The Exploration of Lunar Gravity by VLBI Observations of SELENE (Kaguya)*

Trans. JSASS Space Tech. Japan Vol. 7, No. ists26, pp. Tk_1-Tk_5, 2009

By Hideo Hanada1), Takahiro Iwata2), Noriyuki Namiki3), Nobuyuki, Kawano1), Sho Sasaki1), Koji Matsumoto1), Hirotomo Noda1), Seiitsu Tsuruta1), Kazuyoshi Asari1), Toshiaki Ishikawa1), Fuyuhiko Kikuchi1), Qinghui Liu1), Sander Goossens1), Yoshiaki Ishihara1), Natalia Petrova1), Yuji Harada1), Katsunori Shibata1), Kenzaburo Iwadate1), Osamu Kameya1), Yoshiaki Tamura1), Xiaoyu Hong4, Jinsong Ping4), Yusufu Aili5), Simon Ellingsen6), Wolfgang Schlüter7)

1)National Astronomical Observatory,Oshu, Japan 2)Japan Aerospace Exploration Agency,Sagamihara, Japan 3)Kyushu University,Fukuoka, Japan 4)Shanghai Astronomical Observatory, Shanghai, China 5)Urumqi Observatory, Urumqi, China 6)University of Tasmania, Hobart, Australia 7)Fundamentalstation Wettzell, Germany

(Received May 2nd, 2008)

SELENE (Kaguya), which was successfully launched on Sep. 14, 2007, consists of the main orbiter, and two small free-flying sub-satellites, called Rstar (OKINA) and Vstar (OUNA). We use multi-frequency VLBI to measure the angular distance between the two sub-satellite radio sources Okina and Ouna in order to improve the accuracy of the low degree gravitational harmonics and the gravity field near the limb. The observations are made at three frequencies in S-band, (2212, 2218 and 2287 MHz), and one in X-band, (8456MHz) with carrier waves. The Japanese domestic VLBI network, VERA, will conduct VLBI observations for the whole mission period of one year. In addition, we will conduct two periods of international observations, each one month in duration, which will also include the international stations, Shanghai, Urumqi, Hobart, and Wettzell. We have succeeded in making VLBI observations of Okina/Ouna with VERA and the international network, and have also succeeded in correlating of signals from Okina/Ouna. We obtained phase delays with an accuracy of several pico-seconds in S-band.

Key Words: SELENE, Kaguya, VLBI, Moon, Gravity Field

1. Introduction Hayabusa and Huygens 2-5). We expect it to compensate for some shortcoming in the Doppler measurement since it The Japanese lunar explorer SELENE (SElenological has sensitivity orthogonal to the direction of Doppler and Engineering Explorer) or Kaguya which was launched ranging and ranging rate measurements. The sensitivity on Sep. 14, 2007, will make precise observations of the of Doppler measurements diminishes when the spacecraft gravitational field of the Moon utilizing both 4-way orbits the limb of the Moon as seen from Earth, and the Doppler observations through a relay satellite (RSAT gravity field in this region is less well determined. experiment), and differential very long baseline New technologies, such as the multi-frequency VLBI interferometer (VLBI) observations of two satellites method 6), the same beam VLBI method 7-9) and a new (VRAD experiment), as well as through the 13 other method of measuring the phase characteristics of an scientific instruments that are part of the mission 1). The antenna 10), have been developed during the course of the purpose of these observations is to address the design and development phase of Kaguya. They have inadequacies in existing data, and hence obtain a highly contributed significant improvements to the measurement accurate lunar gravity field model. An improved lunar accuracy and the success of the VRAD experiment. gravity field model is important because it contributes not This paper describes the scientific objectives, new only to understand the structure near the surface by technical developments, mission plan and initial results of analyzing the high-degree gravity field, but it also places Kaguya’s VRAD experiment. strong constraints upon the deep interior through the low-degree terms. 2. Contribution of VLBI observations Differential VLBI can measure an anglular distance between two satellites and we will apply it to the VLBI observations are being carried out by the positioning of the spacecrafts around the Moon. This Japanese domestic VERA network 11) in order to improve technique has been used for interplanetary navigation of the lunar gravity field model through precise orbit spacecrafts such as Mars Pathfinder, Geotail, Nozomi, determination of Okina and Ouna, in addition to 2-way

