5th IAA Planetary Defense Conference – PDC 201715–19 May 2017, Tokyo, Japan

IAA-PDC17-04-04

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

Shota Kikuchia,1,∗, Junichiro Kawaguchib,2

aThe University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8654, Japan, +815033624309bJAXA, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa, 252-0222, Japan, +815033624393

Abstract

Various asteroid mitigation strategies have been proposed to avoid destructive impact events. In sucha mission, the spinning motion of an asteroid prevents a precise and effective deflection maneuver. Tocircumvent this problem, this study investigates a novel de-spin method using a solar sail spacecraft thatis attached to the surface of an asteroid. In this approach, the solar radiation pressure torque inducedby reflectivity control devices on the sail membrane is exploited to cancel out the spin rate of an asteroidwithout requiring fuel. In addition, once three-axis attitude control is achieved after the de-spin, thetrajectory of the asteroid can be deflected by leveraging the solar radiation pressure force acting on thesail attached to the asteroid. This paper constructs general theories on the proposed asteroid de-spinand deflection methods, and provides evidence that this novel strategy would be a feasible option forasteroid 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 aster-oid deflection strategies, including nuclear/kinetic impactors, spacecraft propulsion, mass drivers, solarcollectors, gravitational tractors, and ion beam shepherd [1, 2, 3, 4, 5]. One of the complications in sucha mission stems from the spinning motion of the asteroid. Because asteroids have irregular shapesand their own unique spin axis directions, the spinning motion of an asteroid prevents a precise andeffective deflection operation. For this reason, the de-spinning of a target asteroid provides benefitsfor asteroid impact avoidance. Asteroid de-spin can be achieved by applying the asteroid deflectionmethods described above to reduce the angular momentum of an asteroid [4, 6]. Another possibleapproach for asteroid de-spin is to control the spin rate of an asteroid by capturing them with a net or atether [7]. Although these de-spin strategies have been analyzed in past studies, these methods mightrequire 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 theasteroid.

To solve these problems, this paper proposes a novel asteroid de-spin strategy using a solar-sailspacecraft with reflectivity control devices (RCDs) on its membrane. The basic strategy is to attach asolar sail to an asteroid and generate solar radiation pressure (SRP) torque induced by the differencein the reflectivity of the RCDs, as shown in Fig. 1(a). The RCDs are powered by solar cells mountedon the membrane, and thus, the proposed de-spin mechanism does not require any fuel or mechanicaldevices, leading to a low-cost and reliable operation. Moreover, because this method leverages the

∗Corresponding authorEmail addresses: kikuchi.shota@ac.jaxa.jp (Shota Kikuchi), kawaguchi.junichiro@jaxa.jp (Junichiro Kawaguchi)

1Ph.D. Candidate, Department of Aeronautics and Astronautics2Professor, Institute of Space and Astronautical Science

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(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 anasteroid. Both the solar sail deployment technology and the attitude control maneuver via RCDs havebeen demonstrated in past space missions [8, 11], and therefore, the proposed strategy is promising forasteroid mitigation missions.

As a consequence of the asteroid de-spin, the attitude of the asteroid is under the control of theattached solar sail. This capability can ensure the effective asteroid deflection/disruption operationsproposed in past studies. Moreover, the trajectory of the asteroid can also be deflected due to the SRPacceleration constantly acting on the membrane, as shown in Fig. 1(b). The asteroid deflection using asolar sail enables a safe and fuel-free operation. The idea of using a solar sail for asteroid mitigation hasbeen briefly stated in previous research [1]. However, the paper proposed a method to attach a tetherto a spinning asteroid and therefore concluded that the solar sail approach was unrealistic due to itsmechanical and structural complexities. By contrast, the method introduced in this study assumes thata 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 deflectionmethod using a solar sail is also advantageous in that the motion of an asteroid can be predictedprecisely. This is because of three reasons: first, this method is less dependent on the shape of theasteroid; 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 mech-anism using a solar sail with RCDs. Based on this model, the performance of this novel method isanalyzed with analytical and numerical simulations. It is then demonstrated that the proposed strategywould 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 technolo-gies: 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 thesekey technologies for clarity of discussion in subsequent sections.

