# Demonstration of deep-space synchronous two-way laser ranging with a laser transponder aboard Hayabusa2

Hirotomo Noda, Hiroki Senshu, Toshimichi Otsubo, Hiroshi Takeuchi, Clément Courde, Hiroo Kunimori, Christopher Moore, Ulrich Schreiber, Naoko Ogawa, Takanao Saiki, et al.

► To cite this version:

Hirotomo Noda, Hiroki Senshu, Toshimichi Otsubo, Hiroshi Takeuchi, Clément Courde, et al. Demonstration of deep-space synchronous two-way laser ranging with a laser transponder aboard Hayabusa2. Advances in Space Research, 2023, 71 (10), pp.4196-4209. 10.1016/j.asr.2022.12.057. hal-04394266

HAL Id: hal-04394266

https://hal.science/hal-04394266v1

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1 **Title: Demonstration of deep-space synchronous two-way laser ranging with a**

2 **laser transponder aboard Hayabusa2**

3 **Hirotomo Noda**

4 **hirotomo.noda@nao.ac.jp**

5 **National Astronomical Observatory of Japan, 2-12 Hoshigaoka, Mizusawa, Oshu, Iwate**

6 **023-0861, Japan**

7 **Hiroki Senshu**

8 **senshu@perc.it-chiba.ac.jp**

9 **Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 257-0016, Japan**

10 **Toshimichi Otsubo**

11 **t.otsubo@r.hit-u.ac.jp**

12 **Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan**

13 **Hiroshi Takeuchi**

14 **takeuchi@isas.jaxa.jp**

15 **Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,**

16 **Sagamihara, Kanagawa 252-0222, Japan**

17 **Clément Courde**

18 **courde@geoazur.unice.fr**
19 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

20 Route de l'Observatoire 06460 Caussols France

21 Hiroo Kunimori

22 kuni@nict.go.jp

23 National Institute of Information and Communications Technology, Koganei, Tokyo

24 184-0015, Japan

25 Christopher Moore

26 cmoore@eosspacesystems.com

27 EOS Space Systems, 18 Wormald Street, Symonston ACT, Australia

28 Ulrich Schreiber

29 ulrich.schreiber@tum.de

30 Technical University of Munich, Research Unit Satellite Geodesy - Geodetic

31 Observatory Wettzell - D-93444 Bad Koetzting, Germany

32 Naoko Ogawa

33 naoko.ogawa@isas.jaxa.jp

34 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,
35 Sagamihara, Kanagawa 252-0222, Japan

36 Takanao Saiki

37 saiki.takanao@jaxa.jp

38 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,

39 Sagamihara, Kanagawa 252-0222, Japan

40 Yuto Takei

41 takei.yuto@jaxa.jp

42 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,

43 Sagamihara, Kanagawa 252-0222, Japan

44 Mourad Aimar

45 mourad.aimar@oca.eu

46 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

47 Route de l'Observatoire 06460 Caussols France

48 Julien Chabé

49 chabe@oca.eu

50 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130
51 Route de l'Observatoire 06460 Caussols France

52 Johann Eckl

53 johann.eckl@bkg.bund.de

54 Technical University of Munich, Research Unit Satellite Geodesy - Geodetic

55 Observatory Wettzell - D-93444 Bad Koetzting, Germany

56 Shun'ichi Kamata

57 kamata@sci.hokudai.ac.jp

58 Hokkaido University, N10 W8, Kita-ku, Sapporo, Hokkaido, 060-0810 Japan

59 Arika Higuchi

60 higuchia@cc.kyoto-su.ac.jp

61 Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto

62 603-8555, Japan

63 Takayuki Hirai

64 hirai.takayuki@perc.it-chiba.ac.jp

65 Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 257-0016, Japan

66 Grégoire Martinot-Lagarde
67 gregoire.martinot-lagarde@oca.eu

68 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

69 Route de l'Observatoire 06460 Caussols France

70 Hervé Mariey

71 herve.mariey@oca.eu

72 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

73 Route de l'Observatoire 06460 Caussols France

74 Koji Matsumoto

75 koji.matsumoto@nao.ac.jp

76 National Astronomical Observatory of Japan, 2-12 Hoshigaoka Mizusawa, Oshu, Iwate

77 023-0861, Japan

78 Nicolas Maurice

79 nicolas.maurice@geoazur.unice.fr

80 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

81 Route de l'Observatoire 06460 Caussols France

82 Jun'ichi Nakazono
83 naka.j@nict.go.jp

84 National Institute of Information and Communications Technology, Koganei, Tokyo

85 184-0015, Japan

86 Duy-Hà Phung

87 duy-ha.phung@geoazur.unice.fr

88 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

89 Route de l'Observatoire 06460 Caussols France

90 Julien Scariot

91 scariot@geoazur.unice.fr

92 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

93 Route de l'Observatoire 06460 Caussols France

94 Ryo Suetsugu

95 suetsugu@oshima-k.ac.jp

96 National Institute of Technology Oshima College, 1091-1 Komatsu, Suo-Oshima,

97 Oshima Yamaguchi, 742-2193, Japan

98 Jean-Marie Torre
99 torre@oca.eu

100 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

101 Route de l'Observatoire 06460 Caussols France

102 Alex Pollard

103 apollard@eosspacesystems.com

104 EOS Space Systems, 18 Wormald Street, Symonston ACT, Australia

105 Hervé Viot

106 Herve.Viot@geoazur.unice.fr

107 Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur, 2130

108 Route de l'Observatoire 06460 Caussols France

109 Noriyuki Namiki

110 nori.namiki@nao.ac.jp

111 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588,

112 Japan

113 Takahide Mizuno

114 mizuno.takahide@jaxa.jp
115 Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,

116 Sagamihara, Kanagawa 252-0222, Japan

117

118

119 **Abstract**

120 In December 2020, synchronous two-way laser ranging in deep space was successful for

121 the first time over distances up to 6.46 million km. A laser altimeter aboard spacecraft

122 Hayabusa2 was used as an optical transponder, detecting laser pulses emitted from the

123 ground stations on Earth and retransmitting the pulses from the spacecraft to the ground.

124 These retransmitted pulses were successfully detected at the ground station. The

125 experiment was conducted as a demonstration of the deep-space laser ranging. The

126 repetition frequency of the onboard instrument was limited to 0.5 Hz, and there was a

127 lot of background noise because the experiments were carried out in daytime on the

128 ground. Nevertheless, laser detection on the ground was still possible due to the high

129 time-correlation between the detected and the predicted in the presence of random noise.

