Orbit Determination for Long-term Prediction of Solar Power Sail Demonstrator IKAROS

By ShoTaniguchi1), Takafumi Ohnishi1), Osamu Mori 2), Hideki Kato2), Hiroshi Takeuchi2), Atsushi Tomiki2), Yuya Mimasu2), Naoko Ogawa2), Jun Matsumoto2), Taichi ITO2), Tsutomu Ichikawa2), MakotoYoshikawa2), Shota Kikuchi3) , and Yosuke Kawabata3)

1) Technical computing solutions unit, science solutions div, Fujitsu Limited, Tokyo, Japan 2) Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan 3) Department of Aeronautics and Astronautics, The University of Tokyo, Tokyo, Japan

(Received April 24st, 2017)

The world’s first solar sail IKAROS (Interplanetary Kite-craft Accelerated by Radiation of the Sun) was launched along with the Venus Climate Orbiter Akatsuki in May 2010. IKAROS was full successful of missions that have been planned for first half year. After the Venus flyby in Dec 2010, it was carried out an extended mission. IKAROS has succeeded many additional engineering and scientific missions. We are obtained many orbit determination skill1) in nominal and extended phase. However, the IKAROS was almost run out the fuel in Dec 2011, so attitude and spin rate was out of control .As a result, lost communication with the ground station due to the power shortage on December 24, 2011. After this operation IKAROS began to repeat the hibernation of the 10-month period by substantially fixed attitude in inertial coordinate while maintaining the spin rate between 5rpm and 6rpm without fuel. End of a hibernation, it is necessary to difficult orbit determination and 10 months or more of the long-term trajectory prediction for antenna tracking at USUDA deep space tracking station. In order to perform the orbit determination of long-term arc, an optical model2) of the solar sail back surface was constructed. Also we constructed attitude motion model3) to predict attitude of spin axis motion due to solar radiation pressure (SRP) torque. After Dec 2011, we couldn’t get normal range data, only obtained range rate data which using FFT analysis4) at offline data from open loop receiver. Also azimuth and elevation data when we observed IKAROS at beacon mode were obtained. In a very difficult situation, we study to estimate the uncertainty orbit determination error. And we try to considered search operation using USUDA deep space tracking station and Yamaguchi University tracking station for VLBI. In this paper, we present orbit and attitude determination using few year long-term data and how to search a large area for antenna tracking to find out IKAROS.

Key Words: Orbit determination, IKAROS, Long-Term prediction, Attitude motion

1. Introduction rate between 5rpm and 6rpm without fuel. After wake up from hibernation, it is necessary to difficult orbit determination for The IKAROS (Interplanetary Kite-craft Accelerated by 10 months or more the long-term trajectory prediction. In Radiation Of the Sun) was launched along with the Venus order to perform the orbit determination of long-term arc to Climate Orbiter Akatsuki in May 2010. Fig. 1.1 shows construct an optical model of the solar sail back surface. And IKAROS’s mission sequence. IKAROS was successful we study to estimate the uncertainty orbit determination error. missions that have been planned for first half year. In this For the long-term prediction we have to study attitude phase, we were able to operate a stable orbit determination. motion and spin rate motion dynamics. Attitude motion is And we acquired the skills to consider polarization bias and to strongly related to spin rate, especially at low spin rate. eliminate spin modulation. These were required for orbit Recently we have find out signs that the spin rate is changing determination of the spin solar sail. in deceleration in the telemetry data at 2014 and 2015. After the Venus flyby in Dec 2010, it was carried out at extended mission that IKAROS had achieved a variety of 2. Overview of IKAROS results. One of the results was necessary to correspond to changes in spin rate in orbit determination arc at low spin rate. IKAROS is constructed to maintain the shape of a huge IKAROS was performed a reverse spin operation in order to 14 m x 14m square by spinning, and the square of the solve the problem of spin rate uncontrolled by the fuel quadrilateral have a mass attached. Spin rate and attitude are depletion in Oct 2011. After this operation IKAROS began to controlled through the tether by thruster of the main body in repeat the hibernation of the 10-month period by substantially the center. An outline of IKAROS is shown in Fig 2.1. fixed attitude in inertial coordinate while maintaining the spin