and 4-way Doppler measurements will be conducted by improve the accuracy of the orbit determination of Okina. the Usuda Station of JAXA (Japan Aerospace Exploration Figure 2 shows the difference between the true Okina Agency). Since the accuracy of VLBI positioning position which is calculated based on the true model and depends on baseline length, observations with long that determined by simulated 2-way Doppler data or that baselines are desirable. Currently the Shanghai, Urumqi by 2-way Doppler and VLBI data for one day. This (China), Hobart (Australia) and Wettzell (Germany) shows that the positioning error can be improved by stations are also participating in the international approximately an order of magnitude by adding VLBI observations to improve the accuracy (Figure 1). data, even for periods as short as one day. Although the

positioning errors change according to the orbital plane,

perilune height, amount of data etc., the averages for the

positioning and velocity errors per year are 170 m and 60 mm/s for 2-way Doppler data only and 19 m and 8 mm/s when including VLBI data, respectively.

Fig. 1. VLBI stations for Kaguya

In order to examine the extent to which the VLBI data will contribute to lunar gravity field modeling, Matsumoto Fig. 2. Comparison of Okina positioning accuracy determined by 12) 13) 14) et al. have used the GEODYN II and SOLVE 2-way Doppler measurements only with that by 2-way Doppler and programs to conduct simulations and a covariance VLBI measurements. The horizontal axis indicates modified Julius analysis. The differential VLBI is treated as a doubly day (MJD54608=2008/05/22). differenced 1-way range with 1 mm accuracy, which is based on a targeted X-band phase determination accuracy Figure 3 shows how the VLBI observations contribute 3) of 10 degrees . to the improvement of the lunar gravity field model. There The following conditions are employed in our are three cases; where all the possible Kaguya spacecraft simulations not only for VLBI data but also for 2-way and tracking data are included, where VLBI observations are 4-way Doppler data; not included, and LP100J. The accuracy of all the 1) The mission duration is one year from the fictitious coefficients included in the model will be improved by launch date of Jul. 23, 2005. combining VLBI with 2-way and 4-way Doppler 2) Okina must be fully sunlit during its whole measurements. Here we have accounted for the effect of revolution around the Moon to obtain the 4-way VLBI data on determining the precise orbit of Okina, Doppler and the differential VLBI data. which is a reference for the 4-way Doppler measurements. 3) The 4-way Doppler data arcs are only collected By including VLBI data, the coefficients of degrees less when the Main Orbiter is not visible from Usuda than the 33rd harmonic will be improved by about a factor Deep Space Center (UDSC). of 2, with the best improvement in the 2nd degree 4) Operation time of UDSC for SELENE is assumed coefficient by a factor 2.6. If through proper force modeling we are able to achieve an arc length of Okina to be six hours per day. and Ouna longer than 1 day the final accuracy of the 5) The VLBI ground stations are assumed to operate Kaguya gravity field will be one order of magnitude better for three days per week with eight hours per day. than that of LP100J below approximately degree 30. The foreign stations are assumed to participate in The expected improvements from the Kaguya gravity two VLBI campaigns spanning one month each. field model are important because they contribute not only 6) The arc lengths are assumed to be one day for the to understand the structure near the surface by analyzing Main Orbiter, Okina and Ouna. the high-degree gravity field, but it is also able to put 7) We estimated gravity coefficients of degree and strong constraints upon the deep interior through the order up to 75. low-degree terms. For example, by comparing the 8) The same a priori constraint as used for LP100J is gravitational and topographic data we can estimate the applied for determining gravity field solutions. elasticity of the crust and the mantle, and by combining The first result to highlight is that VLBI data can the low degree gravitational harmonics with the

Tk_2 H. HANADA et al.: The Exploration of Lunar Gravity by VLBI Observations of SELENE (Kaguya)

amplitudes of the lunar physical librations we can then accurately in the case of a polar orbit. constrain the density of the lunar core through the moment of inertia 15). 3. New technologies in VLBI observations of Okina and Ouna