130 Procedures similar to satellite laser ranging were applied to create residuals by
131 subtracting the orbit predictions of the spacecraft from the observed round-trip time.

132 Furthermore, some of the transponder return pulses were uniquely identified, where the

133 time coherence of the measurements had been recovered from the telemetry data of the

134 laser altimeter.

135 **Keywords**

136 Hayabusa2, laser altimeter, laser ranging, optical transponder,

137

138 **Main Text**

139 **1. Introduction**

140 In order to determine the position of a spacecraft in an orbit around the Earth, Moon

141 and planets or interplanetary space cruise, it is common to transmit microwaves from

142 the ground and return them back with the help of a transponder aboard the spacecraft.

143 On the other hand, optical satellite laser ranging is the most accurate technique for the

144 measurement of distance from a ground station to a spacecraft, because the delay due to

145 the ionosphere and interplanetary plasma can be ignored, and the tropospheric delay can

146 be corrected accurately. In the case of Earth orbiting satellites, the only instrument the
147 spacecraft requires a laser retro-reflector package, which does not use electronics, so

148 the instrument is simple, lightweight, and has a long life. Repeated laser ranging to

149 dedicated satellites are routinely used to investigate temporal changes in the Earth's

150 gravity field (e.g. Cox and Chao 2002). Laser ranging to retro-reflector arrays on the

151 Moon is useful for the lunar science (e.g. Dickey et al. 1994; Williams et al. 2001), the

152 lunar reference frames (e.g. Williams et al., 2013) and the verification of the general

153 theory of relativity.

154 During two-way laser ranging to a retro-reflector, the intensity of the received laser

155 pulses on the ground is inversely proportional to the fourth power of the distance, so it

156 becomes unrealistic to measure distances beyond the Moon. To perform laser ranging in

157 deep space, it is necessary to use optical transponders similar to the radio wave ranging.

158 In this case, since the laser link only depends on one-way transmissions, the laser

159 intensity decreases inversely proportional to the square of the distance, so that much

160 larger distance can be covered. This comes at the expense of losing the simple and

161 fail-safe instrumentation on the space segment. The laser ranging has another

162 advantage: unlike radio signals that have a significantly larger lateral signal spread,
163 optical ranging has a very narrow signal cone, therefore much better constrained

164 spacecraft positions in the tangential directions can be obtained. A disadvantage is that

165 the laser ranging is impossible when it is cloudy on the ground. In case of the optical

166 transponder, uncertainties in on-board delay are major cause of range error unless it is

167 precisely measured on board.

168 In this paper we call “synchronous”, when the spacecraft segment receives the laser

169 light from the ground and it emits laser light back with a known time delay. On the

170 other hand, “asynchronous” means that the space and ground segments shot laser pulses

171 and receive them independently. In this case, the range measurement is successful only

172 if both transmitted and received laser pulses are time-tagged with the same time base.

173 There have been some successful demonstrations of establishing a deep space laser

174 link using laser altimeters mounted on a spacecraft, including:

175 - one-way laser link to the Mars Global Surveyor of 81 million km (Abshire et al.

176 2006);

177 - a 24 million km two-way ranging to the Mercury explorer MESSENGER (Smith et

178 al. 2006);
179 - a 6 million km one-way laser link to Hayabusa2 asteroid explorer (Noda et al.

180 2017).

181 The Japanese asteroid explorer Hayabusa2 was launched on December 3, 2014. Key
events of the spacecraft are summarized in Table 1. It made a gravity assist operation by
182 the Earth and accelerated toward the asteroid in December 2015. Before and after this
183 maneuver, a laser link experiment was conducted between the ground and the spacecraft
184 (Noda et al. 2017) but the attempt at synchronous two-way ranging was not successful.

185 It arrived at the asteroid (162173) Ryugu in June 2018 and explored the asteroid until
186 November 14, 2019 (e.g., Watanabe et al. 2019). Two touchdowns were performed to
187 obtain surface material samples, which were stored in a capsule. On December 6, 2020,
188 the capsule landed in the Woomera Desert in Australia, completing the main mission
189 objective of returning the asteroid samples to Earth. The spacecraft itself continued its
190 cruise to explore another asteroid after another gravity assist maneuver by the Earth on
191 the same day (Hirabayashi et al. 2021). Then, another opportunity to repeat the
192 synchronous two-way laser link experiment arose to explore laser ranging using optical
193 transponders. When the ranging is successful, the issues of laser ranging using optical
194
195 transponders are to be identified, which is also one of the purposes of this experiment.

196

197 **2. Experimental setup**

198 **2.1 Geometry of the Earth, Sun, spacecraft, experiment date and time, link budget**

199 The solar panels of the Hayabusa2 were fixed to the spacecraft +Z plane. Since the
200 laser altimeter LIDAR (LIght Detection and Ranging) aboard the Hayabusa2 spacecraft
201 was installed on the -Z plane, the experiments were possible only when the
202 Sun-Probe-Earth angle was greater than 120 degrees, i.e. the -Z plane was oriented
203 towards the Earth with enough light on the solar panels. This condition confined the
204 experiment to the period after the capsule reentry on December 6, 2020. The shorter the
distance to the spacecraft, the better the chance of success. Hence the experiment
205 commenced on the day after the capsule reentry, December 7, 2020. The experimental
206 period continued until December 23, 2020 when the spacecraft was approximately 6.6
207 million km away from the Earth. This was about the farthest distance in the 2015
208 experiment, when a one-way link was demonstrated.

210 Due to the small angular separation of the Sun and the spacecraft at about 30 degrees,
211 experiments were conducted during the evenings in Japan and Australia and in the

212 mornings in Europe. Therefore, the noise from background light was higher than during

213 the 2015 campaign.

214 To minimize the impact of possible poor weather conditions a number of ground laser

215 stations in different locations were selected. From the stations in Asia, Oceania and

216 Europe that were equipped with 1064 nm laser systems, four stations were selected,

217 namely, Koganei in Japan (referenced as KOGC 7308 in the International Laser

218 Ranging Service), Mt. Stromlo in Australia (STL3 7825), Grasse in France (GRSM

219 7845), and Wettzell in Germany (WETL 8834). Key parameters of these ground

220 stations are shown in Table 2 and corresponding estimated link budgets are shown in

221 Fig. 1. Considering the potential dust contamination to the spacecraft's laser emitting

222 and light receiving telescopes at the time of the two asteroid touchdowns in 2019, the

223 value of the telescope transmission is modelled to be decreased by about 13% from the

224 value prior to the first touchdown.

