Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29, pp. Pk_13-Pk_19, 2014 Original Paper

Recent Status of SELENE-2/VLBI Instrument

1) 1) 1) 1) 1) By Fuyuhiko KIKUCHI , Koji MATSUMOTO , Hideo HANADA , Seiitsu TSURUTA , Kazuyoshi ASARI , 1) 1) 2) 3) Yusuke KONO , Ryuhei YAMADA , Takahiro IWATA , Sho SASAKI , 4) 4) 5) 5) Kesato TAKAHASHI , Yasuhiro UCHIBORI , Takashi KOMAI and Takahiro NAKAMURA

1) National Astronomical Observatory of Japan, Oshu, Japan 2) The Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan 3) Department of Earth and Space Sciences, Osaka University, Toyonaka, Japan 4) NEC Corporation, Fuchu, Japan 5) NEC TOSHIBA Space Systems, Ltd., Fuchu, Japan (Received June 24th, 2013)

The internal structure of the Moon is one of the most important clues to the evolution and origin of the Moon. A lunar gravimetry by differential VLBI observation, named dVLBI, is proposed for the SELENE-2 to improve the internal structure model, especially for the core. As a recent review of the dVLBI mission, two topics are shown. First, new operation modes are introduced for the purpose of saving the transmitter’s electric power. The power consumption is reduced from 9.6 W to 2.1 W in the case of the dual frequency and intermittent transmission modes. Error estimation of the lunar potential Love number k2 shows that the desired accuracy can be achieved in the case of the intermittent transmission mode. Second, the S-band survival antenna that will be installed on the lander is designed. A computational simulation using an analytic model shows that the required performances, which are gain of -5 dBi, beamwidth of 60 degrees, and bandwidth of 140 MHz, are achieved at a temperature within a range of -200 to +120 degrees.

Key Words: Moon, VLBI, Orbit Determination, Gravity Field, Internal Structure

1. Introduction the core. Though various data sets and methods are used to estimate the core parameters, the differences between models Since the giant impact model indicates that the Moon was and the errors of the models themselves are too large to made by a collision of a protoplanet with the early Earth, the constrain the evolution model of the Moon. Moon and Earth are inseparable planets and to know the origin of the Moon is to explore our roots. The internal Table 1. Dependency of the k2 for core radius and state. structure of the Moon is important in constructing a model of Core radius Differences of k2 between the evolution of the Moon and inferring its origin. The internal (km) liquid and solid iron core (%) structure provides information on composition and thermal 250 2 condition of the Moon’s interior. We propose a differential 300 3.4 very long baseline interferometry (VLBI) mission, named 350 5.4 dVLBI, for the SELENE-2 to investigate the internal structure 400 8.1 of the Moon especially for the deeper part of the Moon, the core, through lunar gravimetry. The lunar degree 2 potential Love number k2 is one of the The state, radius, and density of the lunar core have been effective observables. As noted by Williams (2005), the k2 estimated by several methods. The lunar laser ranging (LLR) value changes depending on the size of the core. For example, estimated the core radius by analyzing more than 30 years of the k2 value differs by five percent depending on the existence range data between the ground station and the reflector on the or non-existence of the liquid iron core whose size is 350 km4). 1) Moon . The core radius estimated by LLR is between 314 and Differences of the k2 between the liquid and solid iron cores 352 km for a liquid iron core and between 334 and 375 km for calculated for our several models are described in Table 1. If 1) a liquid Fe-FeS eutectic composition . The core radius has the difference between models is detected, the information also been estimated from the moment of inertia of the Moon about the core parameters can be obtained. However, the error by combining gravity and LLR data. The core radius of the k2 is currently large. The k2 value and its error estimated by using the gravity data of Lunar Prospector is 320 estimated by the lunar gravimetry of Kaguya are 0.0255 and +50/-100km when the core is Fe and 510 +80/-180 km when eight percent5). In the case of the LLR, the k2 value and its 2) the core is FeS . The observation of the lunar induced error are 0.0241 and six percent6). The difference between magnetic dipole moment in the geomagnetic tail also models is about 12 %. The error of the k2 must be smaller estimated the core radius that is between 250 and 430 km for than one percent to significantly estimate the core radius. 3) the metallic core . This value depends on the conductivity of Since the k2 also depends on the composition of the lunar

Copyright© 2014 by the Japan Society for Aeronautical and Space Sciences and ISTS. All rights reserved.