1

Reverse spin operation Inertial motion

st Hibernation mode 1 Hibernation Fitr （2012/9/6） flyby Venus (2010/12/8) 2nd Hibernation Fitr （2013/6/20） Extra success (after flyby) 3rd Hibernation Fitr （2014/5/22）

4th Hibernation Fitr Full success （2015/4/16） (in six months) Demonstration of th 5 Hibernation Fiter guidance,navigation and （2016/1～2) plan） Minimum success control by solar sail. 6th Hibernation Fiter (in several weeks) Earth Flyby Demonstration of After Earth Flyby photon propulsion by （2016/11～12 plan） (2016/11～2017/8) solar sail. Power generation by thin film solar cells

Launch (2010/5/21) Membrane deployment

Fig. 1.1 Mission sequence

Fig 3.1 Mission sequence.

The world's深宇宙初のソーラ・セイル宇宙機 first solar sail spacecraft in the deep space.

☆☆展開した衛星の断面積はThe cross-sectional area of 183.93mexpanded 2spacecraft約14m× is14m の183.93m正方形2 The shape is square about 14m ×14m ☆衛星本体は直径☆Cylindrical spacecraft1.6m× 高 さbody0.8m isの円筒形、全部の重さ diameter 1.6m × height 0.8m,the total weight は310kg X band low gain is about 310kg antenna 1(XLGA1)

Fig. 2.1 Overview of IKAROS Fig. 2.2 XLGA1 antenna position

As a characteristic of IKAROS, rotational torque called the hibernation, it was necessary that a long-term prediction wind turbine effect occurred due to unbalance of solar orbital trajectory more than 10 months which considering the radiation pressure caused by unevenness of the large film. solar radiation pressure. Since this torque worked in the direction of gradually For that purpose, we are constructing an attitude dynamics decreasing the spin, nominal operation phase from launch to model 3) to predict attitude in the future, making it possible to Venus swing-by had to spin up by thruster periodically. create a future trajectory over several years. It was possible to maintain spin rate without consuming fuel due to changing direction of spin rate and rotational 3. Orbit determination for nominal phase torque by solar radiation pressure after reverse spin operation carried out. In the nominal phase, it was necessary to remove the spin The attitude of IKAROS is determined by the earth angle rate modulation and perform orbit determination. There was a using the amplitude of Doppler modulation by spin and the polarization bias due to the spin rate and it was necessary to sun angle by the sun sensor. The spin rate was known by consider it in the orbit determination. telemetry. Therefore, the earth angle is obtained using the The equation of Doppler bias due to polarization is shown amplitude magnitude. Fig 2.2 show position of X band Low in (1). Gain Antenna (XLGA). XLGA is located about 715 mm away 1 1 from the spin axis. This location makes Doppler modulation 푓푏푖푎푠 = 퐶 ( + ) 휔 (1) 푓푇 푓푅 and the Earth angle changes amplitude magnitude. The acceleration due to solar radiation pressure is about 100 m / sec in a half year. In search operation after wake up from

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Table 3.1 shows the definition of variables. The estimated value of the solar radiation model was Table 3.1 Doppler bias due to polarization gradually changing in nominal phase. Fig. 3.2 shows the trend C: Speed of light(m/sec) of estimation value of solar radiation presser model.

fT: transmit frequency(Hz) Solar radiation光学パラメータ推定値の推移 model estimation result fR: Receive frequency(Hz) GReflection（鏡面） coefficient D（Diffusion拡散） coefficient T（Transmittance透過） coefficient ω: Spin rate(round/sec) 参考EstimateGのみ推定Ref only 線形Linear(G（Ref鏡面）) 多項式2nd order(G（Ref鏡面）. ) 線形Linear(D（Dif拡散）. ) 多項式2nd order(D（Dif拡散）. ) 線形Linear(参考EstGのみ推定Ref only) fbias: Doppler bias due to polarization(m/sec) 1.5E+00