225

226 **2.2 Definition of observation sessions**
227 The duration of each experiment was about 3 hours (for Japan and Australia) and
228 about 1 - 2 hours (for Europe). During the sessions a microwave link was established
229 between the spacecraft and ground. Since the separation angle between Japanese and the
230 Australian stations as seen from the spacecraft is larger than the LIDAR laser beam
231 divergence, we had to choose one of these stations so that the spacecraft was pointed to
232 the right direction. For the European stations the angular distance was smaller than the
233 LIDAR laser beam divergence and the attitude of the spacecraft could be predetermined.

234 In order to raise the chances of success, the experiment period for Japan and Australia
235 was divided into two and the ground station for each time period was selected based on
236 the weather forecast. Commands for the attitude change of the spacecraft were prepared
237 for each ground station one day before the session, based on the latest spacecraft orbit
238 prediction. One hour before the experiment, the respective ground station was finally
239 selected and corresponding commands were uploaded to the spacecraft. The observation
240 sequence could neither be changed nor cancelled once it has been uploaded. The main
241 reason for canceling a session in advance, was because of predictions of expected poor
242 weather.
243 Noda et al (2017) revealed that the difference between the spacecraft-Z and the boresight direction of the LIDAR is 3.65 mrad. Furthermore, better estimation of the LIDAR boresight was carried out in Noda et al (2021), by comparing the camera images and LIDAR time-series topographic profiles. To confirm the better-estimated boresight direction, and also to find the optimum pointing direction, in the first week of December 7-11, the laser beam pointing was scanned spirally by changing the spacecraft attitude with 0.5 mrad step in the first half of each session. Then, the optimum direction was used for the second half of the next day, since commands to change the attitude of the spacecraft were to be created one day before. During the period of December 14-23, the scanning sessions were carried out only in the experiments for Japan or Australia due to longer operational times, but at that time the optimum direction was almost known, so the experiments were not dependent on that scanning.

255

256 **2.3 LIDAR operational mode and its telemetry data**

257 LIDAR is an instrument that can be used to measure the distance from a spacecraft to a celestial body (Mizuno et al. 2017). It is equipped with a 17-bit time interval counter

258
259 of 300 MHz to measure the ranges with 0.5 m range resolution. The specifications of
260 the LIDAR are shown in Table 3. In addition to the “range measurement mode”, the
261 LIDAR has two more operational modes: "laser link mode", in which the LIDAR is
262 used as optical transponder, and "dust counting mode" for dust detection. This time, the
263 laser link mode is used for all the experiments. In this mode, two laser pulses from the
264 ground can be received within one second after “WAIT-START” command is issued
265 (Fig. 2). If the first light detection is successful, the detection flag for the first pulse is
266 set to "ON", and the laser is triggered. The time interval between the first pulse
detection and the laser trigger (defined as “STOP1 TIMING”) and that between the
267 laser trigger and the laser emission (defined as “START TIMING”) are measured by the
268 time interval counter. If second laser pulse is detected, the second pulse detection flag
269 becomes “ON”, and the time between those two pulses is also measured by the counter
270 (defined as “STOP2 TIMING”), which is used for the calibration of the counter. Since
271 one cycle of the LIDAR counter is about 437 microseconds (~ 2^17 / 300 MHz), there
272 is a cycle ambiguity and the remainder of the pulse interval (for example, 0.1 seconds)
273 divided by 437 microseconds is only recorded as STOP2 TIMING. These items will be
274
275 acquired as telemetry data by the command issued one second later. As a result, the

276 detection frequency of the laser pulses is less than 0.5 Hz.

277 The time between the first laser detection and the laser emission is the internal time

278 delay of the LIDAR in the laser link mode. This is expressed as the sum of two

279 telemetry data items on the downlink from the spacecraft, namely, STOP1 + START.

280 Since the LIDAR emits a laser pulse using a passive Q switch based on a saturable

281 absorber, the time between the laser diode excitation and the laser emission (START)

282 varies depending on the temperature. On the other hand, the temperature range of the

283 laser diode is controlled with a thermostat, with a resultant cycle of about 400 seconds.

284 As a result, as is shown later, the internal delay time changes accordingly by about 4

285 microseconds with the same cycle. Since the variation of the internal delay is known

286 retrospectively from a telemetry data item, this experiment is not an entirely closed

287 system of synchronous transponder, but might be treated as a quasi-synchronous

288 system.

289

290 **2.4 Ground-based laser stations**
291 1064-nm laser pulses are emitted at 10 Hz (Koganei and Grasse) or 170 to 180 Hz

292 (Mt. Stromlo) in the spacecraft direction, based on the predicted orbit information. The

293 detection system for each station uses an avalanching photo diode (APD) in Geiger mode

294 for photon counting. The smallest width of the band pass filter is 0.12 nm for Grasse

295 (Table 2), which is wide enough for the expected Doppler shift of 0.015 nm of the

296 return laser pulses to pass. The range gate of the ground station receiver varies for each

297 station due to the amount of background light, but they are narrower than the variation

298 of the LIDAR's internal delay of 4 microseconds. Since the cycling time of the

299 Q-switch thermal control and hence the internal time delay was not predictable and

300 could not be compensated in the range gate setting ahead of time, some of the downlink

301 pulses would fall outside the range gate. Therefore, the center of the range gate was set

302 to cover the minimum value of internal delay, so that the potential delay values fall into

303 the open gate for as long as possible. For example, the gate width of the Grasse station

304 is 1.6 microseconds, and the fraction of time at which laser pulses from the LIDAR can

305 be detected on the ground is about 2/5 of the total time-range introduced by the Q

306 switch. In addition, the repetition rate of the transmission pulse was gradually shifted so
307 that there was no overlap between the outgoing and incoming laser beam, when the

308 distance between station and spacecraft divided by the speed of light is an exact

309 multiple of the time interval of the outgoing laser pulses. This is because a single

310 telescope is used for both laser emission and reception. The Grasse station carried out

311 this so-called "collision avoidance" all the time, and the Koganei and Mt. Stromlo

312 stations applied this only for short periods of time. Since the experiment was conducted

313 in the daytime, a neutral density (ND) filter (Optical Density = 0.6, 0.7, 0.8 or 1.04) was

314 added to reduce the effect of background noise caused by the sun. However, this has the

315 detrimental effect that the detected laser signal from the LIDAR was also attenuated.

