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Trajectory Design for Jovian Trojan Asteroid Exploration

via Solar Power Sail

By Takanao SAIKI1) , Osam MORI1) and Jun’ichiro KAWAGUCHI1)

) 1)The Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan

JAXA has been preparing for a Trojan asteroid exploration mission via solar power sail. Jovian Trojan asteroids are as one of a few remaining frontiers in our Solar System, which may hold fundamental clues of the Solar System formation and revolution. Visiting Jovian Trojans is much more difficult than reaching near-Earth objects because of the large amount of fuel required to reach them. Generating the sufficient power is also difficult due to the large distance from the sun. A solar power sail which is a new concept proposed by JAXA offers an effective way of realizing such challenging exploration. The solar power sail combines a solar sail with electric power generation capability and high efficient ion engines. Thin flexible solar cells attached on the sail membrane generate the electric power and high efficient ion engines are driven by the large eclectic power supply. This paper outlines a solar power sail spacecraft under consideration and discusses the trajectory design for a Jovian Trojan asteroid exploration.

Key Words: Trajectory Design, Solar Power Sail, Jovian Trojan

1. Introduction JAXA launched a solar sail demonstration spacecraft known as “IKAROS” on May 21, 2010 (Fig. 1). IKAROS is the first interplanetary solar sail spacecraft and a precursor mission to demonstrate the key technologies underpinning the solar power sail concept 1) that JAXA is pursuing for use in deep space exploration. The solar power sail is a new concept proposed by JAXA. It combines a pure solar sail with electric power generation capability and high efficient ion engines. The pure solar sail offers fuel-free space transportation using a large membrane that acquires propulsive force from the reflection of sunlight. 2) However, it is difficult to obtain sufficient propulsive force because the force of the photon is quite small. Huge membranes are necessary to obtain meaningful propulsive forces, but such membranes are difficult to fabricate and deploy. Solar power sails are able to overcome these difficulties because they generate electric power that drives highly efficient ion engines. Thin flexible solar cells attached to a sail membrane generate the electric power needed to drive the ion engines. Solar power sails are not completely fuel-free but can provide flexible and efficient orbital control even in the outer planetary regions of the solar system, without needing a nuclear energy supply.

Fig. 1. IKAROS spacecraft.

JAXA has been preparing to realize a Jovian Trojans exploration mission using the solar power sail (Fig. 2). Jovian Trojan asteroids are as one of a few remaining final frontiers within our Solar System, which may hold fundamental clues of the Solar System formation and revolution. However, exploring the Jovian Trojans is much more difficult than exploring near-Earth objects (NEOs) because of the large amount of fuel required to reach them. Generating the sufficient power is also difficult due to the large distance from the sun. The use of solar power sails could solve this exploration challenge. We are now performing the conceptual study of the spacecraft. We anticipate its launch in the early 2020’s. The spacecraft is a 1500kg class single spinner with ultra-high specific impulse (Isp) ion engines. The planned area of the sail membrane is about 3000 m2. The main payload is a 100kg class small lander which collects the asteroid’s sample and performs in-situ analysis.

Fig. 2. Jovian Trojan exploration via solar power sail.

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This paper presents an outline of the spacecraft and its design trajectory. Preliminary ballistic analysis identified several asteroids that should be within reach using low-thrust trajectories. And then the low thrust trajectory optimization was performed. In this paper, some results of the trajectory design are shown. 2. Mission Sequence Fig. 3 shows the mission sequence of our Jovian Trojan exploration. The spacecraft is supposed to realize the world’s first journey to a Jovian Trojan asteroid around L4/L5 point of the Sun-Jupiter system by using both the Earth and Jupiter gravity assist. It is difficult to inject the spacecraft on the direct transfer orbit to Jupiter because large C3 is required. An Electric Delta-V Earth Gravity Assist (EDVEGA) technique is used to obtain the sufficient interplanetary speed to Jupiter. The first two years is the EDVEGA phase to increase the departure velocity relative to the Earth. After the Earth swing-by, the spacecraft flies to Jupiter. The Jupiter gravity assist is very useful to reduce the required delta-V. Many Jovian Trojan asteroids have the orbital planes with a large inclination with respect to the ecliptic plane. The Jupiter swing-by can change the orbital plane of the spacecraft. And it can also change the energy of the spacecraft’s orbit. As a result, the required delta-V to the Jovian Trojans can be reduced. The direct flight form the Earth to asteroid is possible only when the thrust force of the spacecraft is much larger than our ion engines. However, the required delta-V becomes very large. It means that the transportation of the large payload is impossible. So, we use the Jupiter gravity assist. After the Jupiter swing-by, the spacecraft heads to the asteroid and it rendezvous with the asteroid. During this phase, spacecraft drives the ion engines to cancel the relative velocity to the asteroid. After arriving at the asteroid, a lander is separated from the spacecraft to collect surface and underground samples and perform in-situ analysis. We consider the sample return option. The lander delivers samples to the spacecraft and then spacecraft come back to the Earth by using the Jupiter gravity assist again.