2.1. Solar sailJAXA 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. IKAROSachieved fuel-free propulsion by exploiting the SRP naturally applied to the sail surface. The extensionof the sail membrane is maintained by the centrifugal force exerted by the spinning motion. IKAROSalso demonstrated solar power generation by thin-film solar cells mounted on the sail surface. Thesignificant success of the IKAROS mission expanded the possibility of flight mechanics in space.

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By using the solar-sail technologies demonstrated in the IKAROS mission, JAXA is currently de-veloping 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 ofthe membrane surface to generate a large amount of solar power even at the Jupiter distance, for highIsp ion engines. The solar power sail is scheduled to be launched in the early 2020s, and various solarsail 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].

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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 thuscan control the effect of SRP. Figure 3 compares the behavior of RCDs between the on-state and theoff-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 thischaracteristic, RCDs attached on a sail membrane can induce an imbalance in SRP, thereby generatinga torque to control the spacecraft attitude without requiring any fuel.

Although an RCD offers significant advantages in solar-sail operations, it cannot generate a torquealong the normal direction. To overcome this drawback, an advanced RCD has been recently developedthat can reflect the sunlight obliquely [12, 13]. The unique behavior of an advanced RCD can beobserved in Figure 4. The light normal to the RCD is indeed reflected diagonally when the power ison, as depicted in Fig. 4(b). This property of advanced RCDs enables one to generate a torque aboutthe direction of the solar radiation, which functions as a windmill. The utilization of both conventionaland advanced RCDs constitutes a fuel-free three-axis attitude control system.

3. Asteroid de-spin

3.1. Basic mechanismThis 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 RCDsis deployed immediately after launch. Then, the spacecraft rendezvouses with a hazardous asteroidby using conventional thruster systems or solar-sail propulsion. After the rendezvous, the spacecraftlands on the surface of the asteroid and anchors itself to the asteroid. Once the solar sail is attachedto 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 ofconventional 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 thespinning state such that the SRP torque cancels out the spin rate of the asteroid. Note that the solarsail is assumed to have a rigid boom structure unlike IKAROS, whose membrane is kept extended dueto its spinning motion.

(a) (b) (c)

Figure 5: De-spin mechanism using three-axis control via RCDs.

3.2. Dynamical modelThe 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 orbitwith a radius of 1 AU. The diameter of the asteroid is treated as a parameter. The range of the diameteris presented in Table 1, assuming relatively small asteroids with a diameter of a few hundred metersor less. The rotation axis of an asteroid can take any direction in general, and the proposed de-spinmethod is applicable to arbitrary axis directions, as illustrated in Fig. 5. This paper therefore investigates

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Table 1: Asteroid parameters

Item Symbol Value

Diameter D 10–200 mDistance from the Sun d 1 AU

Density ρ 2.0 g/cm3

Table 2: Solar sail parameters

Item Symbol Value

Sail length L 10–300 m

Optical constants of RCDs Cs,Cd,Ca0.5, 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 tothe ecliptic plane. The bulk density of the asteroid is given as 2 g/cm3.

The parameters for the solar sail used in this study are presented in Table 2. The spacecraft isassumed to equip a square membrane with a side length of 10–300 m. A solar sail spacecraft with a14-m square membrane (IKAROS) has been launched and demonstrated in space [8], while one witha 50 to 55-m square sail is under development for the Jovian Trojan asteroid sample return missionby JAXA [9, 10]. This paper performs analyses for a 100-m-class sail as well, assuming an advancedfuture 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 onexperimental data corresponding to the visible-light wavelength observed in previous research [11]. Cs,Cd, and Ca denote optical constants regarding the modes of specular reflection, diffuse reflection, andabsorption, respectively, which satisfy Cs + Cd + Ca = 1. An RCD exhibits the specular property whenthe power is on, while the diffusive mode becomes predominant when the power is off.

