Asteroid De-spin and Deflection Strategy Using a Solar-sail Spacecraft with Reflectivity Control Devices

Transcription

1 5 th IAA Planetary Defense Conference PDC May 2017, Tokyo, Japan IAA-PDC Asteroid De-spin and Deflection Strategy Using a Solar-sail Spacecraft with Reflectivity Control Devices Shota Kikuchi a,1,, Junichiro Kawaguchi b,2 a The University of Tokyo, Hongo, Bunkyo-ku, Tokyo, , Japan, b JAXA, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa, , Japan, Abstract Various asteroid mitigation strategies have been proposed to avoid destructive impact events. In such a mission, the spinning motion of an asteroid prevents a precise and effective deflection maneuver. To circumvent this problem, this study investigates a novel de-spin method using a solar sail spacecraft that is attached to the surface of an asteroid. In this approach, the solar radiation pressure torque induced by reflectivity control devices on the sail membrane is exploited to cancel out the spin rate of an asteroid without requiring fuel. In addition, once three-axis attitude control is achieved after the de-spin, the trajectory of the asteroid can be deflected by leveraging the solar radiation pressure force acting on the sail attached to the asteroid. This paper constructs general theories on the proposed asteroid de-spin and deflection methods, and provides evidence that this novel strategy would be a feasible option for asteroid mitigation missions. Keywords: Asteroid deflection, Asteroid de-spin, Solar sail, Reflectivity control device (RCD) 1. Introduction To prevent a catastrophic asteroid collision with the earth, past research has proposed various asteroid deflection strategies, including nuclear/kinetic impactors, spacecraft propulsion, mass drivers, solar collectors, gravitational tractors, and ion beam shepherd [1, 2, 3, 4, 5]. One of the complications in such a mission stems from the spinning motion of the asteroid. Because asteroids have irregular shapes and their own unique spin axis directions, the spinning motion of an asteroid prevents a precise and effective deflection operation. For this reason, the de-spinning of a target asteroid provides benefits for asteroid impact avoidance. Asteroid de-spin can be achieved by applying the asteroid deflection methods described above to reduce the angular momentum of an asteroid [4, 6]. Another possible approach for asteroid de-spin is to control the spin rate of an asteroid by capturing them with a net or a tether [7]. Although these de-spin strategies have been analyzed in past studies, these methods might require enormous resources to compensate for the large angular momentum of an asteroid. In addition, the performance of de-spinning an asteroid is significantly dependent on the shape and property of the asteroid. To solve these problems, this paper proposes a novel asteroid de-spin strategy using a solar-sail spacecraft with reflectivity control devices (RCDs) on its membrane. The basic strategy is to attach a solar sail to an asteroid and generate solar radiation pressure (SRP) torque induced by the difference in the reflectivity of the RCDs, as shown in Fig. 1(a). The RCDs are powered by solar cells mounted on the membrane, and thus, the proposed de-spin mechanism does not require any fuel or mechanical devices, leading to a low-cost and reliable operation. Moreover, because this method leverages the Corresponding author addresses: kikuchi.shota@ac.jaxa.jp (Shota Kikuchi), kawaguchi.junichiro@jaxa.jp (Junichiro Kawaguchi) 1 Ph.D. Candidate, Department of Aeronautics and Astronautics 2 Professor, Institute of Space and Astronautical Science 1

