken into account. The center of mass po- are not included here. sition is indicated by the x,y,z location while the sail has a

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local pitch and yaw orientation. Modeling the sail in three Table 2. Orbital characteristics of the binary system Hektor and S/2006. dimensions, expressions were obtained to express the sail Note that the uncertainty on Hektor’s dimensions is about 30%. angle with respect to the declination of the spacecraft. Note Hektor radii (km) [180, 103, 103] Separation distance (km) 1000 that for binary asteroid orbiters, the dynamical equations Density (g/cm3) 2.4 are similar to the R3BP although considering the mass dis- Mass ratio, ν 0.000217 25 27) tribution of the bodies − . Hektor spin period (hrs) 6.92 S/2006 dimensions (km) r=15 Binary orbit rate (hrs) 50 Orbital speed of S/2006 (km/s) 0.0363

give insights on spacecraft operations and the fate of ejecta around Hektor. The near-circular distance where direct or- bits will be stable is 505 km, giving an orbital velocity of 0.05 km/s (using expressions derived in Scheeres (1994) Fig. 3. Three dimensional model of a solar sail spacecraft near an asteroid. 28)). We can also compute analogue orbital parameters for S/2006. Table 3 shows some basic dynamical parameters of both Hektor and S/2006 asteroids, from which some space- 3.3.3.3 Case Studystudy of of (624) hektor Hektor craft operations can be derived. The asteroid (624) Hektor is the biggest Trojan asteroid system at L4. It is also one of the most interesting as it pro- Table 3. Dynamical parameters of Hektor and its moon S/2006, considered 3) vides an opportunity to explore a “double” binary system ; as single asteroids. Hektor has a small moon, S/2006, and is itself a contact bi- Hektor nary system, as shown on Fig. 4. From observational data, Resonance radius (km) 274 Hektor has dimensions of 363 km x 207 km, while S/2006 Eq. pts. on long axis (km) 290.5 has a radius of 15 km. The two bodies are separated by Eq. pts. on interm. axis (km) 266.1 Stable prograde altitude (km) 504.7 about 1000 km and orbit each other with a 50 hours period. Velocity stable prograde (km/s) 0.05 3 Their derived density is 2.4 g/cm which is in the high end Escape velocity (km/s) 0.12 - 0.16 of small body density. Because Hektor is so large, S/2006 Hill radius (km) 556000 contributes to only a small fraction of the total mass, less S/2006 than 0.1 %, and has an associated escape velocity about 10 Resonance radius/Eq. pts. (km) 60.5 times less. Table 2 shows the Hektor binary system orbital Stable prograde altitude (km) 113 Velocity stable prograde (km/s) 0.0016 information. Escape velocity (km/s) 0.0087 Hill radius (km) 33500

The close proximity operations at the Hektor system need careful study. Bellerose and Yano (2009) 15) have discussed exploring the secondary bodies as prime objectives instead of the primaries themselves; comparing the composition and space weathering of the secondary to the primary body, as well as to other systems like the Pluto-Charon system, can give better insights on their origins. Navigating close to a contact binary system, which is suspected for a number of Trojan asteroids, may also involve large pertur- bations as opposed to hovering close to the secondary. For instance, from lightcurve measurements, Hektor itself can be modeled as a contact binary, which, using Roche binary approximation, can be represented as an elongated body in Fig. 4. Hektor and S/2006 binary system. close contact with a more spherical one 4). Figure 5 shows the approximate shape for Hektor along with equilibria for the two bodies (starred points are stable, round points are By looking at Hektor’s dynamics only, the altitude where unstable) as well as equilibria for a large uniform ellip- the point mass gravitational attraction is equal to the cen- soidal asteroid model (square points, all unstable). Each tripetal acceleration due to the asteroid rotation, is 274 km. of these bodies is of different nature as the more spherical Considering Hektor as an ellipsoid gives between 10 and 15 body has some stable equilibrium points, while the elon- km difference with these circular equilibria, along each pla- gated one has unstable points. Having stable and unsta- nar principal axis of the target. We can ﬁnd that this elon- ble transitions would have an important effect on close or- gated asteroid has four unstable equilibrium points, which bit strategies. Note that the real shape of Hektor will also