Fig. 3. Mission sequence.

3. Spacecraft Design 3.1. Configuration Fig. 4 and Fig. 5 shows the configuration of the spacecraft. It is of the same single-spin type that is used with IKAROS. It has cylindrical body and the lander is attached to the main body and the tanks and instruments are arranged inside the body. The sail deployment mechanism is attached to the side panels of the main body. The sail membrane will be deployed and maintained by centrifugal force. The spin rate is about 0.1 rpm. The ion thrusters are attached to the bottom panel of the spacecraft. It has no gimbal mechanism. The direction of the thrust towards the sun side (+Z). The direction of the thrust significantly influences the trajectory design, as described below. The thrust of the ion engines is tilted by several degrees from the spin axis to generate up/down torque. The ion thrusters can also be used to control the direction of the spin axis by throttling the thrust forces.

HGA

Xe Tank

LanderDeploymentMechanism

RCS Thruster

Z

Ion Thruster

Fig. 4. Side view of the solar power sail spacecraft. The lander is attached to the bottom of the spacecraft.

OxidizerTank

Fuel Tank

STT

Ion Thruster

Fig. 5. Bottom view of the spacecraft. Ion thrusters are attached to the bottom panel.

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3.2. Direction of thrust force From the science perspective, there is little to choose between the L4 and L5 targets. However, they require very different trajectory designs. If we focus on the outward journey, L4 targets are more attractive than L5. First, the time of flight (TOF) from Jupiter to an L4 target is shorter than that to an L5 asteroid due to the geometrical reason. And the power generation from Jupiter to the asteroid is grater because the sun’s distance of the flight path is shorter. That means that the thrust force of ion engine is larger and it is possible to reduce the TOF to the asteroid. For these reasons, we choose L4 asteroids as the target body. The direction of thrust of the ion engines also influences the trajectory design. For L4 targets, the thrust force towards the sun side can efficiently cancel the approaching velocity to the target. On the other hand, it is difficult for the thrust with the opposite direction to cancel it. So, the ion thrusters of our spacecraft are attached the bottom of the spacecraft as Fig. 5 shows. 4. Ballistic Analysis A ballistic analysis based on two-body dynamics was carried out to identify candidate targets. As mentioned, many Jovian Trojans have large orbital inclinations. It indicates that the Jupiter swing-by timing can be fixed at the orbital node and we can design the Earth - Jupiter - asteroid ballistic trajectories by changing 1) departure time from the Earth and 2) arrival time at the target body. It is a two-dimensional search and we can get the solution quickly. Table 1 shows the target candidates selected by the ballistic analysis. The asteroids satisfy the following conditions are selected here.

Jupiter swing-by: 2015 L4 asteroids 11.2 <= H (absolute magnitude) <= 12.7 Minimum TOF (Jupiter to Asteoid) < 2000 days Minimum dV < 2000 m/s

We can find several candidate targets even if we change the swing-by year. After the ballistic analysis, the long-term stability analysis of the asteroid’s orbit was performed to judge whether the asteroid is intruder or survivor. Some of the selected asteroids are estimated to be intruders which are not good asteroid from the science perspective.

Table 1. Target candidates (Jupiter swing-by: 2015).