316 In the first half of the second session, the pointing direction of the ground-based

317 telescope was changed and a search carried out for the direction in which the light

318 detection intensity on the spacecraft increased. However, it was difficult to determine

319 the optimum direction in real time, because of delayed onboard response time due to

320 one-way transfer time, infrequent telemetry data updates, and significant temporal

321 changes in the detection intensity caused by atmospheric fluctuations.

322
323 **2.5 Tracking stations**

324 Telemetry, command and tracking operations were performed by establishing a

325 microwave link with the spacecraft at JAXA's Usuda station during Japanese and

326 Australian sessions, and at NASA-JPL / DSN Madrid station during European

327 operations. At both the Usuda and Madrid stations, microwave range measurements

328 were performed for 10 minutes before and after the laser link experiment, respectively.

329 The purpose was to improve the accuracy of the gate setting of the ground stations by

330 refining the estimated position of the spacecraft. The assumed accuracy of the radio

331 wave ranging was a few meters when no orbit or attitude maneuvers were operated.

332 After the experiment, the radio wave ranging data were also used for the validation of

333 the laser ranging results.

334

335 **3. Results**

336 Table 4 shows a summary of the ground stations assigned to each session. Due to

337 continuing bad weather and some delays in the equipment preparation at the Wettzell

338 station, only the Grasse station was operated as the European station. At the southern
339 hemisphere Mt. Stromlo station, many Earth orbiting satellites were close to the
340 Hayabusa2 spacecraft in the field of view of the telescope, so the laser was frequently
341 stopped due to proximity safety interlocks. In addition, some parts of the telescope were
342 exposed to stray off-axis sunlight and was damaged, so Mt. Stromlo was operational
343 only for the first week. Nonetheless, observations were established every day of the
344 total 11 days, and only 3 sessions (the 3rd sessions on Dec. 8, Dec. 11 and the 2nd
345 session on Dec. 14) were cancelled due to bad weather. The laser uplink from the
346 ground to the spacecraft was established at the Koganei, Mt. Stromlo, and Grasse
347 stations, and the optimum spacecraft attitude was determined by spacecraft attitude
348 scans during first-half session in the first and second week, therefore the spacecraft
349 attitude was fixed in the third week. The downlink from the spacecraft to the ground
350 was successful over three days as described below. Because the ranging hardware,
351 including laser repetition rates, at each of the stations is different, the observations were
352 treated in different ways for each station, as described in the following sections.
353
354 **3.1 Initial quick analysis**
355 First, the computed (C) predicted round-trip time were subtracted from the observed

356 (O) value and displayed as a time series. The value of the LIDAR internal delay was

357 converted from the STOP1+START telemetry, using a roughly estimated LIDAR

358 counter count length (3.33566 ns / count). Fig. 3 shows an example of the Grasse station

359 on December 9. The upper panel is the (O-C) value calculated from the raw data from

360 the ground station, the middle is the time series of the LIDAR internal delay, and the

361 lower part is the (O-C) value with the internal delay correction. The width in the Y

362 direction of the upper graph corresponds to the gate width set by the ground station (in

363 this case, 1.6 microseconds). Both noise and signal are included in this figure. Return

364 signals are indistinguishable here because of the onboard delay. In the lower panel, the

365 concentration of data points is seen around -0.5 microseconds on the vertical axis, and

366 these are the return signal candidates from the LIDAR. Most of the time intervals

367 between them are 2 seconds, 3 seconds, or multiples of them. This is a proof of

368 detection, because these values are multiples of the WAIT-START command interval of

369 the LIDAR, thus satisfying a time coherence condition. Koganei and Mt. Stromlo could

370 not detect signals by this method.
372 **3.2 Determination of one-count length of the LIDAR counter**

373 The exact one-count time or the frequency of the time interval counter due to the

374 ambient temperature, had to be determined from the data. For this purpose, LIDAR

375 telemetry data from the Koganei uplink was analyzed, because i) data was obtained

376 from the beginning to the end of the experimental period and ii) the collision avoidance

377 algorithm was not activated for most of the time. Since the interval between the laser

378 pulses from the ground is synchronized with the accurate time reference on the ground,

379 the length of the counter was determined by comparing the STOP2 TIMING telemetry,

380 received by the LIDAR, with the corresponding interval between the two pulses on the

381 ground. This calculation is regarded as a frequency transfer of the ground time to the

382 laser transponder (Noda et al, 2017). However, because the spacecraft clock is not

383 synchronized with that of the LIDAR and UTC time is not transferrable to the

384 spacecraft, it is not a complete time transfer. Fig. 4 shows the LIDAR STOP2 TIMING

385 telemetry of December 9. The order for each session was Mt. Stromlo first, Koganei,

386 and then Grasse. In the first half, when the collision avoidance algorithm was not
387 activated in Mt. Stromlo and Koganei, they were aligned almost in the horizontal

388 direction. Since the Koganei station fired at a rate of 10Hz, we define "skip" up to 9 to

389 express the time interval between two shots, such as skip = 0 when two consecutive

390 shots on the ground were detected by the LIDAR, skip = 1 when skipping one, and so

391 on. For Koganei, the predicted STOP2 values for the skip numbers are presented as

392 dashed lines in Fig. 4. On the contrary, in Grasse, the pulse interval was gradually

393 increased with time due to the collision avoidance. In the graph, there are main positive

394 slope lines for skip =0 and some branches for skip = 1 or higher numbers. If the

395 pointing of the spacecraft and the ground-based telescope were accurate and the

396 diffusion of the laser beam due to atmospheric fluctuations was small, there is a high

397 possibility that the second pulse would have been received by the LIDAR as a skip

398 number of 0 and in fact, the occurrence of skip = 0 appears most frequently in the

399 Koganei data. Since the repetition frequency of Mt. Stromlo is 170 Hz, the predicted

400 STOP2 values for the skip numbers are different from those of Koganei. Considering

401 that the spacecraft moves significantly between successive two pulses, the length of one

402 count τ for each skip number can be calculated using the following equation
$$403 \qquad \tau = \left(1 + \frac{v}{c}\right) \left( \frac{(skip + 1)\Delta t}{2^{17}N(skip) + n_{stop2}(skip)} \right) \quad (1),$$

where v is the spacecraft line-of-sight velocity relative to the ground station, c is the

speed of light, N (skip) the cycle ambiguity of the counter as a function of the skip

value, Δt is the fundamental shot interval of the ground station and n_stop2 (skip) the

STOP2 telemetry value for skip. We used the predicted spacecraft orbit. Actually, the

value of Δt differs for each shot, but since the variation in the shot interval of Koganei

is about ± 30 ns (full width at half maximum), we fix it at Δt = 0.1 seconds and looked

for the central value of the deviation. Note that the equation (1) is applicable to each

shot, and unless the ambient temperature changes significantly, the value τ is expected

to remain the same. In this case, the change of the spacecraft velocity, if any, will be

compensated by n_stop2(skip) so that τ will be kept constant. Throughout the

experimental period, the central value of τ is almost unchanged, so we derived one

value. The histogram of the value τ obtained by the formula (1) up to skip = 5 is shown

in Fig. 5. We obtained the mean value as 3.33566385 ns (equivalent frequency of

299,790,400 Hz; 2.058 kHz shift from the nominal value of 299,792,458 Hz). In the

subsequent analysis, this value is used for the internal delay calculation of the LIDAR
419 instrument.