Pk_13 Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014) crust and mantle, seismic and other geophysical data must be shown in Fig. 1. To remove major error sources of VLBI used to investigate the core parameters. According to the error measurement, the differential VLBI observation will be estimates based on geodetic data from SELENE and LLR and carried out using the orbiter and lander. Major error sources, also Apollo seismic data (Yamada et al., submitted article), which are propagation delay, instrumental delay and clock the current error of the core radius and core density is about offset, are common among the DOR of the orbiter and lander. 33 % and 40 %, respectively7). These errors will decrease These error sources can be canceled out by differentiating the down to 10 % for core radius and 22 % for core density when DOR of the orbiter and lander. The measurement of the the k2 accuracy of one percent is achieved7). If the core differential VLBI observation is doubly differenced one-way density is estimated within the error of 20 %, the composition range (DDOR). The switching VLBI method is used in the and temperature of the lunar core can be inferred. The amount dVLBI mission, in which the orbiter and lander are tracked of metallic iron that is one of the important constraints for the alternately. giant impact simulation can be also estimated from the mass In the case of the differential VLBI radio sources (VRAD) of the core. mission of Kaguya, the orbits of the two free-flyers had to be To measure the k2 within the error of one percent, the estimated simultaneously5). This limited the accuracy of the dVLBI mission is proposed for the SELENE-2. In this paper, orbit determination and lunar gravimetry. The dVLBI mission the overview of the dVLBI mission is described in chapter 2. has an advantage because one of the targets, the lander, is Newly introduced transmission modes that allow the reduction fixed on the lunar surface. The precise orbit determination of of the power consumption of the instrument are described in the orbiter can be expected by referencing the position of the chapter 3. To confirm the validity of new modes, error lander. The lander’s position will be determined by two-way estimations of the VLBI measurement and k2 are carried out. Doppler at the landing phase. An image matching of the lunar The detail of the transmitter that deals with new modes is also surface using the data obtained by Kaguya will also be carried described. The analytical model of the survival antenna that out to determine the landing position. The differential VLBI will be used on the lunar surface temperature is described in observation between the lander and quasar is also considered. chapter 4. Three S-band and one X-band signals are transmitted from the instrument onboard the orbiter and the lander. These Orbiter signals are used to estimate a cycle ambiguity, which is the bias of the observable, by using the multi frequency VLBI S/X-bands radio signals (MFV) method10). The frequencies of the signals are 2205, Lander 2220, 2280, and 8460 MHz. These values are provisional and will be adjusted in the fabrication phase. The 20 m antennas of the four VERA stations11) are used to receive the radio signals. Mission duration is at least three months. Observation will be carried out for six hours per day. The internal structure of the Moon will be estimated from Ground the k2 and other geophysical measurements. The moment stations inertia of the Moon, lunar degree 2 displacement Love number h2, and travel time of the seismic wave of the moonquake will Fig. 1. A concept of the lunar gravimetry in the dVLBI mission be used. These geophysical measurements are represented by proposed for SELENE-2. the function of the internal structure parameters, which are thickness, density, shear modulus, and bulk modulus of the 2. Overview of dVLBI Mission Proposed for SELENE-2 crust, mantle and core of the Moon. The internal structure parameters will be estimated by inversion method. To improve the accuracy of the lunar gravity field modeling, VLBI technique is applied in the dVLBI mission of 3. Introduction of New Transmission Modes SELENE-2. VLBI is one of the tracking tools of spacecraft 8,9) and has been used for many planetary missions . The How to decrease the power consumption of the lander difference in the arrival times of signals from spacecraft to instrument is an important problem, because the power supply two ground stations is measured in VLBI observation. An is severely limited. Target value is 2 W. To address this observable of the VLBI is called a delay. A differenced problem, two kinds of transmission modes are introduced. In one-way range (DOR) that is a product of the delay and speed this chapter, the explanation of the transmission modes is of light is used for orbit determination. Doppler and range that firstly described. Then the error estimation of the VLBI are generally used for the orbit determination have sensitivity measurement and k2 are carried out to confirm the validity of only in the direction of line-of-sight from the ground station to the new transmission modes. The details of the transmitter that the spacecraft. In contrast, DOR has sensitivity in the deals with new modes are also described. direction perpendicular to the line-of-sight. A combination of Doppler, range and DOR improves the three-dimensional positioning of spacecraft. 3.1. Dual and multi-frequency transmission A concept of the lunar gravimetry in the dVLBI mission is To estimate the cycle ambiguity using the MFV method,