Name SWBY date TOF_min

[day] (J2A)

dV_min [m/s] (J2A)

Stability (NG:

intruder) 2001 AT33 2025/12/27 1818 1175 G 2001 BJ26 2025/09/19 1475 705 NG 2002 CC4 2025/12/10 1671 902 G

2000 AX29 2025/11/16 1769 1758 NG 2000 YB131 2025/10/18 1797 1699 NG 2001 DY103 2025/12/02 1937 1729 G

2007 PB9 2025/10/20 1517 1714 G 2005 LZ45 2025/04/30 1601 573 NG

5. Low-thrust Trajectory Design 5.1. Formulation A low-thrust trajectory was designed after identifying the candidate targets. The equations of motion are as follows:

1 23

1 23

23

cos( )cos( )

sin( )cos( )

sin( )

/ sp

Tx x u ur m

Ty y u ur m

Tz z ur m

m T I g

µ g f

µ g f

µ f

= - + + +

= - + + +

= - + +

= -

, (1)

where

( )

( )

( )

max

1

1 2 2

0 1

tan /

tan /

T T

y x

z x y

g

f

-

-

= G £ G £

=

= +

. (2)

G is a throttling parameter, and G , 1u , and 2u are control variables. Two types of objective function were used in this study:

0

ft

tJ adt=ò (3)

and

fJ t= . (4)

Eq. (3) was used to minimize delta-V in both the EDVEGA phase and sample return. Eq. (4) was employed to minimize the TOF and was used for the Jupiter-to-asteroid phase in the one-way mission. 5.2. Conditions Table 2 summarizes the conditions for the low-thrust trajectory design. Each ion thruster has a thrust force of 26.1 mN, a power consumption of 1.6 kW, and an operation rate of 0.7. The power generation for the IES is 2600 W at 5.2 AU. Since the spacecraft is a single spinner design, the direction of the thrust is controlled by changing the attitude of the spacecraft. The sun angle should be less than 45 deg. In this paper, the trajectories for the exploration of 2001 DY103, an L4 asteroid are discussed.

Table 2. Conditions for the low-thrust trajectory design. Spacecraft Mass @ launch 1350 kg Spacecraft Mass @ Jupiter departue 1300 kg Spacecraft Mass @ asteroid departure 1100 kg IES thrust 26.1 mN/unit IES power 1600 W/unit IES Isp 7000 sec IES operation rate 0.7 Power generation for IES 2600W@5.2 AU

(Sun angle=0deg) Attitude Sun angle < 45 deg Target body 2001 DY103

5.3. EDVEGA Trajectory As described, it is difficult to launch a spacecraft directory into a transfer orbit by a launch vehicle because of the high

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orbital energy required. A conventional delta-VEGA strategy has been used to increase the departure velocity of chemically propelled missions relative to the Earth, and this technique can also be applied to our solar power sail spacecraft. In this study, a 2-year EDVEGA was assumed. The spacecraft is accelerated by the ion engines around the aphelion and the Earth encounter date is shifted from 2 year. Fig. 6 shows the EDVEGA trajectory. The C3 at the launch is about 27.6 km2/s2 and the final relative velocity is 11 km/s and the required delta-V is about 1400 m/s.

-2 -1.5 -1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

X[AU]

Y[AU]

Fig. 6. 2-year EDVEGA trajectory

5.4. One-way Fast Trajectory Fig. 7 shows the trajectory from Jupiter to 2001 DY103 viewed in Sun-Jupiter fixed rotation frame. This trajectory is designed by using the objective function shown in eq. (4). Fig. 8 shows the history of the control thrust. The spacecraft is always accelerated by the maximum thrust force to minimize the TOF. Table 3 shows the summary of the one-way mission to 2001 DY103. The total TOF is about 11 years. The total delta-V is larger than 5000 m/s. It is reasonable for our ion engine, but we can reduce the delta-V amount by delaying the arrival date. Table 4 shows the relation between the delta-V amount and TOF. The required delta-V can be significantly reduced by shifting the arrival date slightly. Table 5 shows the TOF and delta-V of the fastest trajectory to other L4 asteroids. Typically, the fastest TOF is about 7-8 years and delta-V is about 4000m/s.

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-0.2

0

0.2

0.4

0.6

0.8

1

SJ-Fix[-]

SJ-F

ix[-]

S/CAsteroid

Fig. 7. Jupiter to 2001 DY103 trajectory (Sun-Jupiter fixed coordinate)

0 500 1000 1500 2000 25000

5

10

15

20

25

30

35

40

Time [day]

Thru

st [m

N]

Fig. 8. History of the thrust force (Jupiter to 2001 DY103)

Table 3. Summary of one-way mission.