420

421 **3.3 Identification of shots from the ground among LIDAR data for Grasse**

422 It was noted that the temporal variation of the pulse interval of Grasse was three

423 orders of magnitude larger than that of Koganei. This variation was relative to the

424 STOP2 telemetry data values of the LIDAR, so identification of the 10 Hz ground shots

425 that were detected by LIDAR was possible. Hence all other data points could be

426 regarded as noise. Since the LIDAR detects laser pulses once in every two or three

427 seconds, the number of noise points can be reduced to 1/20 or less. Fig. 6 shows an

428 example of 20 seconds of data between 11 h 23 m 20 s (= 41000 second of day) and 11

429 h 23 m 40 s on December 9. The horizontal axis corresponds to UTC time of the laser

430 transmission on the ground in second of day units. The onboard time of the LIDAR

431 telemetry data, which is time-stamped to UTC within 31.25 ms resolution of the

432 onboard spacecraft clock with downlinked time-calibration data, was converted to the

433 shot time on the ground by subtracting the one-way propagation time. The vertical axis

434 displays the LIDAR STOP2 data marked as crosses and the STOP2 prediction,
435 calculated from the two pulse intervals on the ground. Green points are the prediction
436 for which the ranges were recorded at the ground station, and purple are the ones for
437 which the ranges were not obtained. Even if "the ranges were recorded at the ground"
438 for green points, most of them are noises caused by the background light. At 41006
439 seconds, the two-pulse interval predictions (green and purple) change by about 5000
440 counts stepwise, which is due to the collision avoidance algorithm. This is an enlarged
441 view of the positive slope that appeared at 11h 23m in Fig.4. Since skip = 1 and 2 are
442 out of the graph, only skip = 0 data, i.e., data with shot intervals of 0.1 s are plotted. The
443 eight points where the points of LIDAR (crosses) and the ground shots (filled green or
444 purple circles) almost overlap are the ground shots received by the LIDAR. Each of the
445 LIDAR STOP2 (crosses) is located on the left side of the shot from the ground, because
446 the time of LIDAR measurements is shown as the WAIT-START time. Seven out of
447 eight LIDAR data points (crosses) are close to the predicted intervals from the ground
448 shots shown as green points, and they are considered to be signal. This figure also
449 confirms that the time length of one count of the LIDAR counter, as discussed above, is
450 an appropriate value, because otherwise the predicted STOP2 values, calculated from
451 the two pulse intervals on the ground and those of the LIDAR data, do not match.

452

453 **3.4 Confirmation of shots detected on the ground based on valid shots identified by**

454 **LIDAR system only**

455 Here we check if the round-trip times of the ground detections by the LIDAR, as

456 identified above, are signal or noise. Fig. 7 shows an example of December 9 data. The

457 upper part shows the LIDAR delay and the lower part shows O-C values with the

458 LIDAR delay correction being applied. The interpolated O-C values of the radio wave

459 ranging before and after the experiment are shown as a green dashed line. Atmospheric

460 and ionospheric delays are not considered in this figure. The format of these graphs is

461 the same as the center and lower panel of Fig. 3, but the amount of data points is

462 reduced to about 1/20 due to the selection procedure discussed in the previous section.

463 The data points showing the same trend as the radio wave ranging data are considered to

464 be valid signals. Data whose O-C falls from -0.52 to -0.48 microseconds (0.04

465 microseconds width) are regarded as signals and marked in red with a regression line

466 overlaid. The same data are also plotted in the upper panel as red points, which appear
467 almost at the same positions in the vertical direction. This means that these data points

468 are located within the range gate of the ground-based detector. Data from December 21

469 was also processed in the same way, because the signals were already found in the

470 initial rapid analysis and the result is shown in Fig. 8. Since the O-C values in the lower

471 panel show a temporal variation, a wider range between y = +0.25 and +0.35

472 microseconds (0.10 microseconds width) were regarded as signals and the respective

473 data points are marked in red. The result of December 22 is shown in Fig. 9. Data from

474 y = -0.72 to -0.66 microseconds (0.06 microseconds width) have been identified as

475 signals and these are marked in red too, but some of them have to be considered as

476 outliers, because they are outside of the range gate near 89 microseconds in the LIDAR

477 delay diagram in the top panel. Because the orbit predictions are updated every 1-2 days,

478 the O-C values differ for each day, which reflects the quality of the orbit prediction.

479

480 **3.5 Range data**

481 An orbit determination software called DMOODS (Takeuchi et al. 2020) developed

482 by JAXA was used to estimate the precise position of the spacecraft for the periods
483 when 2-way laser ranging was established on December 9, 21, and 22. Parameters, such
484 as the initial state vector, the range bias, the solar radiation pressure coefficient, and the
485 delta-v events were estimated by the least square method, so that the root mean square
486 of the O-Cs of all observations of range, Doppler, Delta Differential One-way Range
487 (DDOR), and laser ranges is minimized. Then, based on each estimated parameter, an
488 updated orbit is generated. These schemes are iterated until the root mean square of all
489 observed O-Cs hardly changes. The Vienna Mapping Function 3 (Landskron & Böhm
490 2018) and the Vienna Mapping Functions for optical frequencies (Boisits et al. 2020)
491 are used for the radio and optical tropospheric delay calculation, respectively. Fig. 10
492 and 11 show the residual of the distance between the ground station and the spacecraft.
493 Marks denoted as “DSS” and “USUDA” are the residuals of the radio ranging data from
494 the DSN Madrid and JAXA Usuda stations, and the ones written as “GRASSE_SLR”
495 are presenting the laser link data. The average residual of the laser ranging data is about
496 10 m in two-way range; they are 12.3 ± 1.9 m, 10.4 ± 1.9 m, 10.6 ± 6.0 m for December
497 9, 21 and 22, respectively. Considering that the resolution of the LIDAR is 0.5 m in
498 range, the deviations for December 9 and 21 are considerably small. There is a large
499 variation in the data on December 22, parts of which might be due to noise. Fig. 12 is
500 the enlarged figure of laser ranging data only for each day. The upward linear trend and
501 parabolic trend in the residual is seen for Dec. 9 and 21, respectively, and the deviations
502 of each data group are relatively small compared to the offset value of 10 m. For Dec.
503 22 data, the trend seems flat, but note that the vertical scale is wider than those of other
504 two days. These trends might be related to the difference of two regression curves of
505 lasers and radio waves in Figs. 7, 8 and 9.