Pk_14 F. KIKUCHI et al.: Recent Status of SELENE-2/VLBI Instrument three S-band and one X-band signals are used in the dVLBI transmitted, units of the transmitter except for the oscillator mission in a similar way to the VRAD mission. These four are switched off. The signal-to-noise ratio (S/N) decreases by signals had been simultaneously transmitted in the VRAD 3 dB in mode 1 and 3.9 dB in mode 2 in comparison to the mission. However, there’s no need to always transmit four case of the continuous transmission in which the integration signals. period is 60 seconds. Whether the decrease of the S/N can be acceptable is discussed in the next subsections. Multi freq. case Dual freq. case Multi freq. case 3.3. Error estimation of DDOR The error of the DDOR measurement in case of the intermittent transmission mode is estimated. The DDOR (Ǽ S1 ǼR) is defined as a difference of residual fringe phase (DRFP, ǼǼȭ) between two radio sources: the lander and the orbiter S2 600 s 600 s in the case of the dVLBI mission. The residual fringe phase is the phase of the cross correlation function of the signals S3 600 s 600 s received at two VLBI stations. The relation between the X1 DDOR and the DRFP is written as: ''I  2SN ''R c ˜ (1) : Transmission : Standby 2S f where c is the speed of light, f is the frequency of the radio Fig. 2. Conceptual diagram of the dual and multi-frequency signal, and N is the cycle ambiguity. The cycle ambiguity will transmission cases. be estimated by using the MFV method10). The error sources of the DDOR are thermal noise, Mode 0 ࣭࣭࣭ tropospheric delay, ionospheric delay, and instrumental delay. These can be separated into short-term and long-term Mode 1 15 s 45 s 15 s 45 s ࣭࣭࣭ components. The short-term components are represented by the fluctuations of the DRFP. The error of the DRFPȪǼǼȭ, all Mode 2 10 s 50 s 10 s 50 s ࣭࣭࣭ can be written as:

1 V V 2  V 2  V 2 2 : Transmission : Standby ''I,all ''I,thermal ''I ,trop ''I,inst (2)

whereȪǼǼȭ, thermal is the phase error caused by the thermal Fig. 3. Conceptual diagram of the intermittent transmission modes. noise, ȪǼǼȭ, trop andȪǼǼȭ, inst are the fluctuations of the tropospheric and instrumental delay, respectively. The As a result of the data analysis of the VRAD mission, it is short-term component of the ionospheric delay is discussed shown that the cycle ambiguity takes same value while the 9) later. observation is continuous . In this case, it is acceptable that The error of the DRFP caused by the thermal noise of the the estimation of the cycle ambiguity can be carried out at any radio signal can be represented as: moment of the continuous period. Once the cycle ambiguity is 1 V 2 ˜ (3) estimated by using three S-band and one X-band signals, two ''I ,thermal SNR of three S-band signals are not needed. Only one S-band and where SNR is the S/N of the radio signal. Coefficient X-band signals are used over an entire period to estimate represents the root sum square of the thermal noise of the ionospheric delay. Consequently, two cases are introduced as signals received at two VLBI stations. In the case of the shown in Fig. 2. Three S-band and one X-band signals are dVLBI mission, SNR is 57.54 (17.6 dB) at a 60-second transmitted at the first and last 600 seconds of continuous integration time both for the S/X-bands signals andȪǼǼȭ, observation period. This is named the multi-frequency case. thermal is 1.4 degrees. The antenna parameters of VERA are The cycle ambiguity is estimated in this period. One S-band used to calculate SNR. The aperture efficiencies are 0.15 for and X-band signals are transmitted among the rest of the time. the S-band and 0.3 for the X-band12). The system noise This is named the dual-frequency case. Introducing two cases temperatures are 323 K for the S-band and 522 K for the decreases the power consumption. X-band13). The contribution from the Moon of 150 K for the 3.2. Intermittent transmission mode S-band and 220 K for the X-band is included13). In the case of An intermittent transmission mode is also introduced to the intermittent transmission mode, S/N decreases by 3 dB in reduce the average value of the power consumption. This is mode 1 and 3.9 dB in mode 2. The error of the DRFP is 2.8 applied to both multi- and dual-frequency cases. As shown in degrees in mode 1 and 3.5 degrees in mode 2. Fig. 3, the radio signals are transmitted for 15 seconds in each The error of the DRFP caused by the fluctuation of the 60 seconds in mode 1 and 10 seconds in each 60 seconds in tropospheric and instrumental delays is estimated from the mode 2. The transmitting periods are chosen to meet the result of the VRAD mission. Standard deviation of the DRFP power consumption condition of about 2 W. Mode 0 is the in the case of the switching VLBI is calculated in this paper. continuous transmission mode. While the signals are not The switching interval is 120 seconds. The integration time is