The solar radiation pressure model used is shown in Table 1.0E+00 3.2. A huge thin film of solar sail is thought to emit absorbed sunlight with almost no time delay. Therefore, a model 5.0E-01

considering the thermal radiation was needed. Fig 3.2 shows a 0.0E+00

Invisible Invisible period Invisible Invisible period conceptual view of the model considering the thermal 不 不 不 Invisible period 可 可 可 radiation. -5.0E-01 視 視 視 期 期 期 間 間 間 -1.0E+00 Sun 20106月1/06日/01 82010月31/08日/31 112010月30/11日/30 32011月1/日03/01 52011月31/05日/31

Γ Spin axis Fig. 3.2 The trend of estimation value of solar radiation Unit Vector Ｄ θ presser model. A（absorption） Unbalanced component of radiation Back side A×（Back F-Face F） The red line and the blue line are the trends when both Face side （２Γ COS(θ ）＋２／３ D）×COS(θ ） specular reflection and diffuse reflection parameters are

（２Γ COS(θ ）＋２／３ D）×SIN(θ ） １－Γ －Ｔ＝Ａ＋Ｄ estimated at the same time. The purple line is the trend when Adsorption of diffusion Adsorption of absorption only reflection parameters estimated. The invisible period are 2/3 A（F2-F1)×SIN(θ ） Unbalanced component of radiation the earth angle became about 80 degrees or more. So in this ２Γ COS(θ ）＋２／３ D Specular reflection and diffuse reflection period, telemetry’s link became quite difficult. Fig. 3.3 shows the flight data of the spin rate and the sun Fig. 3.1 Conceptual diagram of solar radiation pressure model angle. Spin rates are roughly decelerating from 2010 to May of IKAROS 2011. Along with this deceleration, the red line and the blue

line change while having a correlation. This difference is The solar radiation pressure acceleration for a plane fairly large, if the estimation result is correct, it may be caused perpendicular to the spin axis Zs is given as follows; by state of wrinkles changed by decreases centrifugal force.

S R 2 S 1    2 2   r The purple line decreases very slowly, but this is thought to r  0 0  1   cos  2cos  D  A(F  F )cos2   srp c m r 2   s s 3 3 2 1 s  r be caused by a change in physical properties due to sunlight. s     

 2 2   r  r   2coss  D  AF2  F1 coss zs    Spin Rate(rpm)  3 3   r  r Flight data of Spin rate (rpm) and Sun Angle (deg)  Sun Angle(deg) 4.0 70 (2) Reverse Spin Operation

The definition of the solar radiation pressure model is shown 60 2.0 in Table 3.2. 50

0.0 ） 40

rpm （ -2.0 Table 3.2 IKAROS solar radiation presser model

30 Sun Angle(deg) Sun

Rate Spin 3 2 -4.0 S0: Solar constant (= 1.35 × 10 [W/m ]) 20 8 R0: 1A.U.(=1.4959787×10 [km]) -6.0 c: Speed of light 10 ms: S / C mass -8.0 0 S: 2010/5/21 2011/5/21 2012/5/20 2013/5/20 2014/5/20 2015/5/21 2016/5/20 Area of the plane Γ: Reflection coefficient Fig. 3.3 Flights data of spin rate and sun angle D: Diffusion coefficient T: Transmittance r: S / C position vector of the sun center 4. Orbit determination for extended phase zs: Unit vector in the inertial space of the S / C spin axis θs Solar orientation angle (cos θ s = (- r / r) ・ Z s) In extended operation, we mainly operated with low spin A Absorption rate A =1 - D - Γ - T: T = 0 rate. We conducted a number of experiments, such as F1 The emissivity ratio of the surface operation and guidance control where the attitude of the spin F2 Emissivity ratio on the back side axis was largely changed. In anticipation of depletion of fuel,

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reverse spin operation was carried out to stabilize the spin rate Declination (DEC), the scale in the Dec direction is enlarged without fuel. As a result, the spin rate gradually increased twice the RA direction. without fuel and the moment of inertia increased gradually, so the attitude changed from solar tracking to inertial fixation. In the end, IKAROS could not maintain the power and Error ellipse from Earth Center 3σ hibernated. 1st Hibernation Fiter 3σ 2nd Hibernation Fiter 3σ 3th Hibernation Fiter 3σ In this phase, the spin rate/rate in the trajectory 0.15 determination arc became large and spin modulation could not be removed with fixed parameters. In addition, the quality of tracking data worsened as the distance to the earth gradually 0

increased. The uncertainty of attitude by low spin rate has also Dec(deg) appeared. The accuracy of orbit determination worsened than the previous phase. Therefore we have constructed a system that simultaneously -0.15 performs attitude motion and orbit determination. We were -0.60 -0.45 -0.30 -0.15 0.00 0.15 0.30 0.45 0.60 Ra(deg) able to achieve highly accurate orbit determination.