4 Pk_42 J. BELLEROSE and H. YANO: Trojan Binary Asteroid Systems as Future Mission Targets

influence the location and properties of these points. On Table 4. Ecliptic crossing timeline for Jovian Trojan suspected binary con- 2) the other hand, it is easy to accommodate a 50 hours win- tact asteroids at L4 (targets listed in Mann et al. (2007) ). dow and spherical asteroid like S/2006. In the same line Crossing Trojans i (deg) 09/2024, 05/2031 2146 Stentor 39.2 of thoughts, if surface operations are to be performed, the 07/2025, 08/2031 624 Hektor 18.2 large escape velocity of Hektor (refer to Table 3) indicates 05/2026, 04/2032 9694 Lycomedes 4.9 that it would be very costly to perform close approach or 06/2026, 08/2032 4068 Menestheus 17.5 surface study of Hektor itself as opposed to S/2006. 07/2026, 03/2032 1999 YY2 21.3 12/2026, 04/2033 3709 Polypoites 19.6 Hence, since the secondary is likely to come from the 02/2027, 12/2032 9431 1996 PS1 21.3 primary, the science objectives at Trojans can be directly 02/2027, 01/2033 1583 Antilochus 28.5 verified in a low cost manner by exploring the secondary 03/2027, 05/2033 11668 Balios 4.7 03/2027, 09/2033 2001 CE21 22.5 first. A strategy would be to observe the whole system 07/2027, 07/2033 1868 Thersites 16.8 from afar, including Hektor and its moon, before approach- 07/2027, 03/2033 1999 XW261 31.7 ing S/2006. In the first stage of the proximity operations, 11/2027, 09/2033 2920 Automedon 21.1 hovering S/2006 would allow to further refine the asteroid 08/2028, 05/2034 1869 Philoctetes 4.0 08/2028, 05/2034 1998 VA50 32.0 shapes and system dynamics, while requiring less fuel from 09/2028, 09/2034 1647 Menelaus 5.6 operating at a less massive component. The subsequent ap- 04/2029, 11/2034 1999 XJ55 36.6 proach to Hektor would then involve less risks. 05/2029, 02/2035 2260 Neoptolemus 17.8 06/2029, 03/2035 4834 Thoas 28.5 09/2029, 12/2034 2002 EZ13 7.0 09/2030, 12/2035 4833 Meges 34.7

Fig. 5. Hektor modeled as a contact binary from Roche approximation 4). Equilibrium points are shown for each binary body (starred points are stable, round points are unstable), and for Hektor as a one solid ellipsoid (square points, all unstable).

4. Jovian Trojans Target Opportunities As the L Jovian Trojans have 11 inclination on aver- 4 ∼ ◦ age, timing for rendezvous and flyby becomes critical. Ta- ble 4 gives a summary of the ecliptic crossing timeline for the same suspected contact binary system targets as presented in section 2, between 2025 and 2035, including the asteroid orbit inclination (i). A rapidly rotating asteroid such as Hektor or 1999 YY2 can indicate a more packed or rocky body as internal strength needs to be higher, although Fig. 6. Hektor trajectory at the 2031 ecliptic crossing, including a close- up view of the projected positions of Stentor and Lycomedes during their it will make approach, and sampling if planned, more diffi- 2031 and 2032 ecliptic passage, respectively. cult due to the rapid surface speed. Fig. 6 shows the orbit of Hektor around the Sun at its 2031 ecliptic passage. We looked at the feasibility of visit- ing a sequence of currently known and best observed Jovian asteroids. The close-up view in Fig. 6 shows the approxi- we discuss rationales and strategies for investigating these mate relative position Stentor and Lycomedes projected for bodies, especially binary systems. For a solar sail mission, their respective ecliptic crossing in 2031 and 2032, respec- which is one of the most suitable technologies to use at tively. Note that the detailed solar sail navigation is kept these low gravity bodies, we briefly describe the dynam- for further study. Coming observation campaigns will give ics involved near such asteroid targets. We also investigate more details on these remote bodies. a case study for a mission to one of the biggest Jovian Tro- jans, Hektor and its moon S/2006, making the case for ex- 5. Conclusion ploring the secondary as prime objective. Finally, we show As the international space community is preparing a flag- a timeline of available targets. Future work involve more ship mission to the Europa Jupiter System, possibly involv- detailed studies of navigation and control needed for such ing a solar sail mission to Trojan asteroids, in this paper, mission.