Pk_15 Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014) set to 60 seconds. The baseline is the Ishigaki-Iriki of the DDOR and the intermittent transmission mode is acceptable VERA network11). The duration of the data is from January 7 for reducing the power consumption of the instrument. to December 26, 2008. The result shows that the standard deviation of the DRFP is 6.8 degrees for the S-band and 14.8 Table 2. The error of the short-term components of the DRFP. degrees for the X-band. These values corresponds to ȪǼǼȭ, Mode 0 Mode 1 Mode 2 all of Eq. (2). In the case of the VRAD mission, the thermal Operating rate 100 % 25 % 16.7 % noise calculated from the S/N is 0.2 degrees and 0.23 degrees Frequency band S X S X S X 14) for the S-band and X-band signals, respectively . These are Thermal noise 1.4 2.8 3.5 small enough compared to the standard deviations of the (deg.) DRFP. The error of the DRFP caused by the fluctuation of the Tropopheric and 6.8 14.8 6.8 14.8 6.8 14.8 tropospheric and instrumental delays is considered to be 6.8 instrumental degrees for the S-band and 14.8 degrees for the X-band. delays (deg.) The total error for the DRFP in the dVLBI mission of RSS (deg.) 6.9 14.9 7.4 15.1 7.6 15.2 SELENE-2 is calculated fromȪǼǼȭ, thermal of the dVLBI Ȫ2 Ȫ2 1/2 mission and ( ǼǼȭ, trop + ǼǼȭ, inst) of the VRAD mission Table 3. The error of the DDOR. by using Eq. (2). The results are summarized in Table 2. The Mode 0 Mode 1 Mode 2 total error is 6.9 degrees for the S-band and 14.9 degrees for Operating rate 100 % 25 % 16.7 % the X-band in mode 0. In the case of the intermittent Frequency band S X S X S X transmission mode, the total error is somewhat larger than that Short-term (mm) 2.6 1.5 2.8 1.5
.9 1.5 of mode 0. The total error is 7.4 degrees for the S-band and Long-term (mm) 0.6 15.1 degrees for the X-band in mode 1, and is 7.6 degrees for the S-band and 15.2 degrees for the X-band in mode 2. Ionospheric (mm) 3.0 0.2 3.2 0.2 3.3 0.2 Although the estimated S-band DRFP error is larger than RSS (mm) 4.0 1.6 4.3 1.6 4.4 1.6 the critical value of 4.3 degrees to resolve the cycle ambiguity by using the MFV method10), it can be reduced by employing 3.4. Simulations of k2 estimation a shorter switching interval. According to the result of the error estimation of the DDOR, The error of the DDOR caused by the short-term the error of the k2 in the dVLBI mission is estimated by a components ȪǼǼR,short is rewritten from Eq. (1) as: computer simulation. Simulation conditions are as follows: The elliptical polar orbit with periapsis height of 100km and V ''I ,all (4) apoapsis height of 800 km is assumed. Because the orbit of V ''R ,short c ˜ 2S f SELENE-2 is not fixed, the orbit that is almost the same as 5) The error ȪǼǼR, short is 2.6 mm for the S-band and 1.5 mm for Vstar of Kaguya is referred . The landing site is not fixed the X-band. The errors are almost the same among the mode 0, either and assumed to be sub-earth point of the Moon. The 1, and 2. Increase of the error in the case of mode 1 and 2 is a position of the lander does not affect the result. Observables small percent. are DDOR and two-way Doppler. The ground stations of the As for the error caused by the long-term component of the VLBI are four stations of VERA and those for two-way tropospheric delay, the error estimation of Kikuchi et al. Doppler are JAXA ground network stations. Mission duration (2008) is referred. The error depends on the elongation and is three months and observation is carried out six hours per elevation of the two spacecraft and is smaller than 0.6 mm14). day. The GEODYN ϩ and SOLVE are used for orbit The error cause by the ionospheric delay which include both determination and gravity field estimation15). The arc length is of the short-term and long-tem components can be estimated set to 14 days in the data processing. The covariance matrix of from the error of the DRFP of the S-band and X-band signals SGM100h, which is SELENE Gravity Model version h, is 1 as: 2 § 2 2 ·2 used as initial covariance. The error of the Doppler is 1 mm/s c f V ''I V ''I V S ˜ X ˜ ,all,S  ,all,X ''R,ion 2 2 ¨ 2 2 ¸ (5) at 60-second integration time. The error of the DDOR is set to 2S fS  fX © fS fX ¹ 1 0.5, 1, 1.6, 2.0, and 3.0 mm to examine the dependency of the 2 § 2 2 ·2 c f V ''I V ''I V X ˜ S ˜¨ ,all,S  ,all,X ¸ (6) k2 error on the DDOR error. ''R,ion 2S f 2  f 2 f 2 f 2 S X © S X ¹ The result is summarized in Table 4. The error of the k2 is S X where Ȫ ǼǼR,ion andȪ ǼǼR,ion are the error of the S-band and evaluated as 10 times higher than the formal error considering X-band signals, fs is frequency of S-band signal, fX is the errors in solar radiation pressure modeling and in lander frequency of X-band signal. The error is from 3.0 to 3.3 mm position. The error of the k2 is smaller than the critical value for the S-band signal and 0.2 mm for the X-band signal. of one percent to estimate the core parameters of the Moon The results of the error estimation of the DDOR are when the error of the DDOR is 1.6 mm. The mission duration summarized in Table 3. The error of the DDOR evaluated as of three months is assumed for the current estimate of k2 the root sum square (RSS) of the error sources is 1.6 mm in accuracy. If an extended mission is available, the better k2 the case of the X-band signal. The result is almost the same accuracy is expected with the longer duration of the extended for both the continuous and intermittent transmission modes. mission. This means that the increase of the thermal noise due to shorter transmission time has little impact on the error of the

