Jupiter Trojans Rendezvous Mission Design

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1 Jupiter Trojans Rendezvous Mission Design Triwanto Simanjuntak 1, Masaki Nakamiya, and Yasuhiro Kawakatsu 1 The Graduate University for Advanced Studies (SOKENDAI) Japan Aerospace Exploration Agency (JAXA) Abstract Triangular Lagrangian points of the Sun-Jupiter system contains Asteroids which are well known as Trojans. These Asteroids are believed to contain primitive information on the early formation of our Solar System. Furhtermore their origin is also unclear. Considering these significances, we report in this paper mission analysis on the Trojans rendezvous mission using two body approach. The mission design includes the selection of the target Asteroids and the design of the nominal mission sequence. Three types of trajectories are presented, direct transfer, using gravity assists of Mars, Jupiter and also employed low-thrust propulsion to each type in finding reasonable time and V transfer among selected Asteroids. 1 Introduction The importance of space mission to Jupiter Trojans has been argued by scientists since the 197 s. Their main reasons are firstly to answer the mystery of Trojan s origin, whether it originated near Jupiter s orbit or farther out in the solar system, and to find out the regions of the solar nebula in which they formed from the information of the compositions of these Asteroids contain. Rendezvous missions, as we propose here, is one of the best options in helping us to answer these questions. A rendezvous mission will not just provide scientific data from in situ observations but also lay a stepping stone for future sample return missions. It s well known that the primary challenges to send spacecraft to Jupiter Trojans are the large amount of impulse ( V) and comparatively a long transfer time ( t) required to reach the nearby triangular Lagrangian points L and L 5 where Trojans reside. However Jupiter Trojans don t stay all the time at their corresponding triangular points but naturally librate around them and we conjecture this feature can be exploited to find a reasonable lower V and shorter t. Furthermore, the Trojans population is approximately more than one million and the L swarm alone is predicted to hold between 1, asteroids with diameters larger than Km and, with diameters larger than 1 Km [1, ], and this give us higher chance to find Asteroids which meet our requirements. Our strategy is to search Asteroids that librate closer to Jupiter and allow encounter with a spacecraft in an acceptable ange of V and t in a period of time of interest. In this mission design planetary gravity assists of Mars, Jupiter and Solar Electric Propulsion (SEP) are also utilized in finding the potential missions. In sum, we expect from this mission design to identify potential missions to Jupiter Trojans in near future and their bounded challenges and limitations. The results also can serve as the baseline for the possible, improved and more sophisticated design method, such as the use of the restricted three body problem approach. Trajectory Analysis Scheme The trajectory analysis consits two steps, Asteroids selection and detailed trajectory design. In the first step, a few candidates are selected based on ballistic trajectory analysis. Ballistic trajectory analysis allows light computational global search. Keeping the few candidates obtained previously, local search Corresponding Author, triwanto.simanjuntak@jaxa.jp 1

2 is conducted in the second step. This local search take into accound SEP therefore demand heavy computational load but still affordable since only applied to few selected candidates. In selecting the Asteroids, additional to dynamical feasibility we also considered scientific objectives. On Asteroid selection we construct the mission sequence procedure using trajectory parts connection method developed by Kawakatsu [3]. In the method, the mission sequence is constructed as series of keplerian orbits connected with impulsive velocity changes (see Fig. 1). The dynamical feasibility of the mission sequence is evaluated quantitatively by V required to complete the sequence. This V despite obtained from patch conic approach is sufficient to be used as evaluation parameter to find the dynamical feasibility of the sequences if using SEP. Figure 1: Mission Schematic Sequences The detailed design is divided into two layers (see Fig. ), trajectory arc design (inner loop) and sequence design (outer loop). We perform optimization on booth loops. In the inner loop optimization is performed by treating it as an optimal control problem to maximize the final mass. The optimal control problem is directly collocated with nonlinear programming problem [], which then solved by the sequential quadratic programming method. Three parameters are set fixed as boundary conditions: departure time, departure v and spacecraft mass at departure. While on the sequence design (outer loop) optimization is carried out to optimize these three parameters. 3 Trojans Data Set In a broad definition, Jovian Trojans are defined as large group of Asteroids that share the orbit of Jupiter around the Sun. Viewed from the Sun-Jupiter three body problem system, the Trojans exist in the L, L 5 points of the system and their semijajor axis, are in the range f 5. ±.15 AU []. In this research, we obtained the known Trojans list from the minor the Minor Planet Center (MPC) per December 1, 9[5]. There were 377 Asteroids in the list and we acquired their osculating orbital elements from the Asteroid Orbital Elements Database (Astorb) by Edward Bowell []. Mission Design Constraints The mission design constraints we used for the direct transfer, Mars and Jupiter gravity assits, are shown in Table 1 & respectively.