Phase Start End dV[m/s] 2yr EDVEGA 2022/09/20 2024/07/24 1358 Earth to Jupiter 2024/07/24 2026/12/22 - Jupiter-to-Asteroid 2026/12/22 2033/10/22 3808

Total TOF: 4050d (11.1yr)

Table 4. Delta-V vs TOF (2001 DY103, one-way). Arrival dV[m/s] Tf

2033/10/20 (Fastest) 3808 2494d, 6.83yr 2034/01/01 2885 2567d, 7.03yr 2035/01/01 1813 2932d, 8.03yr 2036/01/01 1600 3297d, 9.03yr

Table 5. Fastest trajectory to L4 asteroids.

Target TOF[yr] dV[m/s] 1999 XG91 7.59 3675 2007 RQ278 7.32 4143 2005 YJ15 7.62 3554

2003 CM208 6.76 3259 2004 HZ11 6.50 4230 2009 SK78 7.11 4347

5.5. Sample Return Option Fig. 9 shows the whole sample return trajectory of 2001 DY103 mission. Table 6 shows the summary of the trajectory. The total mission duration exceeds 30 years. In a sample return mission, reducing the TOFs from Jupiter to the asteroid and from the asteroid to Jupiter does not shorten the total mission, because the timing of the Jovian swing-by is restricted.

-5

0

5 -5

0

5-2

0

2

Y[AU]X[AU]

Z[A

U]

S/CSunEarthJupiterAsteroid

Fig. 9. Sample return trajectory (2001 DY103)

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Table 6. Summary of sample return mission. Phase Start End dV[m/s]

2yr EDVEGA 2022/09/25 2024/07/24 1442 Earth to Jupiter 2024/07/24 2026/12/22 - Jupiter-to-Asteroid 2026/12/22 2036/01/01 1471 Proximity Op. 2036/01/01 2037/01/01 - Asteroid-to-Jupiter 2037/01/01 2050/09/12 3686 Jupiter to Earth 2050/09/12 2053/07/29 -

5.6. Multi Rendezvous Option Instead of the sample return option, the multi rendezvous option is shown hear. The candidate targets can be selected by the ballistic analyses and the low-thrust trajectory is designed. Fig. 10 shows the trajectory from 2001 DY103 to 1998 WJ5. The trajectory likes Hohmann transfer orbit. We can find the asteroid connected to 1998 WJ5 . The summary is shown in Table 7.

-8 -6 -4 -2 0 2 4

-4

-2

0

2

4

X[AU]

Y[AU]

Fig. 10. 2001 DY103 to 1998 WJ5 trajectory

Table 7. Multiple rendezvous option. Phase Start End dV[m/s]

2001 DY103 -> 1998 WJ5 2035/01/01 2042/03/08 2660

1998 WJ5 -> 2006 UB63 2043/01/01 2047/10/13 4224

6. Conclusions In this paper, we described a Jovian Trojan exploration via solar power sail. The solar power sail, in which a solar sail is combined with a high Isp IES, is an original concept of JAXA and makes it possible to carry a large payload to a Jovian Trojan asteroid. The outline of the solar power sail spacecraft, its trajectory design, and the results were presented in this paper.

References 1) Tsuda, Y., Mori, O., Funase, R., Sawada, H., Yamamoto, T., Saiki,

T., Endo, T., Yonekura, K., Hoshino, H. and Kawaguchi, J.: Achievement of IKAROS—Japanese Deep Space Solar Sail Demonstration Mission, Acta Astronautica, 82 (2013), pp.183-188.

2) McInnes, C. R.: Solar Sailing, Technology, Dynamics and Mission Applications, Springer-Praxis, 1999.

3) Kawaguchi, J.: A power sailer mission for a Jovian orbiter and Trojan asteroid flybys, COSPAR04-A-01655, Abstracts of 35th COSPAR Scientific Assembly, Paris, France, 18-25 July, 2004.

4) Funase, R., Mori, O., Shirasawa, Y. and Yano, H: Trajectory Design and System Feasibility Analysis for Jovian Trojan Asteroid Exploration Mission Using Solar Power Sail, Transactions of the Japan Society for Aeronautical and Space Sciences, Aerospace Technology Japan, 12 (2014), pp. Pd_85-Pd_90.

5) Kawaguchi, J,: Solar Electric Propulsion Leverage: Electric Delta-VEGA (EDVEGA) Scheme and its Application, AAS 01-213, AAS/AIAA Space Flight Mechanics Meeting, Santa Barbara, California, Feb. 11-14, 2001.