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References 20) McInnes, I.: Strategies for Solar Sail Mission Design in the Circular Restricted Three Body Problem, M.S.Thesis, School of Aeronautics 1) Barucci, M. A., Cruikshank, D. P., Mottola, S., Lazzarin, M.: Physical and Astronautics, (2000), Purdue Univ., West Lafayette, IN. Properties of Trojan and Centaur Asteroids. In: Bottke, W., Cellino, 21) Farres, A. and Jorba, A.: Solar Sail Surfing along Families of Equi- A., Paolicchi, P., Binzel, R.P. (Eds.), Asteroids III (2002), pp. 273– librium Points, International Astronautical Congress (2007), IAC-07- 287. C1.4.04. 2) Mann, R. K., Jewitt, D. C., Lacerda, P.: Fraction of Contact Binary 22) Morrow, E., Scheeres, D.J., Lubin, D.: Solar Sail Orbit Operations at Trojan Asteroids, The Astronomical Journal 134 (2007), pp.1133– Asteroids, Journal of Spacecraft and Rocket 38 (2001), pp.279–286. 1144. 23) Rios-Reyes, L. and Scheeres, D.J.: Solar Sail Navigation: Estima- 3) Marchis, F., Hestroffer, D., Descamps, P., Berthier, J., Bouchez, A. tion of Force, Moments, and Optical Parameters, Journal of Guidance, H., Campbell, R. D., Chin, J. C. Y., van Dam, M. A., Hartman, S. K., Control, and Dynamics 30 (2007), pp.660–668. Johansson, E. M., Lafon, R. E., Le Mignant, D., de Pater, I., Stom- 24) Trivailo, O.: Spacecraft Stability, Dynamics and Control neat the ski, P. J., Summers, D. M., Vachier, F., Wizinovich, P. L., Wong, M. Triangular Lagrange Points Influenced by Multiple Trojan Asteroids, H.: A Low Density of 0.8 g/cm3 for the Trojan Binary Asteroid 617 Acta Astronautica 60 (2007), pp.658–675. Patroclus, Nature (2006), pp.565–567. 439 25) Gabern, F., Koon, W. S., Marsden, J. E.: Parking a Spacecraft near 4) Lacerda, P. and Jewitt, D. C.: Densities of Solar System Objects from an Asteroid Pair, Journal of Guidance, Control, and Dynamics 29-3 their Rotational Light Curves, The Astronomical Journal 133 (2007), (2006), pp.544–553. pp.1393–1408. 26) Fahnestock, E.G. and Scheeres, D.J.: Characterization of Space- 5) Goldreich, P., Lithwick, Y., Sari, R.: Formation of Kuiper-belt binaries craft and Debris Trajectory Stability within Binary Asteroid Systems, by dynamical friction and three-body encounters, Nature 420 (2002), AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Hawaii pp.643–646. (2008), AIAA 2008-7203. 6) Marzani, F., Scholl, H., Murray, C., Lagerkvist, C.: Origin and Evo- 27) Bellerose, J. and Scheeres, D. J.: The Restricted Full Three-Body lution of Trojan Asteroids, in R.P. Binzel, W.F. Bottke, A. Cellino, P. Problem: Application to Binary System 1999 KW4, Journal of Guid- Paolicchi (Eds.), Asteroids III (Space Science Series) , Univ of Ari- ance, Control, and Dynamics 31 (2008), pp.162–171. zona Pr (2002), pp.725-738. 