3.3. SRP torqueThe SRP force acting on a small sail element dA is given by the equation below [14].

dF = −P(n · s)(2(n · s)Cs + B f Cd)n + (Cd + Ca)sdA (1)

where n is a unit vector normal to the sail surface; s is a unit vector pointing from the spacecraft to theSun; B f = 2/3 is the Lambertian coefficient; and P = P0/d2 is the SRP exerted on the surface of the solarsail, where P0 ' 1×1017 kg m/s2 is the solar flux constant [15]. The geometrical relationship between theunit vectors n and s is illustrated in Fig. 6. These two vectors and the Sun angle α satisfy the followingequation:

n · s = cosα (2)

Then, the SRP force component normal to the sail surface is calculated as follows:

dFn = P cosα2 cosα ·Cs + (B f + cosα)Cd + cosα ·CadA (3)

The SRP torque acting on the spacecraft-asteroid system is produced by the difference in the magnitudeof the SRP force between the on-state and off-state RCDs. Therefore, the resultant SRP torque isexpressed as the product of the SRP force dFn and the arm length ξ, yielding the equation below [11].

T (α) =

∫ξ × |dFn,ON − dFn,OFF |

=

∫ L2

0ξ × |P cosα2 cosα · ∆Cs + (B f + cosα)∆CdLdξ|

=18

PL3| cosα2 cosα · ∆Cs + (B f + cosα)∆Cd + cosα · ∆Ca| (4)

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Figure 6: Geometrical relationship between the Sun vector, the normal vector, and the Sun angle.

where ∆Cs ≡ Cs,ON − Cs,OFF and ∆Cd ≡ Cd,ON − Cd,OFF . Assuming that the SRP torque is applied onlywhen the front side of the sail surface is illuminated by the Sun, the torque is represented as a functionof the Sun angle α by the following equation:

T (α) =

18

PL3| cosα2 cosα · ∆Cs + (B f + cosα)∆Cd + cosα · ∆Ca|

(|α| ≤

π

2

)0

(π

2< |α| ≤ π

) (5)

When the angular velocity of an asteroid is approximated as constant during one rotation, the SRPtorque can be averaged over one period τ as follows:

T =

∫ τ

0 Tdt∫ τ

0 dt

=1

2π

∫ π

−π

T (α)dα

=PL3

8π

∫ π2

0cosα2 cosα · ∆Cs + (B f + cosα)∆Cd + cosα · ∆Cadα

=PL3

32

2∆Cs +

(1 +

4B f

π

)∆Cd + ∆Ca

(6)

3.4. De-spin performanceThe change in the angular velocity of an asteroid due to the SRP torque exerted via the RCDs is

formulated by the equation below.Iω = −T (7)

where ω is the angular velocity of the asteroid and I is the moment of inertia. Considering that themoment of inertia of a solar sail is negligible compared with that of an asteroid, I is obtained from thefollowing equations:

M = ρ ·πD3

6, I =

MD2

10(8)

Let Ω denote the initial spin rate of an asteroid. Then, the required time to de-spin an asteroid is givenby

treq =IΩ

T(9)

Equation (9) can be calculated by specifying the following three parameters: the asteroid diameterD, the sail length L, and the spin rate of the asteroid Ω (or the rotation period). Table 3 provides therequired time to de-spin an asteroid for different sets of the parameters. The table indicates that a 55-msolar sail, which is based on a current technology, has the capability to de-spin relatively small asteroidsin a reasonable time duration. In addition, a larger solar sail can make more effective use of SRP due

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Table 3: Calculation results of the asteroid de-spin.

Asteroid diameter [m] Sail length [m] Rotation period [hr] Duration [yr]

20 55 2 1.730 55 10 2.650 300 10 0.2

100 300 20 3.3

(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 adiameter of 100 m in approximately 3 years, a task that would require enormous amounts of resourcesunder conventional de-spin strategies.

Figure 7 provides contour maps that illustrate the performance of the proposed asteroid de-spinstrategy. 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, whileFig. 7(b) illustrates the change in the spin rate that can be achieved in a time duration of 2 years. Thebroken line in Fig. 7(b) labeled “Spin barrier” represents the maximum spin rate for larger asteroids thatseparates them from smaller fast rotators [15]. Both of these figures demonstrate that if a sufficientlylarge sail size is selected, the proposed method using RCDs would be effective for asteroid de-spinmissions.

4. Asteroid deflection

Once the de-spin of an asteroid is completed and three-axis attitude control is achieved for thespacecraft-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 sailsurface, and thus, it does not require any fuel to produce a delta-V. This section demonstrates thefeasibility of this novel strategy by performing several numerical simulations.