VRAD (differential VLBI RADio sources) are on-board two sub satellites, Okina and Ouna, and will be used for differential VLBI observations of the trajectories of the satellites with the Japanese network VERA (VLBI Exploration of Radio Astrometry) and an international network. We will apply a multi-frequency VLBI (MFV) method to measurements of the angular distances between two radio sources in Okina and Ouna using three frequencies in S-band, 2,212, 2,218 and 2,287 MHz, and one in X-band, 8,456MHz 6). Through cross correlation between the four sets of two carrier waves received at two ground stations the MFV method produces 4 fringe phases for each integration time Four differenced fringe phases are obtained by Fig. 3. Anticipated coefficient sigma degree variances are shown differencing the corresponding fringe phases for the two for the following three cases; LP100J, Kaguya without VLBI radio sources. The final observables are the phase delays observations, and Kaguya with VLBI (after Matsumoto et al 12)). in the carrier wave at X-band, which are obtained by resolving cycle ambiguities step-by-step from the lowest frequency in S-band to X-band. In order to achieve the differential phase delay estimation by the MFV method, the phase error of the differential residual fringe phase of the signals from two nearby spacecraft must be less than 4.3 degrees in the S-band signals and 179 degrees in the X-band signal, which are equivalent to 5.4 ps and 59.2 ps in time, respectively 6,7). The phase delay will be measured to an accuracy of better than 0.17 radians (10 degrees) in X-band, which is equivalent to a positional accuracy of about 20cm on the Moon for a VLBI network with a baseline length of 2,000 km. Preliminary VLBI experiments showed that the cycle ambiguity could not always be resolved using the conventional switching VLBI method. In addition, the accuracy of the delay was not always sufficient to yield Fig. 4. A simulation which shows how the surface mass anomaly improvement of the lunar gravity field, although the group will be recovered only by Doppler measurements. The initial delay could be obtained without cycle ambiguity. There model is shown on the upper left. The east-west structures at the are two reasons why the cycle ambiguity sometimes can limb are poorly recovered (after Sugano and Heki 16)). not be resolved using switched VLBI: one is that a phase error in the differential residual fringe phase is larger than The third contribution of VLBI is the improvement of expected, the other occurs when the estimated total the gravity field model at the limb. Figure 4 shows how electron content (TEC) included in the differential the gravity anomaly will be recovered only by Doppler residual fringe phase is significantly in error, either due to measurements at various longitudes. Structures in the a large tropospheric fluctuation or because of a traveling direction parallel to the line-of-sight direction are poorly ionospheric disturbance crosses the line of sight between recovered near the lunar limb compared to those near the the radio source and the VLBI station. center 14). The new data of VLBI will help to constrain the Kikuchi 7) evaluated a number of possible error sources orbit during the face-on orbit geometries (the orbital plane in the MFV method, including the tropospheric delay and is perpendicular to the line-of-sight from the Earth), when the ionospheric delay based on the results of the the Doppler measurements are less sensitive to the gravity preliminary VLBI experiments. They proposed using a structure in that particular direction. The VLBI same beam differential VLBI observation method in order observations have the highest sensitivity in the direction to resolve every cycle ambiguity for each of the four of the baseline, and this is orthogonal to the line-of-sight frequencies. The same beam differential VLBI technique direction for which Doppler measurements have succeeds even for large tropospheric fluctuations and/or sensitivity. Therefore only VLBI can observe the gravity the traveling ionospheric disturbances. In the same beam signal near the limb (other than the polar region), differential VLBI method, a ground antenna sees two

Tk_3 Trans. JSASS Space Tech. Japan Vol. 7, No. ists26 (2009)

objects simultaneously when the angular distance between them is less than the angular dimensions of the main beam of the antenna. Kikuchi 7) also showed that the accuracy of the delay depends upon the average elevation angle of the two spacecraft and the angular distance between them. The same beam differential VLBI method is possible for both S- and X-bands when the angular separation of the two spacecrafts is less than 0.1 degrees, which is the beam width of the antenna for X-band. The accuracy of differential phase delay at X-band is expected to be 3.3 ps or less for average elevation angles greater than 15 degrees (as well as satisfying the angular distance condition ). The phase characteristics, especially systematic phase offsets across the main beam of an actual telescope may cause a problem in the same beam differential VLBI method. Liu et al. 17) measured the phase characteristics Fig. 5. The schedule of the first international VLBI observations. of the 20-m and 10-m telescopes at Mizusawa at 2,237.5 Mi (Mizusawa), Ir(Iriki), Is(Ishigaki), Og(Ogasawara), and 2,280.7 MHz with an error of approximately 0.04 Sh(Shanghai), Ur(Urumqi), Ho(Hobart) and Wz(Wettzell) were radians rms. in order to determine the likely influence on participated in the observations. the same beam differential VLBI method. The phase characteristics were 0.06 radians rms. for both the 20m and the 10m telescopes in the main beams, and the post-fit residuals decreased to 0.03 radians rms. for the 20m and 0.04 radians rms. for 10m telescope, respectively, after correction using quadratic fits. These results confirmed the effectiveness of the same beam differential VLBI method for Kaguya.