Fig. 5.1 1st～3rd Error Ellipse from Earth Center 5. Orbit determination for Long-term prediction and search operation In addition, in the third search operation after hibernation, not only the conventional time offset search but also the offset IKAROS hibernated because the spin rate increased and the search in the RA DEC direction converting to the AZ EL inertial directivity increased. After that, the search operation offset using the instantaneous azimuth / latitude gradient by became necessary. the predicted value was also performed. The problem of this phase was the long-term orbit prediction, highly reliable trajectory determination and prediction of 5.4 Fourth search operation attitude motion model was necessary. The initial attitude The fourth search operation1) started searching on March 5, motion model was roughly classified into three models3). As a 2015 and spent a period of one and a half months until result, it was discovered using a model with strong inertial discovery. We have succeeded in searching by applying a new orientation. search method 4) such as post-processing analysis using 1-way data with open loop receiver. 5.1 First search operation In this search operation, since the distance between the In the first recapture1), the radiation pressure parameter 2) on satellite and the earth was close, three Doppler data could be the back side was also studied, and the orbital error was obtained with a normal Doppler receiver, but the range data propagated after considering the thermal radiation model from could not be acquired. the large film. In this operation, totally four Doppler data by off line FFT 5.5 Fifth search operation analysis from Open Loop receiver and AZ, EL data when it In the 5th search operation, a program was created so that a was successfully received signals were newly added for search in a wide range can be automatically carried out by observation data. adding an offset of the search area planned in advance to the antenna prediction value. It is possible to detect weak received 5.2 Second search operation data by FFT analyzing the received frequency data at offline. In the second search operation1), we had predicted that the The 5th search is very close in terms of distance but search area due to propagation 3 sigma errors were about 10 IKAROS's transmitting and receiving antennas are facing the times the half beam-width of Usuda, but it was able to be back side and could not be found. Perhaps it seems that radio found in the initial search operation. In this operation, 7 waves were weaker than assumed, or it was hibernating rather Doppler data created by post processing from Open Loop than being as expected. The search area is shown in Fig. 5.2. receiver and AZ EL data when it was receiving signals were It was searched that about 1.5 deg. x 0.5 deg. range. added as observation data. RA,DEC Offset Search Range For Auto Search CASE 160122d Ra Dec Offset(dec) 0.60 01-24 CASE7 5.3 Third search operation 0.50 01-24 CASE8 01-24 CASE9 1) 0.40 01-24 CASE10 In the third search operation , at the first search was 01-24 CASE11 01-24 CASE12 0.30 01-24 CASE7 RER 01-24 CASE RER BIAS conducted on April 22, 2014 and succeeded in the third search. 0.20 01-24 CASE13 01-24 CASE160122b 0.10 01-24 CASE13 RER We succeeded in searching using forecast values improved on 01-24 CASE13 BIAS 0.00 01-24 CASE160122c 01-24 CASE160122d the back and surface optical parameters by observation data Dec(dec) -0.10 01-24 CASE160122e 01-24 CASE160122f -0.20 01-24 CASE 160122g 01-24 CASE12 RA acquired in 2012 and 2013. -0.30 01-24 CASE160122h Search at 1/24 -0.40 Search at 1/25 Fig. 5.1 shows the transition of the assumed error ellipse 3σ Search at 1/26 -0.50 Search at 1/27 2/4- 2/5- of the search operation from the first search operation to the -0.60 Remark point -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 third. Although the axes are Right Accession (RA) and Ra(dec) Fig. 5.2 RA DEC Offset Search Area