3 Figure : Optimization Scheme Table 1: Conditions for Direct Transfer Design V departure 7-1 Km/s V departure settings 11 Departure date 1/1/ 1/31/5 Departure time setting 1 week interval Max transfer time 195 days V max 1 Km/s Table : Conditions for Swingby Design Swingby V 5-15 Km/s No. settings Swingby V 1 Departure date 1/1/ 1/1/8 Earth to Planet Max. transfer time 195 days Planet to Aster. Max. transfer time 185 days Earth departure V max 1 Km/s V max Km/s Swingby r min (in Rp) for Jupiter & 1.1 for Mars 5 Results and Analysis 5.1 Direct Transfer In table 3, ranked based on their total V, 1 best Trojans for direct transfer are listed. Additionally figure 3 shows typical direct transfer trajectory to Trojan. We minimize our intesrest into Trojans with total V 1 Km/s. What obvious to to see from the list is their total V are not much different. This is due to the variation of their semimajor axis is not so high. However since in deep space manuver 3

4 V is more critical compared to the departure, therfore it s worth to notice the last two Trojans, BH57 and QV33, despite their V departure is comparatively higher than others but their V arrival is significantly lower less than Km/s. As will be shown later, we can use VEGA to reduce thir departure V, to harvest their arrival V. Jupiter Earth Y [AU] 9 SV19 8 Figure 3: 9 SV19 Direct Transfer Trajectory Table 3: Trojans for Direct Transfer No Departure Date V 1 Arrival Trojan Arrival Date V Total V [UTC] [Km/s] [UTC] [Km/s] [Km/s] 1 /1/ SV19 7/1/ // EQ39 7// /7/ EU18 8/7/ // WD 3// /11/ SJ 7/11/ /9/ 9.5 Sthenelos 5/7/ /8/ SG // /1/1 9.5 Atreus /9/ /1/ RK11 /9/ /11/ WO 7/9/ /9/ TE91 5/5/ /7/ GA78 8// // DM8 /11/ /9/3 1 Guneus /8/ //1 1 BH57 /11/ /1/ 1 QV33 7/11/ Jupiter Swingby With its massive mass, Jupiter is an ideal to planet to gain extra velocity by swingby. Considering the harsh radiation from Jupiter, we limited our swingby radius to minimum of times of Jupiter radius. Tabel contains 8 Trojans which have V arrival 5 Km/s. Based on V arrival 5 JL1 is the best

5 target. As expected, Jupiter able to be used to gain energy therfore to reduce the deep space required magnitude V, in 5 JL1 case 3 Km/s. Its trajectory is shown in Figure & Figure 5. Jupiter swingby /5/18 Y [AU] Earth departure //7 8/8/5 Figure : 5 JL1 Jupiter Gravity Assits Trajectory-Inplane Z [AU] 8/8/5 Earth departure //7 Jupiter swingby /5/18 Figure 5: 5 JL1 Jupiter Gravity Assits Trajectory-Outplane 5.3 Mars Swingby Beside Jupiter, we also considered Mars, despite to its relatively small mass, for garvity assist to Trojan. As shown in tabel 5, albeit Mars provides smaller V departure, but unfortunately we found no target with V arrival 5 Km/s and acceptable radius swingby, Rp 1.1. Typical trajectory to Trojan using Mars gravity assits is shown in Figure & Figure 7. 5

6 Y [AU] Earth departure /1/9 Mars swingby 5//8 8//18 Figure : 7 RC88 Mars Gravity Assits-Inplane 5. VEGA VEGA is a technique to use earth gravity assist to reduce V launch. The schematic for VEGA is presented in figure 8. The main idea is to find the correct combination V launch and V a aphelion Table : Trojans for Direct Transfer with Jupiter Swingby No Departure Date V 1 Swingby Date V 1 Arrival Trojan Arrival Date V [UTC] [Km/s] [UTC] [Km/s] [UTC] [Km/s] 1 //7 1. /5/ JL1 8/8/ /7/ /1/31. CN3 3/11/ // 9.51 //1 8.5 BH57 9// 1.9 3/7/ /9/ EL 3/9/ // /3/ JS119 9/1/. /9/ 9.7 7/5/8 5.5 CN9 3//8.5 7 /5/ 9.95 /1/5. AT1 9/9/7.7 8 // /9/1. 9 BJ 9/8/ /7/ //7. 8 WG1 31/1/ /5/7 1.1 /1/19. XN9 9/1/5.3 Table 5: Trojans for Direction Transfer with Mars Swingby No Departure Date V 1 Swingby Date V 1 Arrival Trojan Arrival Date V [UTC] [Km/s] [UTC] [Km/s] [UTC] [Km/s] 1 /1/ // SM3 8//18.8 /8/ /1/ SO7 /7/1.9 3 /9/7 8.9 /1/ TE91 /1/1.5 /8/ /11/ SA7 5/1/.5 5 /8/ /1/ SG 5/11/13.59 /8/ 9.5 /1/1 13. Atreus 5/1/. 7 /1/ // SH 7/1/. 8 /9/ 8.3 /1/ 13. AD1 5/11/ /8/9 9. /1/ TQ7 //3.7 1 /8/9 9. /1/ SY 5/1/11.8