4.1. Dynamical modelThe present study investigates the motion of an asteroid based on the circular restricted three-body

problem (CR3BP). In this model, two massive bodies, M1 and M2, are moving in circular orbits abouttheir barycenter. On the other hand, the third smaller body P does not exert an influence on the motionof M1 and M2. The schematic of the CR3BP is presented in Fig. 8. M1, M2, and P correspond to theSun, the Earth, and an asteroid, respectively, in our current problem.

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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 frameby the following equations of motion.

x = 2y + x − (1 − µ)x + µ

r31

− µx − (1 − µ)

r32

+ aS RP,x

y = −2x + y − (1 − µ)yr3

1

− µyr3

2

+ aS RP,y

z = −(1 − µ)zr3

1

− µzr3

2

+ aS RP,z

(10)

where µ is the gravitational constant; aS RP,x, aS RP,y, and aS RP,z are the SRP accelerations in the corre-sponding axis directions; and r1 and r2 are the distances of the asteroid from the Sun and the Earth,which are calculated from the equations below.

r1 =

√(x + µ)2 + y2 + z2

r2 =

√(x − (1 − µ)2 + y2 + z2

(11)

Note that Eq. (10) is normalized such that the Sun-Earth distance and the angular velocity of the circularmotion are unitary, and the non-dimensional gravitational constant of the Sun-Earth system is µ '3.04× 10−6. The SRP acceleration acting on a spacecraft that is attached to an asteroid is derived in thesubsequent subsection.

4.2. SRP forceAssuming 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)Cs + B f Cd)n + (Cd + Ca)s (12)

Figure 9: Tangential component of SRP force as a function of the Sun angle

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Let t denote a transverse vector that satisfies t ⊥ s and lies in the plane formed by n and s. To enhancethe asteroid deflection performance, it is desirable to achieve the largest SRP acceleration/decelerationin 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, 2014Semi-major axis 1.379966506 × 1011 m

Eccentricity 0.1906379171Inclination 3.689765803 deg

Longitude of the ascending node 203.2095710 degArgument of periapsis 125.7492147 deg

True anomaly 169.4862799 deg

(a) Inertial frame

(b) Rotating frame

Figure 10: Asteroid orbital diagram

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SRP force, which is parallel to the t direction, is given by the equation below.

Ft = PA sinα cosα(2 cosα ·Cs + B f Cd) (13)

Figure 9 plots Ft as a function of the Sun angle α, where the vertical axis is normalized by the char-acteristic SRP force F0 = PA. This figure indicates that there exists an optimal attitude to maximizethe 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 valueof 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. Thenormal direction n is specified to satisfy the following conditions:

n · s = cosα∗, n · ez = 0 (14)

where ez is a unit vector along the z axis of the Sun-Earth rotating frame. Then, the SRP force vector iscalculated from Eq. (12), and the SRP acceleration vector is expressed as

aS RP =FM

(15)

By substituting Eq. (15) into the equations of motion presented in Eq. (10), the orbital motion of anasteroid 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

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4.3. Impact trajectory of the asteroidTo evaluate the performance of the asteroid deflection mechanism using a solar sail, this paper as-

sumes a hypothetical asteroid that impacts with the Earth in the future. The trajectory of the hypotheticalasteroid is given based on that of the asteroid Apophis, which is predicted to have a close encounterwith the Earth on April 13th, 2029 [16]. For analyses in this study, the orbital elements of Apophis areslightly modified such that it actually impacts on that day under the CR3BP dynamics. The orbital ele-ments 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 inthe Sun-Earth rotating frame in Fig. 10(b). The orbit is numerically propagated based on Eq. (10) from2014 to 2029. The position of the Earth is expressed as a fixed point in Fig. 10(b), and the enlargedview in the figure shows that the asteroid collides with the Earth on April 13, 2029. The subsequentsubsections investigate the feasibility to avoid this asteroid impact by applying the mitigation strategyusing a solar sail.