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5.6 Sixth search operation we constructed the spin torque motion model at section 6. In the sixth search operation, the range data was created pseudo by using at the timing when the frequency sweep 0.8 u64.IKAROS.160122d_new_RA2_rev10 u64.IKAROS.160122d_new_RA2_rev11 ended. It was possible to create one point pseudo range data 0.6 u64.IKAROS.160122d_new_RA2_rev12 u64.IKAROS.160122d_new_RA2_rev13 u64.IKAROS.160122d_new_RA2_rev14 0.4 u64.IKAROS.160122d_new_RA2_rev15 for each period at 2013 and 2015. It was formulating spin u64.IKAROS.160122d_new_RA2_rev16 u64.IKAROS.160122d_new_RA2_rev17 u64.IKAROS.160122d_new_RA2_rev18 0.2 u64.IKAROS.160122d_new_RA2_rev19 modulation and statistically processing, we were able to u64.IKAROS.160122d_new_RA2_rev20 u64.IKAROS.160122d_new_RA2_rev21 u64.IKAROS.160122d_new_RA2_rev22 reduce the error of each data to 8000 km and 1000 km 0.0 u64.IKAROS.160122d_new_RA2_rev23 u64.IKAROS.160122d_new_RA2_rev24 u64.IKAROS.160122d_new_RA2_rev25 -0.2 u64.IKAROS.160122d_new_RA2_rev26 respectively. As a result of orbital determination while u64.IKAROS.160122d_new_RA2_rev27 u64.IKAROS.160122d_new_RA2_rev28 u64.IKAROS.160122d_new_RA2_rev29 assigning parameters using these data, the search area could -0.4 u64.IKAROS.160122d_new_RA2_rev30

DEC.(deg) u64.IKAROS.160122d_new_RA2_rev31 u64.IKAROS.160122d_new_RA2_rev32 -0.6 u64.IKAROS.160122d_new_RA2_rev33 be reduced as shown in Fig. 5.3. In January 2016, the search u64.IKAROS.160122d_new_RA2_rev34 u64.IKAROS.160122d_new_RA2_rev35 u64.IKAROS.160122d_new_RA2_rev36 area when sweep timing pseudo range data is used is indicated -0.8 u64.IKAROS.160122d_new_RA2_rev37 u64.IKAROS.160122d_new_RA2_rev38 u64.IKAROS.160122d_new_RA2_rev39 u64.IKAROS.160122d_new_RA2_rev40 by red solid line. The search area when sweep timing pseudo -1.0 11/2（UT） 11/3（UT） 11/4（UT） range data is not used is indicated by a pink dashed line. -1.2 11/6（UT） 11/7（UT） RA.(deg) 系列1 系列2 -1.4 系列3 Azimuth and elevation by predicted trajectory of each orbit determination 系列4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 系列5 result at 2016/1/24 01:00:23 (distance form Earth 70,000,000km) 16 - - Search range not using sweep range data Fig. 5.5 Search area by Yamaguchi Univ.’s 32m antenna 15.8 ━ Search range using sweep range data 15.6 Search range reduction efect by 6. Consideration of spin motion sweep timeing range data 15.4 3,5) u64.IKAROS.160122d_new_RA2_rev16 The model of the spin rate motion was formulated by 15.2 EL(deg) fitting the motion model to the rate of spin rate acquired from 15 01-24 CASE11 the flight data. However, this model was formulated as fixed u64.IKAROS_2016_CASE14 14.8 u64.IKAROS_2016_CASE18 for distortion angle ξ indicating the windmill effect and the u64.IKAROS_2016_CASE17 01-24 CASE12 14.6 deflection angle η as like as the shape of the umbrella. In this u64.IKAROS_2016_CASE19 paper, ξ and η are divided and formulated as in Eq. 6.1 so that 14.4 106 106.2 106.4 106.6 106.8 107 107.2 AZ(deg) it can be adapted to long-term spin motion. Fig. 5.3 Search area for IKAROS in 2016/1/24 Spin rate is from 0 to 1.2 rpm