506

507 **3.6 Received laser intensity on the spacecraft**

508 A special telemetry packet format called “NAVSENS” (which stands for navigation
509 sensors) was acquired in the first-half of the second session and a part of the first-half
510 session, which is used to obtain the laser detection intensity with the LIDAR. Fig. 13
511 shows a histogram of the received intensities of the ground shots that were identified as
512 the ones from the Grasse station. The maximum value of the laser intensity as
513 instrumental output is 1515.4 millivolts, which is equivalent to 3 x 10^(-6) W, by using
514 the APD’s responsivity of 500 kV/W. On December 22, about 30% (= 167/546) of the
515 whole laser intensity readings reached the saturated value, but on December 9, no

516 saturated data was obtained. This means that the detected laser intensity by the LIDAR

517 at the farther distance (6.4 million km) on December 22 was higher than for the case at

518 1.45 million km distance on December 9. The intensity data from Koganei also varied

519 daily and no clear relationship between the intensity and the spacecraft distance was

520 seen. It was concluded that the laser intensity significantly depends on the pointing of

521 the spacecraft, the orientation of the ground-based telescope, as well as the atmospheric

522 scintillation. Therefore it is expected that the uplink from the ground to the LIDAR

523 could have reached much farther than the distance on December 22.

524

525 **4. Discussion**

526 **4.1 Achievements and issues extracted**

527 In this experiment, the following are achieved:

528 -It is the first two-way synchronous laser ranging at a 6-million km distance. In

529 contrast, the other experiments like MESSENGER were conducted as an asynchronous

530 transponder, in which space-based and Earth-based laser terminals independently fired
531 pulses.

532 -In terms of the ground station operation, it was a big step to make observations

533 successful during daylight and near the Sun, because daytime operation can create more

534 data than the case in the night-time operation only.

535 One of the purposes of this experiment was the identification of issues of the laser

536 ranging using optical transponders. The main function of Hayabusa2 LIDAR was the

537 optical ranging from the spacecraft in orbit to the celestial body; the transponder

538 function was an add-on opportunity for demonstration purposes. Therefore, it did not

539 perform as a dedicated instrument for optical transponder applications. Specifically, the

540 internal delay of the LIDAR varied periodically by about 4 microseconds, which

541 produced a significant complication. This range was much wider than the gate width of

542 the ground laser ranging stations. Although values of the internal delay were obtained

543 by telemetry data, they were acquired more than 30 seconds later, therefore real-time

544 adjustment of the gate width during the measurement sequence was difficult.

545 To optimize a future transponder design to increase data rate and data quality, the

546 following points should be considered:
547 - The repetition rate of the onboard instrument should be higher: The fastest repetition

548 rate of Hayabusa2 LIDAR is one second, and when combined with the command to

549 fetch data, the LIDAR can only detect laser pulses once in every two seconds. It is

550 desirable to raise the onboard repetition rate to the same level as the laser fire rate of the

551 ground stations.

552 - Suppression of the onboard jitter to values much smaller than the ground station range

553 gate width. Since a passive Q-switch with a saturated absorber is incorporated for laser

554 emission, the time from the laser diode excitation to laser emission is random and

555 unpredictable. Therefore, the application of an active Q-switch, which can fix the

556 excitation time will be better.

557 - The LIDAR clock is used for the estimation of the internal delay. In general, crystal

558 oscillators are used for the onboard clock and the rate of the clock must be estimated

559 with an independent method. Two-pulse intervals from the ground laser station were

560 used in this experiment. The use of the onboard clock, which is synchronized with the

561 uplink radio wave based on a hydrogen maser on the ground for the laser transponder

562 can improve this process.
563 - Onboard techniques to allow better identification of ground shots. In this experiment,

564 up to two shots from the ground could be received in one second, and the pulse intervals

565 could be determined from telemetry data. As shown above, there were significant

566 differences in the interval between two pulses at the ground station which assisted in the

567 identification of the lasers from the ground.

568 Finally, in terms of the ranging, the average value of the difference from the radio

569 wave range was in the order of 10 m for two-way (5 m in distance) as shown in Fig. 12.

570 Both optical and radio wave measurement error must be responsible for the difference,

571 but we do not have good reasons for the difference so far. The typical deviation of the

572 delay of the X-band transponder of a recent JAXA's deep-space spacecraft is order of 2

573 m as range (Toda et al., 2004). The main error in the optical ranging might be due to the

574 optical transponder, but the internal delay of the LIDAR is obtained from the telemetry

575 data, and it has been corrected properly. After the experiment, we measured the delay of

576 the LIDAR engineering model in the laboratory and confirmed that the average

577 difference between the telemetry data and the measured value is about 2 m in two-way

578 (6.0 ns) with a smaller deviation. There might be many uncertainties in this
579 experimental ranging setup that it is easy to obtain differences at the 10 m level, but in

580 other words, 10 m difference with deviation of a few meters over 6 million km distance

581 is already a considerable achievement with the limited setup of the experiment.

582

583

584 **5. Conclusion**

585 Using the Hayabusa2 laser altimeter as an optical transponder, it was demonstrated

586 that synchronous two-way laser ranging is possible. Infrared laser pulses of 1064 nm

587 wavelength emitted from a ground-based laser station are received and retransmitted

588 back by the spacecraft and received on the ground. The experiment was conducted as a

589 demonstration using a planetary laser altimeter, and issues for future deep space laser

590 ranging were extracted. The following points should be met in the future missions:

591 - the temporal variation of the internal delay of the optical transponder on the

592 spacecraft should be smaller than the gate width (order of a few microseconds) that can

593 be set by a ground laser ranging station;

594 - for this purpose, use of the active Q switching is preferable as the onboard laser
595 emission mechanism;

596 - onboard laser repetition rate should be as high as on the ground to get more data

597 points;

598 - if there is some function that can identify the laser pulses from the ground on the

599 spacecraft, it will be easier to distinguish the signals from noise in the ground-based

600 data.