4.4. Deflection performanceSeveral 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 byinducing SRP acceleration via solar sails. It can be observed in Fig. 11(a) that the current state-of-the-art technology of a 55-m sail has a sufficient capability to deflect the trajectory of a relatively smallasteroid that would have originally impacted with the Earth. When the SRP acceleration is exerted onan asteroid for a longer duration, a larger distance deviation can be achieved. The result indicates thata 10-yr operation allows the system to deflect the asteroid toward the altitude of geostationary Earthorbit (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 toleverage the effect of SRP.

Figure 12 illustrates the influence of the sail size on the deflection performance. These simulationsare also performed for asteroids with two different diameters. The vertical axes in these figures indicatethe minimum distance of a deflected asteroid from the surface of the Earth, which is expressed in Earthradii Re. The small oscillations appearing in these profiles stem from the deviation of the magnitude ofthe SRP force depending on the distance from the Sun. Because the SRP acceleration is constantlyapplied 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 showthe 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 toachieve 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

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(a) Contour map of the time duration (b) Contour map of the minimum distance from theEarth

Figure 13: Performance of the asteroid deflection method

distance that can be achieved after a 10-yr deflection maneuver. These contour maps enable us tovisually identify the sail length required to accomplish the deflection of a hazardous asteroid.

5. Solar sail design

5.1. Design strategyThis study performs analytical and numerical analyses, assuming that the surface of the sail mem-

brane is entirely covered with RCDs. Although this design is reasonable to maximize the de-spin perfor-mance, 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 suchas by using an aluminized polyimide film. Given that the magnitude of the SRP torque is proportionalto the arm length, mounting RCDs outside of the sail membrane is effective. The conceptual diagramregarding the design of the solar sail is depicted in Figure 14. The optimal area ratios of the RCDs andspecular surfaces can be determined by evaluating the required de-spin and deflection capabilities fora 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 detailedanalyses must be performed on the power requirement for the entire spacecraft system. Another aspectto be considered in future studies is the structural mass necessary to support a load applied to a sailmembrane due to the SRP force and asteroid gravitational force.

Figure 14: Solar sail design and the performances of asteroid de-spin and deflection

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5.2. Mass calculationThe 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 thisassumption, the mass of a membrane can be calculated as a function of the RCD area ratio, κRCD, asfollows:

Msail = L2(1 − κRCD)σPI + κRCD(σPI + σRCD) (16)

Here, σPI and σRCD are the surface densities of the polyimide base film and the RCD, which are givenin Table 5. σPI is calculated from a mass density of 1.4 g/cm3 and a thickness of 10 µm, while σRCD isestimated 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 treatingthe sail length L and the RCD area ratio κRCD as parameters. From this figure, the sail mass appearsto be feasible in our current mass model; for example, a sail with L = 100 m and κRCD = 40% weighs500 kg, and a sail with L = 150 m and κRCD = 60% weighs 1500 kg. Even the mass of the heaviest modelwith L = 300 m and κRCD = 100% is less than 9.5 tons. It is important to reiterate that structural massis not included in this calculation. Although detailed mass calculations are required to be comparedwith other asteroid deflection methods previously proposed, it can be concluded at this point that theasteroid 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 σPI 14 g/m2

RCD σRCD 90 g/m2

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 mountingreflectivity control devices (RCDs). The basic concepts of these methods and the dynamical modelsnecessary to analyze the performances were introduced. First, the de-spin mechanism, which exploitsthe SRP torque induced by the RCDs, was evaluated by analytical analyses. It has been clarified thata 55-m sail and a 300-m sail can potentially de-spin asteroids with a diameter of 20–30 m and 100m, respectively, within a reasonable time duration. Then, the feasibility of the deflection strategy wasinvestigated by numerically propagating the trajectory of an asteroid subject to SRP acceleration. Thesimulations demonstrated that a 100-m asteroid that is originally set to impact with the Earth can bedeflected toward GEO altitude within 10–15 years, using a 300-m-class sail. Finally, the mass of the sailmembrane with the RCDs was calculated based on a simple model. According to the result, the massof a 150-m sail is approximately several tons, and even the heaviest model with a sail length of 300 mis less than 9.5 tons.

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Although detailed analyses must be performed to evaluate the strategy’s superiority against otherde-spin/deflection methods previously proposed, it can be concluded that the asteroid de-spin/deflectionstrategy 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 Societyfor the Promotion of Science.

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