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Table 4. The error of the lunar degree 2 potential Love number k2. dual-frequency case, in which one S-band and X-band signals are transmitted continuously, the PLOs of S2 and S3 are Error of DDOR (mm) Error of k2 (%) switched off. All of the PLOs and amplifiers are turned off in 0.5 0.4 the standby case. 1 0.7 While the signals are transmitted continuously, which is 1.6 0.9 mode 0, the power consumption of the analog type is smaller 2 1.1 than that of the digital one. On the other hand, the relation is 3 1.4 turned over in the case of the standby mode. The average power consumptions in the case of the intermittent 3.5. Designing of transmitter transmission modes 1 and 2 are described in Table 6. The transmitter that deals with the new transmission modes Percentage of the transmission time is 25 % for mode 1 and is newly designed. The transmitter consists of a 16.7 % for mode 2. In the case of intermittent transmission temperature-compensated crystal oscillator (TCXO), mode, the power consumption of the digital type is smaller amplifiers, filters, phase-locked oscillators (PLO), and an than that of the analog type. Target value of 2 W is almost operation control unit. satisfied. Consequently, the digital type is selected in the dVLBI. The digital PLO also makes the system redundant. Analog Because the hardware of the digital PLO is the same for three S-band signals, any PLO can synthesize any S-band signal PLO (S1) when one of the PLOs breaks down.