4. Observation schedule

The Japanese domestic VLBI network, VERA, will conduct VLBI observations on a regular basis (8 hours/day, 3 days/week) for the whole mission period of one year from the beginning of November, 2007 to the end of October, 2008. In addition, we will conduct two periods of international observations, each month in Fig. 6. An estimated differential Phase delay for Okina and Ouna duration, which include the international stations, in S1 (2212 MHz) for the baseline between Ishigaki and Iriki. Shanghai, Urumqi, Hobart, and Wettzell. The first international observation period occurred in January, 2008 5. Initial results as shown in Figure 5. The second international observation period will be from the middle of May to the VLBI observations commenced on Nov. 5, 2007 after middle of June, 2008. the initial checkout of Okina and Ouna. There were The primary aim of the VLBI scheduling is to conduct many opportunities to utilize the same beam differential VLBI observations when the orbit plane is in a "face-on" VLBI method during this period and we have confirmed configuration in order to obtain more powerful constraints that the cycle ambiguity for the differential phase delay in for the orbit determination, which compensates for the the MFV method can be solved using the same beam loss of line-of-sight sensitivity coming from 2-way differential VLBI method. An estimated differential Doppler measurements. The "face-on" configuration takes phase delay for Okina and Ouna at 2212 MHz for the place twice a month and we conduct a 4-day "core baseline between Ishigaki and Iriki stations is shown in 18) observation" for each fortnightly occurrence. The Figure 6 as an example . The error in the differential contribution from VLBI is also important to precisely phase delay is smaller than 2 ps in a 30 s integration determine the orbit of Okina which serves as a reference interval. If the baseline is assumed to be 2000 km, 2 ps for 4-way Doppler observation, playing an important role corresponds to position accuracy of 12 cm at the distance mainly in the "edge-on" configuration. Therefore it is of the Moon. highly desirable to extend the VLBI observation times to Although we have not yet included VLBI data routinely the period other than "face-on" configuration, which we in the process for orbit determination and gravity field refer to as "extended observations". model estimation, we have undertaken preliminary analysis showing overlap orbit differences in radial, along

Tk_4 H. HANADA et al.: The Exploration of Lunar Gravity by VLBI Observations of SELENE (Kaguya)