2 In the sixth search, it can be considered that the transmitting ξ = ξ1(c + bΩ + aΩ ) / receiving antenna is facing the earth, so it is an assumption η = η1 that stronger radio waves can be received than the fifth search. (3) For this reason, it is possible to search an area wider than the Spin rate from 1.2 rpm to 2.7 rpm 5th search area. Fig. 5.4 shows the search area up to the present. ξ = ξ1、η = η1 (4) RA DEC offset search area by Orbit Determination results in 2016/11/03 20:00:30 Spin rate from 2.7 rpm to 7 rpm u64.IKAROS.160122d_new_RA2_rev10 0.6 u64.IKAROS.160122d_new_RA2_rev11 u64.IKAROS.160122d_new_RA2_rev12 u64.IKAROS.160122d_new_RA2_rev13 0.4 u64.IKAROS.160122d_new_RA2_rev14 2 u64.IKAROS.160122d_new_RA2_rev15 ξ = ξ 휉 /(푚 푚 Ω + (퐶 + 휉 )) u64.IKAROS.160122d_new_RA2_rev16 1 2 푠 푐 1 2 u64.IKAROS.160122d_new_RA2_rev17 0.2 2 u64.IKAROS.160122d_new_RA2_rev40 u64.IKAROS.160122d_new_RA2_rev18 η = η 휂 /(푚 푚 Ω + (퐶 + 휂 )) u64.IKAROS.160122d_new_RA2_rev19 1 2 푠 푐 2 2 u64.IKAROS.160122d_new_RA2_rev20 0.0 u64.IKAROS.160122d_new_RA2_rev39 u64.IKAROS.160122d_new_RA2_rev21 u64.IKAROS.160122d_new_RA2_rev22 (5) u64.IKAROS.160122d_new_RA2_rev23 u64.IKAROS.160122d_new_RA2_rev24 -0.2 u64.IKAROS.160122d_new_RA2_rev25 u64.IKAROS.160122d_new_RA2_rev26 u64.IKAROS.160122d_new_RA2_rev27 DEC(deg) -0.4 u64.IKAROS.160122d_new_RA2_rev28 Table 6.1 spin motion model u64.IKAROS.160122d_new_RA2_rev29 u64.IKAROS.160122d_new_RA2_rev30 -0.6 u64.IKAROS.160122d_new_RA2_rev31 u64.IKAROS.160122d_new_RA2_rev32 u64.IKAROS.160122d_new_RA2_rev33 Values name Values mean u64.IKAROS.160122d_new_RA2_rev34 -0.8 u64.IKAROS.160122d_new_RA2_rev35 u64.IKAROS.160122d_new_RA2_rev36 ξ Distortion angle indicating the windmill effect u64.IKAROS.160122d_new_RA2_rev37 -1.0 u64.IKAROS.160122d_new_RA2_rev38 u64.IKAROS.160122d_new_RA2_rev39 ξ Windmill effect coefficient 1 u64.IKAROS.160122d_new_RA2_rev40 1 11/7（UT）Search Area -1.2 11/3（UT）Search Area ξ2 Windmill effect coefficient 2 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 11/4（UT）Search Area RA(deg) η Deflection angle Fig. 5.4 Search area by Usuda deep space station for 3 days η Deflection angle coefficient 1 1 η2 Deflection angle coefficient 2 At the same time, the search operation was also carried out a Polynomial second order coefficient using Yamaguchi Univ.'s 32m antenna. Fig. 5.5 shows the b Polynomial first order coefficient search area by Ra. Dec. It was used when the Earth's distance c Polynomial zero order coefficient is relatively close. A line of each color is search area for a C1 Continuity securing coefficient for ξ day. C2 Continuity securing coefficient for ξ

I expect it to analyze offline, but it has not been discovered ms Sail membrane total weight as of Fabray 2017. It seems that the spin torque force is mc Sail membrane center radius reversed by the observed spin rate data in Fig. 3.3. Therefore,

5

Here ξ and η are divided into three sections and formulated up from hibernation changes. Therefore, the search time so that fitting can be made based on the flight data obtained changes greatly. The solar angle related to orbital propagation during the hibernation mode. almost same as the conventional model until 2015, but after Here, it differentiates into three sections of formula (5) 2016 the chaotic behavior becomes stronger. Therefore we where centrifugal force and wrinkle elastic force dominate, will be regularly operating the search operation once per a formula (4) treated as a constant value, and formula (3) fitted month. to actual data. The division of these equations made it possible to match the spin rate and the sun angle to the actual flight 7. Summary data as shown in Fig. 6.1 and 6.2. Especially assuming that the windmill effect of ξ is reversed at about -7 rpm because the Search operation of IKAROS due to hibernation has been spin rate is decelerating from the spin rate flight data in 2014 successful as a result of trial and error in the past 4 times. In and 2015. the fifth time, there was a possibility of receiving signal but we could not catch the signal from the IKAROS's antenna.