2 (a) Asteroid de-spin (b) Asteroid deflection Figure 1: Concept of asteroid de-spin and deflection using a solar-sail spacecraft. SRP force acting on a sail membrane, it is less dependent on the shape and surface properties of an asteroid. Both the solar sail deployment technology and the attitude control maneuver via RCDs have been demonstrated in past space missions [8, 11], and therefore, the proposed strategy is promising for asteroid mitigation missions. As a consequence of the asteroid de-spin, the attitude of the asteroid is under the control of the attached solar sail. This capability can ensure the effective asteroid deflection/disruption operations proposed in past studies. Moreover, the trajectory of the asteroid can also be deflected due to the SRP acceleration constantly acting on the membrane, as shown in Fig. 1(b). The asteroid deflection using a solar sail enables a safe and fuel-free operation. The idea of using a solar sail for asteroid mitigation has been briefly stated in previous research [1]. However, the paper proposed a method to attach a tether to a spinning asteroid and therefore concluded that the solar sail approach was unrealistic due to its mechanical and structural complexities. By contrast, the method introduced in this study assumes that a solar sail is directly attached to an asteroid and achieves three-axis attitude control via RCDs; thus, our mechanism is much simpler than that of the strategy proposed in the previous work. The deflection method using a solar sail is also advantageous in that the motion of an asteroid can be predicted precisely. This is because of three reasons: first, this method is less dependent on the shape of the asteroid; second, this method does not involve an impact event; and third, the asteroid is de-spinned, and thus, the Yarkovsky effect is diminished. This paper constructs the dynamical model of the proposed asteroid de-spin and deflection mechanism using a solar sail with RCDs. Based on this model, the performance of this novel method is analyzed with analytical and numerical simulations. It is then demonstrated that the proposed strategy would be useful for collision avoidance operations for potentially hazardous asteroids. 2. Key Technology The asteroid de-spin and deflection strategies introduced in this research rely on two key technologies: solar sails and RCDs. Both technologies have already been demonstrated in past space missions. Therefore, the proposed method is expected to be promising and reliable. This section reviews these key technologies for clarity of discussion in subsequent sections Solar sail JAXA launched the world s first deep-space solar-sail spacecraft, IKAROS, in 2010 [8]. IKAROS succeeded in deploying a 14-m square sail membrane with a minimum thickness of 7.5 µm. IKAROS achieved fuel-free propulsion by exploiting the SRP naturally applied to the sail surface. The extension of the sail membrane is maintained by the centrifugal force exerted by the spinning motion. IKAROS also demonstrated solar power generation by thin-film solar cells mounted on the sail surface. The significant success of the IKAROS mission expanded the possibility of flight mechanics in space. 2

3 By using the solar-sail technologies demonstrated in the IKAROS mission, JAXA is currently developing the next generation of solar power sails for the Jovian Trojan asteroid sample return mission [9, 10]. The sail size is 50 to 55-m square, and thin-film solar cells are attached to most of the area of the membrane surface to generate a large amount of solar power even at the Jupiter distance, for high Isp ion engines. The solar power sail is scheduled to be launched in the early 2020s, and various solar sail technologies have been progressed for the mission. Figure 2: Solar sail demonstrator IKAROS. (a) Off state (b) On state Figure 3: Reflectivity control device (RCD) [11]. (a) Off state (b) On state Figure 4: Advanced RCD [12]. 3

4 2.2. Reflectivity control device (RCD) Another important achievement of the IKAROS mission was the demonstration of fuel-free attitude control using RCDs [8]. An RCD can change the optical properties of its surface electrically and thus can control the effect of SRP. Figure 3 compares the behavior of RCDs between the on-state and the off-state [11]. Figure 3(a) shows that the RCD exhibits a diffusive characteristic when the power is off; in contrast, a specular behavior appears when the power is on, as shown in Fig. 3(b). By virtue of this characteristic, RCDs attached on a sail membrane can induce an imbalance in SRP, thereby generating a torque to control the spacecraft attitude without requiring any fuel. Although an RCD offers significant advantages in solar-sail operations, it cannot generate a torque along the normal direction. To overcome this drawback, an advanced RCD has been recently developed that can reflect the sunlight obliquely [12, 13]. The unique behavior of an advanced RCD can be observed in Figure 4. The light normal to the RCD is indeed reflected diagonally when the power is on, as depicted in Fig. 4(b). This property of advanced RCDs enables one to generate a torque about the direction of the solar radiation, which functions as a windmill. The utilization of both conventional and advanced RCDs constitutes a fuel-free three-axis attitude control system. 3. Asteroid de-spin 3.1. Basic mechanism This subsection provides the basic concept of the asteroid de-spin strategy using a solar sail with RCDs. The proposed method begins with the phase where the sail membrane with the mounted RCDs is deployed immediately after launch. Then, the spacecraft rendezvouses with a hazardous asteroid by using conventional thruster systems or solar-sail propulsion. After the rendezvous, the spacecraft lands on the surface of the asteroid and anchors itself to the asteroid. Once the solar sail is attached to the target asteroid, it achieves the capability to exert a torque on the asteroid by controlling the on- /off-state of the RCDs. Although the spin axis of an asteroid can take an arbitrary direction, the use of conventional and advanced RCDs enables three-axis attitude control, as described in Fig 5. Therefore, a solar sail can de-spin an asteroid by changing the reflectivity of the RCDs in accordance with the spinning state such that the SRP torque cancels out the spin rate of the asteroid. Note that the solar sail is assumed to have a rigid boom structure unlike IKAROS, whose membrane is kept extended due to its spinning motion. (a) (b) (c) Figure 5: De-spin mechanism using three-axis control via RCDs Dynamical model The physical parameters for an asteroid for the analysis of the de-spin dynamics are provided in Table 1. The asteroid is modeled as a uniform sphere and is assumed to be moving in a circular orbit with a radius of 1 AU. The diameter of the asteroid is treated as a parameter. The range of the diameter is presented in Table 1, assuming relatively small asteroids with a diameter of a few hundred meters or less. The rotation axis of an asteroid can take any direction in general, and the proposed de-spin method is applicable to arbitrary axis directions, as illustrated in Fig. 5. This paper therefore investigates 4