28) Scheeres, D. J.: Dynamics about Uniformly Rotating TriAxial Ellip- 7) Marzari F. and Scholl H.: Capture of Trojans by a growing proto- soids: Applications to Asteroids, Icarus 110 (1994), pp.225–238. Jupiter, Icarus 131 (1998), pp.41-51. 8) Gomes R. S.: Dynamical Effects of Planetary Migration on Primordial Trojan-Type Asteroids, Astronomical Journal 116 (1998), pp.2590- 2597. 9) Morbidelli, A., Levison, H. F., Tsiganis, K., Gomes, R.: Chaotic Cap- ture of Jupiter’s Trojan Asteroids in the Early Solar System, Nature 435 (2006), pp.462–465. 10) Kawaguchi, J., Morimoto, M., Mori, O., Funase, R., Jupiter and Trojans Exploration WG Preparation Team: Trajectory Analysis for Jupiter and Trojan Asteroids by Large Solar Cell Membrane, 27th ISTS (2009), k-45. 11) Yano, H., Yoshida, F., Takao, N., Kokubo, E., JAXA Jupiter and Tro- jans Exploration: Science of Trojan Asteroid Exploration as Clues of the Origin and Evolution of the Jovian System, 27th ISTS, 2009-k-47. 12) Sasaki, S., Fujimoto, M., Kasaba, Y., Kawaguchi, J., Kawakatsu, Y., Mori, O., Takashima, T., Tsuda, Y., Yano H., and Jupiter Exploration Working Group: Exploration of Jovian Magnetosphere and Trojan As- teroids by a Solar Power Sail Mission, Geophysical Research, EGU General Assembly 2009 11 (2009), EGU2009-8108. 13) Matsumoto, M. and Kawaguchi, J.: Optimum Trajectory for Low- thrust Multiple Trojan Asteroids Flybys, Proceedings of the 18th In- ternational Symposium on Space Flight Dynamics (ESA SP-548), (2005), pp.499–504. 14) Guo, Y. and Farquhar, R.W.: Baseline Design of the New Horizons Mission to Pluto and the Kuiper Belt, Acta Astronautica 58 (2006), pp.550–559. 15) Bellerose, J. and Yano, H.: Exploration of Binary Asteroid Systems: from Near Earth Asteroids to Jovian Trojans, submitted to Planetary and Space Sciences. 16) Yano, H., Hasegawa, S., Kasaba, Y., Matsuura, S., Usui, F., Yonetoku, D.: Scientific Observations onboard the JAXA/ISAS Solar Powered Sail Mission, 35th COSPAR Scientific Assembly (2004), Paris, France, p.3954. 17) Gold, R. E., McNutt, R. L., Napolillo, D. H., Schaefer, E. D., Tanz- man, J. R., Fiehler, D. I., Hartka, T. J., Mehoke, D. S., Ostdiek, P. H., Persons, D. F., Prockter, L. M., Vernon, S. R.: Paris to Hektor: A Con- cept for a Mission to the Jovian Trojan Asteroids, American Institute of Physics Conference Proceedings 880 (2007), pp.217–223. 18) Klesh, A., Wang, J., Westlake, J., Burke, C., Cartwright, M., Gadre, R., Horodyskyj, L., Milam, K., Moskovitz, N., Oiler, J., Ostrowski, D., Pagano, M., Smith, R., Springmann, A., Taniguchi, S., Townsend- Small, A., U-yen, K., Vance, S., Zacny, K., Budney, C.: SHOTPUT: A JPL Planetary Science Summer School Study, 2009 IEEE Aerospace Conference (2009), pp.1–13. 19) Gold, R. E., Rivkin, A. S., Benson, S. W., Emery, J. P., Hibbitts, C. A., Lisse, C. M.: ILion: A Jovian Trojan Asteroid Orbiter and Lander Mission Concept, Asteroids, Comets, Meteors (2008), 8127.

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