601 The obtained ranges have a difference of the order of 10 m in the two-way

602 compared to the radio wave ranging data; the main factor is thought to be the internal

603 delay of the transponder, but the reasons are currently unclear, considering that the

604 uncertainty of the internal delay estimated from the onboard telemetry data is about the

605 order of 2 m, and that the tropospheric delay must be properly estimated.

606

607

608 Figures and captions

609

610
<figure><img src="image_2.png" /></figure>

612

613 Fig. 1 The link budget calculations for uplink (top) and downlink (bottom). Both uplink

614 and downlink photons can be detectable during the experimental period between Dec. 7

615 and Dec. 23.

616
<figure><img src="image_3.png" /><figcaption>Fig. 2 Explanation of the telemetry data in the laser link mode.</figcaption></figure>

<figure><img src="image_4.png" /></figure>
Fig. 3 An example of the initial quick analysis of the round-trip time of the lasers on December 9. (Top) The O-C (Observed minus Computed) value calculated from the raw data of the ground station. (Center) The time series of the LIDAR internal delay.

(Bottom) The O-C with the internal delay correction applied. The concentrated data points around -0.5 microseconds are considered as the returned signals from the LIDAR

<figure><img src="image_5.png" /></figure>

Fig. 4 The time-series STOP2 data of the LIDAR of Dec. 9 for Mt. Stromlo, Koganei, and Grasse stations, respectively. The unit of the vertical axis is counts. The full scale of
632 the vertical axis corresponds to one cycle of the LIDAR counter, which is about 437

633 microseconds (~ 2^17 / 300 MHz), For Koganei, the predicted locations of the counts

634 for each skip number are overlaid with the skip number.

635

<figure><img src="image_6.png" /></figure>

636

637 Fig. 5 The histogram of the one-count length of the counter (τ in equation 1) up to skip
638 = 5.

639

640

<figure><img src="image_7.png" /></figure>

641

642 Fig. 6 The variation of two-pulse intervals of the Grasse station on December 9 with the

643 LIDAR STOP2 telemetry data overlaid as crosses. The pulse intervals are converted to

644 the equivalent of STOP2 telemetry data using determined one count length.

645
<figure><img src="image_8.png" /></figure>

646

647 Fig. 7 The LIDAR delay for the ground data identified as detected with LIDAR (top),

648 and the O-C (Observed minus Computed) residuals in microseconds with the LIDAR

649 delay correction being applied (bottom). Data points regarded as signals are marked in

650 red with a grey regression line overlaid, which align the interpolated radio wave ranging

651 data before and after the experiment shown in a green dashed line. This is for Dec. 9

652 case.

653

654
<figure><img src="image_9.png" /></figure>

655

656 Fig. 8 Same as Fig.7, except that the date is Dec. 21.

657

<figure><img src="image_10.png" /></figure>

658

659 Fig. 9 Same as Fig.7, except that the date is Dec. 22.

660
661

<figure><img src="image_11.png" /></figure>

662

663

Fig. 10 The residuals of the two-way distance between the ground station and the

664

spacecraft for Dec. 9. Marks denoted as “DSS” and “USUDA” are the residuals of the

665

radio ranging data at the DSN Madrid and JAXA Usuda stations, respectively, and the

666

ones written as “GRASSE_SLAVE” are the laser link data.
<figure><img src="image_12.png" /><figcaption>Fig. 11 Same as Fig. 10, except that the data is for Dec. 21 and 22.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Fig. 12 The enlarged residuals of the laser range data for three days. Note that the</figcaption></figure>

vertical tics of Dec. 22 is wider than other two days' plots.
Grasse Dec. 09 Rx intensity histogram for identified shots

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>
673 Fig. 13 A histogram of the intensities of the detected shots with LIDAR that were

674 identified as ones from the Grasse station. If we assume the pulse width of the detected

675 laser pulses as the same value of the ground station parameter (0.150 ns), we get

676 2.4x10^3 photons / shot for the maximum value of the laser intensity (1515.4 mV,

677 equivalent to 3x 10^-6 W).

678

<table><caption>679 Table 1. Events of Hayabusa2</caption><thead><tr><td>Date (yyyy/mm/dd-dd)</td><td>Events</td></tr></thead><tbody><tr><td>2014/12/03</td><td>Launch</td></tr><tr><td>2015/10/13-15, 2015/11/10-14</td><td>Laser link experiment (1)-1</td></tr><tr><td>2015/12/03</td><td>Earth gravity assist</td></tr><tr><td>2015/12/11-19</td><td>Laser link experiment (1)-2</td></tr><tr><td>2018/06/27</td><td>Arrival at (162173)Ryugu</td></tr><tr><td>2019/02/21</td><td>Touchdown (1)</td></tr><tr><td>2019/07/11</td><td>Touchdown (2)</td></tr><tr><td>2019/11/14</td><td>Departure to Earth</td></tr><tr><td>2020/12/06</td><td>Sample capsule reentry, gravity assist</td></tr><tr><td>2020/12/07-23</td><td>Laser link experiment (2) (this work)</td></tr></tbody></table>

680

<table><caption>681 Table 2. Specifications of the ground stations</caption><thead><tr><td></td><td>Grasse</td><td>Koganei</td><td>Mt. Stromlo</td><td>Wettzell</td></tr></thead><tbody><tr><td>Laser</td><td></td><td></td><td></td><td></td></tr><tr><td>Wavelength [nm]</td><td>1064</td><td>1064</td><td>1064</td><td>1064</td></tr></tbody></table>
<table><caption>Table 3. Specification of LIDAR</caption><tr><td>Energy [J]</td><td>0.3</td><td>1</td><td>2.2</td><td>1.2</td></tr><tr><td>Pulse width [nsec]</td><td>0.150</td><td>10</td><td>15</td><td>0.020</td></tr><tr><td>Beam divergence [arcsecond]</td><td>1 to 10</td><td>10</td><td>12</td><td>1 to 40</td></tr><tr><td>Repetition rate [Hz]</td><td>10</td><td>10</td><td>170 - 180</td><td>500</td></tr><tr><td>Receiver</td><td></td><td></td><td></td><td></td></tr><tr><td>Diameter [m]</td><td>1.5</td><td>1.5</td><td>1.8</td><td>0.75</td></tr><tr><td>Detector</td><td>InGaAs-InP APD</td><td>InGaAs APD-array</td><td>IR enhanced Si-APD</td><td>InGaAs-InP APD</td></tr><tr><td>Bandwidth [nm]</td><td>0.12</td><td>0.4</td><td>2</td><td>0.3</td></tr></table>