5 Table 1: Asteroid parameters Item Symbol Value Diameter D m Distance from the Sun d 1 AU Density ρ 2.0 g/cm 3 Table 2: Solar sail parameters Item Symbol Value Sail length L m Optical constants of RCDs C s, C d, C a 0.5, 0.3, 0.2 (ON) 0.1, 0.5, 0.4 (OFF) the de-spin performance for a specific case as an example, where the rotation axis is perpendicular to the ecliptic plane. The bulk density of the asteroid is given as 2 g/cm 3. The parameters for the solar sail used in this study are presented in Table 2. The spacecraft is assumed to equip a square membrane with a side length of m. A solar sail spacecraft with a 14-m square membrane (IKAROS) has been launched and demonstrated in space [8], while one with a 50 to 55-m square sail is under development for the Jovian Trojan asteroid sample return mission by JAXA [9, 10]. This paper performs analyses for a 100-m-class sail as well, assuming an advanced future solar-sail technology. The surface of a sail in our current model is entirely covered by RCDs. The optical constants of the RCDs are also provided in Table 2. These values are specified based on experimental data corresponding to the visible-light wavelength observed in previous research [11]. C s, C d, and C a denote optical constants regarding the modes of specular reflection, diffuse reflection, and absorption, respectively, which satisfy C s + C d + C a = 1. An RCD exhibits the specular property when the power is on, while the diffusive mode becomes predominant when the power is off SRP torque The SRP force acting on a small sail element da is given by the equation below [14]. df = P(n s){(2(n s)c s + B f C d )n + (C d + C a )s}da (1) where n is a unit vector normal to the sail surface; s is a unit vector pointing from the spacecraft to the Sun; B f = 2/3 is the Lambertian coefficient; and P = P 0 /d 2 is the SRP exerted on the surface of the solar sail, where P kg m/s 2 is the solar flux constant [15]. The geometrical relationship between the unit vectors n and s is illustrated in Fig. 6. These two vectors and the Sun angle α satisfy the following equation: n s = cos α (2) Then, the SRP force component normal to the sail surface is calculated as follows: df n = P cos α{2 cos α C s + (B f + cos α)c d + cos α C a }da (3) The SRP torque acting on the spacecraft-asteroid system is produced by the difference in the magnitude of the SRP force between the on-state and off-state RCDs. Therefore, the resultant SRP torque is expressed as the product of the SRP force df n and the arm length ξ, yielding the equation below [11]. T(α) = ξ df n,on df n,off = L 2 0 ξ P cos α{2 cos α C s + (B f + cos α) C d }Ldξ = 1 8 PL3 cos α{2 cos α C s + (B f + cos α) C d + cos α C a } (4) 5