Spin rate new model Flight data spin rate IKAROS Ωz O-C(rpm) In the sixth search operation, automatic offset program Spin rate conventional model 8.0E+00 makes search area larger, offline FFT analysis made it

6.0E+00 possible to pick up weak signal. Pseudo-created range greatly

reduced search area. As these results, the search area is 4.0E+00 considered to be no problem. We are extending the attitude 2.0E+00 motion model. It is the spin motion model changes possible to 0.0E+00 rpm deal with all direction from handling the angle around the sun -2.0E+00 orientation. As a result, it is possible to predict a more precise -4.0E+00 period of wake up from hibernation. -6.0E+00 8. Conclusion -8.0E+00 2011 2012 2013 2014 2015 2016 2017 2018 2019 Fig. 6.1 Spin rate by observation data and motion model IKAROS's orbit determination requires technical elements that are not ordinary operation such as construction of attitude motion model and long - term prediction due to hibernation. IKAROS Sun angle O-C(deg) Sun angle new model Flight data sun angle Sun Angle conventional model These technical elements to be useful in next solar power sail 200 spacecraft. 180

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140 References

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100 1) ShoTaniguchi, Takafumi Ohnishi , Osamu Mori , Hideki Kato,

angle(deg) Hiroshi Takeuchi, Atsushi Tomiki, Yuya Mimasu, Naoko Ogawa, 80 sun Tsutomu Ichikawa, MakotoYoshikawa, and Shota Kikuchi, Orbit 60 determination of Interplanetary Kite-craft Accelerated By 40 Radiation of the Sun (IKAROS), The Fourth International symposium on Solar Sailing in Kyoto Japan(2016). 20 2) Sho Taniguchi, Takafumi Ohnishi, Yuya Mimasu, Yuji Shirasawa, 0 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Katsuhide Yonekura, Mori Osamu, Hiroshi Takeuchi, Tsutomu Ichikawa, and Makoto Yoshikawa, Orbit Determination and Fig. 6.2 Sun angle by observation data and motion model Evaluation of Prediction Error to Acquire IKAROS, 57th Space Science and Technology Conference. (2013). The structure constituting the windmill effect of the sail 3) Yuya Mimasu, Sho Taniguchi, Hiroshi Takeuchi, Yuji Shirasawa, Katsuhide Yonekura, Osamu Mori, Ryu Funase, Takano Saiki and membrane would had been eventually destroyed by the Yuichi Tsuda, LONG-TERM ATTITUDE AND ORBIT centrifugal force becoming larger as the spin rate increases. PREDICTIN OF SOLAR SAILING IKAROS WHILE BEING Perhaps, as a result of multiple breakdowns of it, we believe LOST IN SPACE, ASS 13-406 (23rd AAS/AIAA Spaceflight Mechanics Meeting, Kauai, Hawaii in 2013) that the windmill effect was reversed. 4) Shota Kikuchi, Hiroshi Takeuchi, Osamu Mori, Yuya Mimasu, Parameters surveys were performed with these formulated Yoji Shirasawa, Hideki Kato, Naoko Ogawa and Sho taniguchi, models and the parameters were estimated to minimum values. Progress of Search Operation for IKAROS by means of Open-loop At the same time, we simultaneously estimated the attitude Tracking Data, 30th International Symposium on Space and the orbit using observation data of Doppler, azimuth and Technology and Science, (2015). 5) Yuichi Tsuda, Takano Saiki, Yuya Mimasu, Ryu Funase, Modeling pseudo range from 2011 to 2015. of Attitude Dynamics for IKAROS Solar Sail Demonstrator, ASS The attitude motion shows chaotic dynamics when the spin 11-112 (The 21rd AAS/AIAA Spaceflight Mechanics Meeting, New rate through around 0 rpm. In the orbit determination, the Orleans, Louisiana, USA, Feb.13-17,2011) estimation of the tracking data has a greater influence on the search range than the change of attitude model. However, the attitude motion changes greatly like chaos, the period of wake

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