<table><caption>Table 4. Summary of observation sessions</caption><thead><tr><th>item</th><th>value</th></tr></thead><tbody><tr><td>Measurement range</td><td>30 [m] – 25 [km]</td></tr><tr><td>Range resolution</td><td>0.5 [m]</td></tr><tr><td>Laser</td><td></td></tr><tr><td>Wavelength</td><td>1064 [nm]</td></tr><tr><td>Energy</td><td>15 [mJ]</td></tr><tr><td>Pulse width</td><td>7 [nsec]</td></tr><tr><td>Beam divergence</td><td>2.4 [mrad]</td></tr><tr><td>Repetition rate</td><td>1 [Hz] Max., external triggered</td></tr><tr><td>Receiver</td><td></td></tr><tr><td>Long range (&gt; 1 km)</td><td>Diameter 110[mm], FOV 1.5 [mrad]</td></tr><tr><td>Short range(&lt; 1 km)</td><td>Diameter 3 [mm], FOV 20.4 [mrad]</td></tr><tr><td>Detector</td><td>Si-APD-HIC</td></tr></tbody></table>

<table><thead><tr><th>month/day</th><th>session</th><th>start - end time (hh:mm UTC)</th><th>ground station</th><th>Uplink data points</th><th>Downlink data points</th><th>condition</th></tr></thead></table>
<table><tr><td rowspan="3">12/7</td><td>1</td><td>04:11 - 05:46</td><td>Mt. Stromlo</td><td>--</td><td>wrong setting in LIDAR</td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Koganei</td><td>1360</td><td></td></tr><tr><td>3</td><td>09:03 - 10:36</td><td>Grasse</td><td>95</td><td></td></tr><tr><td rowspan="3">12/8</td><td>1</td><td>04:11 - 05:46</td><td>Koganei</td><td>202</td><td>mostly cloudy</td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Mt. Stromlo</td><td>295</td><td></td></tr><tr><td>3</td><td>Cancelled</td><td></td><td>--</td><td></td></tr><tr><td rowspan="4">12/9</td><td>1</td><td>04:11 - 05:46</td><td>Mt. Stromlo</td><td>512</td><td></td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Koganei</td><td>1245</td><td>thin cloud</td></tr><tr><td>3</td><td>08:58 - 10:31</td><td>Grasse</td><td>181</td><td>clear -> thin cloud</td></tr><tr><td>4</td><td>10:35 - 11:13</td><td>Grasse</td><td>1143</td><td>cloud -> clear -> thin cloud</td></tr><tr><td rowspan="4">12/10</td><td>1</td><td>04:11 - 05:46</td><td>Koganei</td><td>1265</td><td></td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Koganei</td><td>511</td><td>some clouds</td></tr><tr><td>3</td><td>08:58 - 10:31</td><td>Grasse</td><td>5</td><td>mostly cloudy</td></tr><tr><td>4</td><td>10:35 - 11:13</td><td>Grasse</td><td>3</td><td>mostly cloudy</td></tr><tr><td rowspan="3">12/11</td><td>1</td><td>04:11 - 05:46</td><td>Mt. Stromlo</td><td>531</td><td>proximity interlocks</td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Mt. Stromlo</td><td>81</td><td>proximity interlocks, elevation limited (t</td></tr><tr><td>3</td><td>Cancelled</td><td></td><td>--</td><td></td></tr><tr><td rowspan="3">12/14</td><td>1</td><td>04:11 - 05:46</td><td>Koganei</td><td>1</td><td>NAVSENS in first-half, cloudy</td></tr><tr><td>2</td><td>Cancelled</td><td></td><td>--</td><td></td></tr><tr><td>3</td><td>13:40 - 14:16</td><td>Grasse</td><td>--</td><td>wrong S/C attitude</td></tr><tr><td rowspan="3">12/16</td><td>1</td><td>04:11 - 05:46</td><td>Koganei</td><td>730</td><td>NAVSENS in first-half, cloudy</td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Koganei</td><td>1532</td><td>NAVSENS in first-half, cloudy</td></tr><tr><td>3</td><td>09:00 - 09:36</td><td>Grasse</td><td>2</td><td>foggy</td></tr><tr><td rowspan="3">12/18</td><td>1</td><td>04:11 - 05:46</td><td>Koganei</td><td>1393</td><td>NAVSENS in first-half</td></tr><tr><td>2</td><td>05:51 - 07:24</td><td>Koganei</td><td>1381</td><td>NAVSENS in first-half</td></tr><tr><td>3</td><td>08:50 - 09:44</td><td>Grasse</td><td>268</td><td></td></tr><tr><td rowspan="3">12/21</td><td>1</td><td>03:41 - 05:16</td><td>Koganei</td><td>1362</td><td>no S/C scan in first-half</td></tr><tr><td>2</td><td>05:16 - 06:54</td><td>Koganei</td><td>1968</td><td>no S/C scan in first-half</td></tr><tr><td>3</td><td>08:25 - 09:19</td><td>Grasse</td><td>1190</td><td>63</td></tr><tr><td rowspan="3">12/22</td><td>1</td><td>03:41 - 05:16</td><td>Koganei</td><td>1825</td><td>no S/C scan in first-half</td></tr><tr><td>2</td><td>05:16 - 06:54</td><td>Koganei</td><td>1912</td><td>no S/C scan in first-half</td></tr><tr><td>3</td><td>08:25 - 09:01</td><td>Grasse</td><td>945</td><td>41</td></tr></table>
<table><tr><td>12/23</td><td>1</td><td>03:41 – 05:16</td><td>Koganei</td><td>2103</td><td>no S/C scan in first-half</td></tr><tr><td></td><td>2</td><td>05:16 – 06:54</td><td>Koganei</td><td>2124</td><td>no S/C scan in first-half</td></tr><tr><td></td><td>3</td><td>09:00 – 09:54</td><td>Grasse</td><td>505</td><td>some clouds -&gt; cloudy</td></tr></table>

686

687

688

689

Acknowledgements

690

Authors would like to express sincere thanks to the whole Hayabusa2 team for prompt support for the experiment, and to the NASA DSN Madrid station for the radio tracking, telemetry and command operations for the laser ranging experiments in Europe. The data are analyzed using SPICE toolkit developed by NASA JPL NAIF team (Acton, 1996).

691

692

693

694

695

696

697

698

699

700

701
702

703

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