6 Figure 6: Geometrical relationship between the Sun vector, the normal vector, and the Sun angle. where C s C s,on C s,off and C d C d,on C d,off. Assuming that the SRP torque is applied only when the front side of the sail surface is illuminated by the Sun, the torque is represented as a function of the Sun angle α by the following equation: 1 T(α) = 8 PL3 cos α{2 cos α C s + (B f + cos α) C d + cos α C a } 0 ( α π ) ( 2 π ) (5) 2 < α π When the angular velocity of an asteroid is approximated as constant during one rotation, the SRP torque can be averaged over one period τ as follows: T = τ Tdt 0 τ dt 0 = 1 2π = PL3 8π = PL3 32 π π π 2 0 T(α)dα cos α{2 cos α C s + (B f + cos α) C d + cos α C a }dα ( 1 + 4B ) } f C d + C a π { 2 C s + (6) 3.4. De-spin performance The change in the angular velocity of an asteroid due to the SRP torque exerted via the RCDs is formulated by the equation below. I ω = T (7) where ω is the angular velocity of the asteroid and I is the moment of inertia. Considering that the moment of inertia of a solar sail is negligible compared with that of an asteroid, I is obtained from the following equations: M = ρ πd3 6, I = MD2 (8) 10 Let Ω denote the initial spin rate of an asteroid. Then, the required time to de-spin an asteroid is given by t req = IΩ (9) T Equation (9) can be calculated by specifying the following three parameters: the asteroid diameter D, the sail length L, and the spin rate of the asteroid Ω (or the rotation period). Table 3 provides the required time to de-spin an asteroid for different sets of the parameters. The table indicates that a 55-m solar sail, which is based on a current technology, has the capability to de-spin relatively small asteroids in a reasonable time duration. In addition, a larger solar sail can make more effective use of SRP due 6

7 Table 3: Calculation results of the asteroid de-spin. Asteroid diameter [m] Sail length [m] Rotation period [hr] Duration [yr] (a) Contour map of the time duration (b) Contour map of the change in spin rate Figure 7: Performance of the asteroid de-spin method. to its larger arm length. As observed in the table, a 300-m sail-craft could de-spin an asteroid with a diameter of 100 m in approximately 3 years, a task that would require enormous amounts of resources under conventional de-spin strategies. Figure 7 provides contour maps that illustrate the performance of the proposed asteroid de-spin strategy. The asteroid diameter and the sail length are treated as variables in both contour maps. Figure 7(a) shows the required time to de-spin an asteroid with a rotation period of 10 hours, while Fig. 7(b) illustrates the change in the spin rate that can be achieved in a time duration of 2 years. The broken line in Fig. 7(b) labeled Spin barrier represents the maximum spin rate for larger asteroids that separates them from smaller fast rotators [15]. Both of these figures demonstrate that if a sufficiently large sail size is selected, the proposed method using RCDs would be effective for asteroid de-spin missions. 4. Asteroid deflection Once the de-spin of an asteroid is completed and three-axis attitude control is achieved for the spacecraft-asteroid system, the attached solar sail can also be utilized to deflect the orbit of the asteroid. The proposed asteroid deflection method exploits the SRP acceleration naturally acting on the sail surface, and thus, it does not require any fuel to produce a delta-v. This section demonstrates the feasibility of this novel strategy by performing several numerical simulations Dynamical model The present study investigates the motion of an asteroid based on the circular restricted three-body problem (CR3BP). In this model, two massive bodies, M 1 and M 2, are moving in circular orbits about their barycenter. On the other hand, the third smaller body P does not exert an influence on the motion of M 1 and M 2. The schematic of the CR3BP is presented in Fig. 8. M 1, M 2, and P correspond to the Sun, the Earth, and an asteroid, respectively, in our current problem. 7

8 Figure 8: Sun-Earth rotating coordinate frame. The classical CR3BP formulation can be extended to incorporate the effect of SRP acceleration. Then, the orbital motion of P (the asteroid) subject to SRP is expressed in the Sun-Earth rotating frame by the following equations of motion. ẍ = 2ẏ + x (1 µ) x + µ r 3 1 x (1 µ) µ + a r 3 S RP,x 2 ÿ = 2ẋ + y (1 µ) y µ y + a r 3 1 r 3 S RP,y 2 z = (1 µ) z µ z + a r 3 1 r 3 S RP,z 2 where µ is the gravitational constant; a S RP,x, a S RP,y, and a S RP,z are the SRP accelerations in the corresponding axis directions; and r 1 and r 2 are the distances of the asteroid from the Sun and the Earth, which are calculated from the equations below. r 1 = (x + µ) 2 + y 2 + z 2 (11) r 2 = {(x (1 µ)} 2 + y 2 + z 2 Note that Eq. (10) is normalized such that the Sun-Earth distance and the angular velocity of the circular motion are unitary, and the non-dimensional gravitational constant of the Sun-Earth system is µ The SRP acceleration acting on a spacecraft that is attached to an asteroid is derived in the subsequent subsection SRP force Assuming a uniform and flat sail surface, the SRP force exerted on a solar sail is derived from Eq. (1) as follows: F = PA(n s){(2(n s)c s + B f C d )n + (C d + C a )s} (12) (10) Figure 9: Tangential component of SRP force as a function of the Sun angle 8