7 Mars swingby 5//8 Earth departure /1/9 Z [AU] 8//18 8 Figure 7: 7 RC88 Mars Gravity Assits-Outplane combination to reencounter earth for gravity assits. Much detail explanation is made available by the work of Sims et al.[7, 8]. In this mission design we consider : 1 VEGA and its effectiveness is shown in Figure 9. V a Sun V launch Earth Encounter Figure 8: VEGA If : 1 VEGA is considered, and the cost of the mission is defined as the total of : 1 Vlaunch, V a and V arrival, in the case of direct transfer, the rank of preferable Asteroid becomes changed, as seen in tabel. 7

8 1 1 8 Vgain [Km/s] V aphelion [Km/s] Figure 9: Effectiveness of : 1 VEGA 5.5 Using Low Thrust Propulsion As electric propulsion technology has become more reliable, we also consider the use of EDVEGA (Electric V Earth Gravity Assits instead of VEGA. This option allows us to improve mass efficiency of the spacecraft. Here we also presented the use of electric propulsion from Jupiter swingby to Asteroid arch to improve mass efficiency even more. In short an alternative sequnce of the mission, e.g. for 5 JL1, becomes, EDVEGA-Jupiter Swingby- 5 JL1. The trajectory for DVEGA and low-thrust from Jupiter to Asteroid sequnces are availablein Figure, 5 and Figure 1, 13 respectively. The use of electric propylsion is optimized by minimzing the maximum thrust force and maximizing the final mass. If initial mass of the spacecraft is 18 Kg and assuming HA kick motor provides the lanuch V then in this case we obtain the final mass is 15 Kg with maximum thrus force is 1 mn. Table : Trojans for Direction Transfer with V-EGA No Departure Date V 1 Arrival Arrival Date V V launch V a Total V [UTC] [Km/s] Trojan [UTC] [Km/s] [Km/s] [Km/s] 1 /8/18 1 BH57 /11/ //1 1 QV33 7/11/ / SV19 7/1/ /8/ EQ39 7// /9/ EU18 8/7/

9 8 Jupiter swingby Y [AU] Earth departure/reencounter -5-1/ Figure 1: 5 JL1 DVEGA Trajectory-Inplane 8 Z [AU] 9--5 Earth departure/reencounter -5-1/--7 Jupiter swingby Figure 11: 5 JL1 DVEGA Trajectory-Outplane Conclusion In this paper mission design for Jupiter Trojans rendezvous mission is presented. Feasible targets along with their trajectories also are reported. References [1] David C. Jewitt, Chadwick A. Trujillo, and Jane X. Luu. Population and size distribution of small jovian trojan asteroids. The Astronomical Journal, 1():11 117, August. 9

10 Figure 1: F(t) for JL1 DVEGA Trajectory Figure 13: m(t) for JL1 DVEGA Trajectory [] F Yoshida and T Nakamura. Size distribution of faint jovian l trojan asteroids. The Astronomical Journal, 13():9 911, December 5. [3] Yasuhiro Kawakatsu. Near-earth asteroids sample return mission opportunities in early 1s. Space Technology Japan, the Japan Society for Aeronautical and Space Sciences, :87 9, 7. [] P. J. Enright and B. A. Conway. Optimal finite thrust spacecraft trajectories using colocation and nonlinear programming. Journal of Guidance and Control, 1(5): , [5] [] ftp://ftp.lowell.edu/pub/elgb/astorb.html. [7] J.A. Sims and. Delta-V Gravity-Assist Trajectory Design: Theory and Practice. PhD thesis, Purdue University, [8] J.A. Sims, J.M. Longuski, and A.J. Staugler. Vinf leveraging for interplanetary missions: Multiplerevolution orbit techniques. ournal of Guidance, Control, and Dynamics, (3):9 15, May-June