and cross track direction between the case with Doppler doi:10.1029/2005JE002640. and range data only and that including VLBI data, and we 6) Kono, Y., Hanada, H., Ping, J., Koyama, Y., Fukuzaki, Y. and Kawano, N., Precise positioning of spacecraft by get better results when including VLBI data. Further multi-frequency VLBI, Earth Planets Space, 55(2003), pp. analysis of the new VLBI data will establish the 581-589. effectiveness of VLBI observations for orbit 7) Kikuchi, F.: Differential phase delay estimation by same determination and gravity field estimation. beam VLBI method, Ph. D. thesis, The Graduate University for Advanced Studies, (2006), pp. 83. 8) Liu, Q., Matsumoto, K., Kikuchi, F., Ping, J., Asari, K., 6. Summary Hanada, H. and Kawano, N.: Same-beam differential VLBI technology using two satellites of the SELENE spacecraft, We have succeeded in making VLBI observations of IEICE trans. Commun., J89B-B(2006), pp.602-617. (in Okina/Ouna with VERA and the international network, Japanese) and confirmed that the receiving, the tracking, and the 2006. 9) Liu, Q., Kikuchi, F., Matsumoto, K., Asari, K., Tsuruta, S., recording system work well, and that the signals from Ping, J., Hanada, H. and Kawano, N.: Error Analysis of Okina/Ouna are normal. We have succeeded in correlating Same-beam differential VLBI technique using two satellites signals from Okina/Ouna, and confirmed that the signals of SELENE, Adv. Space Res., 40(2007), pp.51-57. have a S/N high enough to allow the resolution of cycle 10) Liu, Q., Tsuruta, S., Asari, K., Ping, J., Kikuchi, F., ambiguity with our multi frequency VLBI method. We Matsumoto, K. and Kawano, N.: New method of measuring phase characteristics of antenna using Doppler frequency have succeeded in obtaining phase delays with an measurement technique, IEEE Trans. Antenna Propagation, accuracy of several pico-seconds at S-band. 52(2004), pp. 3312-3318. 11) Kobayashi, H., Sasao, T., Kawaguchi, N., Manabe, S., Acknowledgements Omodaka, T., Kameya, O., Shibata, K. M., Miyaji, T., Honma, M., Tamura, Y., Hirota, T., Kuji, S., Horiai, K., Sakai, S., Sato, K., Iwadate, K., Kanya, Y., Ujihara, H., Jike, The authors appreciate the contribution of all engineers T., Fujii, T., Oyama, T., Kurayama, H., Suda, H., of NEC/Toshiba Space Systems Ltd. (NTS), Nippon Sakakibara, S., Kamohara, R. and Kasuga, T.: VERA Antenna Co. Ltd., and Nippi Corporation who diligently Project, ASP Conference Series, 306, New Technologies in developed the onboard instruments and sub-satellites. The VLBI, ed. Y. C. Minh (San Francisco: ASP), (2003), pp.367. authors are grateful to the entire staff of the Kaguya 12) Matsumoto, M., Hanada, H., Namiki, N., Iwata, T., Goossens, S., Tsuruta, S., Kawano, N. and Rowlands, D. D.: mission as well. The authors also wish to express their A simulation study for anticipate accuracy of lunar gravity gratitude to Dr. Dirk Behrend and Dr. Yasuhiro Koyama field model by SELENE tracking data, Adv. Space. Res., 42 of the IVS committee for their support and encouragement. (2008), pp.331-336. The gravity experiments of Kaguya would never have 13) Pavlis, D. E., Moore, D., Luo, S., McCarthy, J. J. and been achieved without a prominent technique and the Lutheke, S. B.: GEODYN Operations Manual, 5 Volumes, Hughes/STX, prepared for NASA Goddard Space Flight profound knowledge of Mr. Fumio Fuke who was an Center, Greenbelt, Maryland, (1997). engineer of NTS and passed away 2 months after the 14) Ullman, R. E.: SOLVE Program, Mathematical formulation launch. We express sincere thanks to his contribution and and guide to user input, Hughes/STX contractor report, grieve over the loss for Japanese space development. contract NAS5-31760, NASA Goddard Space Flight Center, Greenbelt, Maryland, (1994). 15) Hanada, H., Iwata, T., Namiki, N., Kawano, N., Asari, K., References Ishikawa, T., Kikuchi, F., Liu, Q., Matsumoto, K., Noda, H., Tsuruta, S., Goossens, S., Iwadate, K., Kameya, O., Tamura, 1) Kato, M., Sasaki, S., Tanaka, K., Iijima, Y. and Takizawa, Y., Hong, X., Ping, J., Aili, Y., Ellingsen, S. and Schlüter, Y.: The Japanese lunar mission SELENE: Science goals and W.: VLBI for Better Gravimetry in SELENE, Adv. Space. present status, Adv. Space. Res., 42 (2008), pp.294-300. Res., 42 (2008), pp.341-346.. 2) Folkner, T. C., Yoder, C. F., Yuan, D. N., Standish, E. M. 16) Sugano, T. and Heki, K.: High resolution lunar gravity and Preston, R. A.: Interior structure and seasonal mass anomaly map from the Lunar Prospector line-of-sight redistribution of Mars from radio tracking of Mars acceleration data, Earth Planets Space, 56(2004), pp.81-86,. Pathfinder, Science, 278(1997), pp.1749-1752. 17) Liu, Q., Kikuchi, F., Tsuruta, S., Matsumoto, K., Hanada, 3) Kikuchi, F., Kono, Y., Yoshikawa, M., Sekido, M., Ohnishi, H., Kameya, O., Tamura, Y., Asari, K. and Kawano, N.: M., Murata, Y., Ping, J., Liu, Q., Matsumoto, K., Asari, K., Effect of phase characteristics of telescope on same-beam Tsuruta, S., Hanada, H. and Kawano, N.: VLBI observation differential VLBI, IEEE trans. Antenna Propagation, of narrow bandwidth signals from the spacecraft, Earth 55(2007), pp.1466-1470. Planets Space, 56(2004), pp.1041-1047. 18) Kikuchi, F., Liu, Q., Matsumoto, K., Ishihara, Y., Ping, J., 4) Konopliv, A. S., Yoder, C. F., Standish, E. M., Yuan, D-N. Hanada, H., Iwata, T., Namiki, N., Kawano, N., Sasaki, S.: and Sjogren, W. L.: A global solution for the Mars static and Differential Phase Delay Estimation in VRAD Mission of seasonal gravity, Mars orientation, Phobos and Deimos SELENE (KAGUYA), Proc. 26th. Int. Symp. Space masses, and Mars ephemeris, Icarus, 182(2006), pp.23-50. Technology and Science, (2008). (this issue) 5) Witasse, O., Lebreton, J. P. Bird, M. K., et al.: Overview of the coordinated ground-based observation of Titan during the Huygens mission, J. Geophys. Res., 111(2006), E07S01,

Tk_5