9 Let t denote a transverse vector that satisfies t s and lies in the plane formed by n and s. To enhance the asteroid deflection performance, it is desirable to achieve the largest SRP acceleration/deceleration in the transverse direction, as illustrated in Fig. 1(b). The magnitude of the transverse component of the Table 4: Orbital elements of the hypothetical asteroid Item Value Epoch January 1 st, 2014 Semi-major axis m Eccentricity Inclination deg Longitude of the ascending node deg Argument of periapsis deg True anomaly deg (a) Inertial frame (b) Rotating frame Figure 10: Asteroid orbital diagram 9

10 SRP force, which is parallel to the t direction, is given by the equation below. F t = PA sin α cos α(2 cos α C s + B f C d ) (13) Figure 9 plots F t as a function of the Sun angle α, where the vertical axis is normalized by the characteristic SRP force F 0 = PA. This figure indicates that there exists an optimal attitude to maximize the transverse component of the SRP force. The optimal Sun angle in this system is α = 36.7 deg, assuming the optical constants of an on-state RCD presented in Table 3. It is to be noted that the value of α is dependent on the optical constants of the sail surface. The attitude of a solar sail is controlled via RCDs to perform an effective deflection maneuver. The normal direction n is specified to satisfy the following conditions: n s = cos α, n e z = 0 (14) where e z is a unit vector along the z axis of the Sun-Earth rotating frame. Then, the SRP force vector is calculated from Eq. (12), and the SRP acceleration vector is expressed as a S RP = F M (15) By substituting Eq. (15) into the equations of motion presented in Eq. (10), the orbital motion of an asteroid subject to SRP can be computed. (a) D = 30 m, L = 55 m (b) D = 100 m, L = 300 m Figure 11: Deflected asteroid trajectory 10

11 4.3. Impact trajectory of the asteroid To evaluate the performance of the asteroid deflection mechanism using a solar sail, this paper assumes a hypothetical asteroid that impacts with the Earth in the future. The trajectory of the hypothetical asteroid is given based on that of the asteroid Apophis, which is predicted to have a close encounter with the Earth on April 13th, 2029 [16]. For analyses in this study, the orbital elements of Apophis are slightly modified such that it actually impacts on that day under the CR3BP dynamics. The orbital elements and orbital diagrams of the Apophis-like hypothetical asteroid are provided in Table 4 and Fig. 10, respectively. Figure 10(a) depicts the orbit of the asteroid observed in the inertial frame, while it is expressed in the Sun-Earth rotating frame in Fig. 10(b). The orbit is numerically propagated based on Eq. (10) from 2014 to The position of the Earth is expressed as a fixed point in Fig. 10(b), and the enlarged view in the figure shows that the asteroid collides with the Earth on April 13, The subsequent subsections investigate the feasibility to avoid this asteroid impact by applying the mitigation strategy using a solar sail Deflection performance Several simulation results for asteroid deflection operations are provided here for different sizes of asteroids and solar sails. Figure 11 shows simulated asteroid trajectories that are deflected by inducing SRP acceleration via solar sails. It can be observed in Fig. 11(a) that the current state-ofthe-art technology of a 55-m sail has a sufficient capability to deflect the trajectory of a relatively small asteroid that would have originally impacted with the Earth. When the SRP acceleration is exerted on an asteroid for a longer duration, a larger distance deviation can be achieved. The result indicates that a 10-yr operation allows the system to deflect the asteroid toward the altitude of geostationary Earth orbit (GEO). On the other hand, Fig. 11(b) shows the result for an asteroid with a diameter of 100 m. Even such a large asteroid can be deflected within a reasonable time span using a larger solar sail to leverage the effect of SRP. Figure 12 illustrates the influence of the sail size on the deflection performance. These simulations are also performed for asteroids with two different diameters. The vertical axes in these figures indicate the minimum distance of a deflected asteroid from the surface of the Earth, which is expressed in Earth radii R e. The small oscillations appearing in these profiles stem from the deviation of the magnitude of the SRP force depending on the distance from the Sun. Because the SRP acceleration is constantly applied to the sail membrane, the distance deviation grows exponentially in terms of the time duration. This characteristic makes the proposed method a feasible option for asteroid deflection missions. The other simulation results are presented in Fig. 13. This figure provides contour maps that show the performance of the asteroid deflection as a function of the asteroid diameter and the sail length. The contour map given in Fig. 13(a) depicts the required time to deflect the trajectory of the asteroid to achieve a safe distance equal to the altitude of GEO. On the other hand, Fig. 13(b) shows the minimum (a) D = 30 m (b) D = 100 m Figure 12: Comparison between different sizes of solar sails for asteroid deflection 11

12 (a) Contour map of the time duration (b) Contour map of the minimum distance from the Earth Figure 13: Performance of the asteroid deflection method distance that can be achieved after a 10-yr deflection maneuver. These contour maps enable us to visually identify the sail length required to accomplish the deflection of a hazardous asteroid. 5. Solar sail design 5.1. Design strategy This study performs analytical and numerical analyses, assuming that the surface of the sail membrane is entirely covered with RCDs. Although this design is reasonable to maximize the de-spin performance, it is not necessarily favorable for asteroid deflection due to its low specular property. Therefore, the deflection performance can be enhanced by increasing the area ratio of the specular surface such as by using an aluminized polyimide film. Given that the magnitude of the SRP torque is proportional to the arm length, mounting RCDs outside of the sail membrane is effective. The conceptual diagram regarding the design of the solar sail is depicted in Figure 14. The optimal area ratios of the RCDs and specular surfaces can be determined by evaluating the required de-spin and deflection capabilities for a specific target asteroid. A portion of the sail surface might be used for thin-film solar cells to generate electric power [8]. Although the required power to drive the RCDs can be regarded as negligible in general, further detailed analyses must be performed on the power requirement for the entire spacecraft system. Another aspect to be considered in future studies is the structural mass necessary to support a load applied to a sail membrane due to the SRP force and asteroid gravitational force. Figure 14: Solar sail design and the performances of asteroid de-spin and deflection 12

13 5.2. Mass calculation The mass of a sail membrane for the asteroid mitigation mission is calculated here. For brevity, it is assumed that the masses of a base film and RCDs are the two predominant factors. Under this assumption, the mass of a membrane can be calculated as a function of the RCD area ratio, κ RCD, as follows: M sail = L 2 {(1 κ RCD )σ PI + κ RCD (σ PI + σ RCD )} (16) Here, σ PI and σ RCD are the surface densities of the polyimide base film and the RCD, which are given in Table 5. σ PI is calculated from a mass density of 1.4 g/cm 3 and a thickness of 10 µm, while σ RCD is estimated from the design of IKAROS presented in a previous paper [8]. The result of the mass calculation is shown in Fig. 15. The mass is obtained from Eq. (16) by treating the sail length L and the RCD area ratio κ RCD as parameters. From this figure, the sail mass appears to be feasible in our current mass model; for example, a sail with L = 100 m and κ RCD = 40% weighs 500 kg, and a sail with L = 150 m and κ RCD = 60% weighs 1500 kg. Even the mass of the heaviest model with L = 300 m and κ RCD = 100% is less than 9.5 tons. It is important to reiterate that structural mass is not included in this calculation. Although detailed mass calculations are required to be compared with other asteroid deflection methods previously proposed, it can be concluded at this point that the asteroid de-spin and deflection method using a solar sail with RCDs is promising for some applications. Table 5: Surface densities of a base film and an RCD Item Symbol Value Polyimide film σ PI 14 g/m 2 RCD σ RCD 90 g/m 2 Figure 15: Sail mass as a function of the sail size and the RCD area ratio. 6. Conclusion This paper proposed a novel asteroid de-spin and deflection strategy using a solar sail mounting reflectivity control devices (RCDs). The basic concepts of these methods and the dynamical models necessary to analyze the performances were introduced. First, the de-spin mechanism, which exploits the SRP torque induced by the RCDs, was evaluated by analytical analyses. It has been clarified that a 55-m sail and a 300-m sail can potentially de-spin asteroids with a diameter of m and 100 m, respectively, within a reasonable time duration. Then, the feasibility of the deflection strategy was investigated by numerically propagating the trajectory of an asteroid subject to SRP acceleration. The simulations demonstrated that a 100-m asteroid that is originally set to impact with the Earth can be deflected toward GEO altitude within years, using a 300-m-class sail. Finally, the mass of the sail membrane with the RCDs was calculated based on a simple model. According to the result, the mass of a 150-m sail is approximately several tons, and even the heaviest model with a sail length of 300 m is less than 9.5 tons. 13

14 Although detailed analyses must be performed to evaluate the strategy s superiority against other de-spin/deflection methods previously proposed, it can be concluded that the asteroid de-spin/deflection strategy using a solar sail with RCDs opens up new possibilities for asteroid mitigation. Acknowledgments This work was supported by Grant-in-Aid for Scientific Research (15J06932) from the Japan Society for the Promotion of Science. References [1] H. J. Melosh, I. V. Nemchinov, Y. I. Zetzer, Non-nuclear strategies for deflecting comets and asteroids, Hazards due to Comets and Asteroids 1 (1994) [2] E. T. Lu, S. G. Love, Gravitational tractor for towing asteroids, Nature 438 (2005) [3] D. Izzo, Optimization of interplanetary trajectories for impulsive and continuous asteroid deflection, Journal of Guidance, Control, and Dynamics 30 (2007) [4] J. P. Sanchez, C. Colombo, M. Vasile, G. Radice, Multicriteria comparison among several mitigation strategies for dangerous near-earth objects, Journal of Guidance, Control, and Dynamics 32 (2009) [5] C. Bombardelli, J. Peláez, Ion beam shepherd for asteroid deflection, Journal of Guidance, Control, and Dynamics 34 (2011) [6] C. Bombardelli, D. Pastor-Moreno, H. Urrutxua, Contactless ion beam asteroid despinning, in: AIAA/AAS Astrodynamics Specialist Conference, Vail, CO. August 9 13, Paper number AAS [7] R. P. Hoyt, K. J. James, Wrangler: Nanosatellite architecture for tethered de-spin of massive asteroids, in: AIAA Space Forum, Pasadena, CA. August 31 Sep 2, Paper number AIAA [8] Y. Tsuda, O. Mori, R. Funase, H. Sawada, T. Yamamoto, T. Saiki, T. Endo, J. Kawaguchi, Flight status of ikaros deep space solar sail demonstrator, Acta Astronautica 69 (2011) [9] J. Matsumoto, R. Funase, O. Mori, Y. Shirasawa, G. Ono, T. Hamasaki, N. Hayashi, T. Chujo, N. Motooka, K. Tanaka, Mission analysis of sample return from jovian trojan asteroid by solar power sail, Trans. JSASS Aerospace Tech. Japan 12 (2014) Pk43 Pk50. [10] O. Mori, T. Saiki, H. Kato, Y. Tsuda, Y. Mimasu, Y. Shirasawa, R. Boden, J. Matsumoto, T. Chujo, S. Kikuchi, J. Kikuchi, Y. Oki, K. Akatsuka, T. Iwata, T. Okada, H. Yano, S. Matsuura, R. Nakamura, Y. Kebukawa, J. Aoki, J. Kawaguchi, Jovian trojan asteroid exploration by solar power sail-craft, Trans. JSASS Aerospace Tech. Japan 14 (2016) Pk1 Pk7. [11] R. Funase, Y. Shirasawa, Y. Mimasu, O. Mori, Y. Tsuda, T. Saiki, J. Kawaguchi, On-orbit verification of fuel-free attitude control system for spinning solar sail utilizing solar radiation pressure, Advances in Space Research 48 (2011) [12] T. Chujo, Y. Shirasawa, O. Mori, J. Kawaguchi, Study and development of advanced reflectivity control device for spin rate control, in: 30th International Symposium on Space Technology and Science, Kobe, Japan. July 4 10, Paper number 2015-d-24. [13] T. Chujo, Y. Shirasawa, O. Mori, J. Kawaguchi, Development of advanced reflectivity control device and its application to solar power sail, in: The Fourth International Symposium on Solar Sailing, Kyoto, Japan. January 17 20, Paper number [14] C. R. Mclnnes, Solar Sailing: Technology, Dynamics and Mission Applications, First edition, Springer Praxis, Chichester, UK, [15] D. J. Scheeres, Orbital Motion in Strongly Perturbed Environments, First edition, Springer Praxis, Chichester, UK, [16] J. D. Giorgini, L. A. Benner, S. J. Ostro, M. C. Nolan, M. W. Busch, Predicting the earth encounters of (99942) apophis, Icarus 193 (2008)