PLO (S2) LPF Table 5. Power consumption of transmitter. Power consumption PLO (S3) Analog type Digital type (W) (W) PLO (X1) LPF Mode 0 Multi-frequency case 8.7 9.6 (100 %) Dual-frequency case 7.4 7.6 Fig. 4. Diagram of the transmitter. The analog PLOs are used to Standby case 1.4 1 generate radio signals. Table 6. Power consumption of transmitter. Digital Power consumption Analog type Digital type PLO (S1) (W) (W) Mode 1 Multi-frequency case 3.2 3.2 LPF PLO (S2) (25 %) Dual-frequency case 2.9 2.7 PLO (S3) Mode 2 Multi-frequency case 2.6 2.4 (16.7 %) Dual-frequency case 2.4 2.1 PLO (X1) LPF 4. Designing of S-band Survival Antenna Fig. 5. Diagram of the transmitter. The digital PLOs are used to generate radio signals. Both S-band and X-band patch antennas with conical beam will be installed on the upper deck of the lander. To avoid Two kinds of circuit configuration are considered and the interference between S-band and X-band antennas when these power consumption is compared. One uses analog PLOs, type are installed at a nearby site, a patch antenna is selected A, and the other uses digital PLOs, type B. Diagram of the instead of a dipole antenna. One of the important transmitter is shown in Fig. 4 and Fig. 5. In the case of type A, characteristics required for the antenna is resistance to the the analog PLOs are assumed to be the similar PLOs that were temperature environment of the lunar surface. The used in the VRAD mission. This type of PLO generates the temperature of the lunar surface rises up to about 117 Υ in output frequency by multiplying the reference frequency by the daytime and drops down to about -173 Υ in the power of two. To generate the four frequency signals of 2205, nighttime16). A machinable glass-ceramic, which is called 2220, 2280, and 8460 MHz, corresponding four different MACOR that has adequate resistance to the temperature reference frequencies are necessary, which requires four environment, is selected for a substrate of the patch antennas. TCXOs. In the case of type B, one TCXO and four digital Low relative permittivity and good machinability of MACOR PLOs are used. Because the transmit frequency can be flexibly are also valid for achieving the required performance of the changed in digital PLO, only one TCXO is used in this case. antennas. The required characteristics of the antennas are The power consumptions of the transmitters are described in summarized in Table 7. Wide-angle conical beam whose Table 5. Among the multi-frequency case, in which three width is 60 degrees from the antenna boresight is needed for S-band signals and one X-band signal are transmitted accommodating each landing site under discussion. The gain continuously, all of the units are turned on. Among the

Pk_17 Trans. JSASS Aerospace Tech. Japan Vol. 12, No. ists29 (2014) of -5 dBi is necessary based on the link budget for VLBI observations. Extremely wide bandwidth of the S-band antenna, which is 140 MHz, is required to cover the frequencies of the three signals and temperature change of the antenna resonant frequency. The analytical model of the S-band antenna is developed and its performances have been confirmed in the computational simulation. The radiation pattern of the S-band antenna at the temperature of -200 Υ, +20 Υ, and +120 Υ are shown in Fig. 6. Frequency is 2212 MHz. We confirm that the gain is larger than -5 dBi in the range of +/- 60 degrees from the antenna boresight for all the temperatures. The antenna pattern at 2218 MHz and 2287 MHz are almost the same. The frequencies in the simulation are slightly different from the current frequencies, which are 2205, 2220, and 2280 MHz. This is because the simulation is carried out before the current frequencies are determined as a result of the introduction of the intermittent transmission mode. However, the result is considered to be almost the same. In the future, a breadboard model of the antenna will be Fig. 6. Radiation patterns of the S-band antenna. developed and its performance will be measured. Table 7. Characteristics of the patch antennas installed on the lander. Frequency S-band X-band Operating -200 Υ to +120 Υ -200 Υ to +120 Υ temperature range Gain -5 dBi -5 dBi Beam width +/- 60 degrees +/- 60 degrees Bandwidth 140 MHz 100 MHz

5. Conclusion

The lunar gravimetry by the differential VLBI observation of the orbiter and lander of the SELENE-2 is proposed with the aim of estimating the internal structure of the Moon. One of the most important problems in dVLBI mission is saving the instrument’s power consumption. To reduce power consumption, two kinds of transmission mode are newly introduced. The error estimation of the VLBI measurement and k2 in the case of the intermittent transmission modes is carried out to confirm the validity. The result shows that the error of the k2 is smaller than the one percent needed to significantly estimate the core parameters of the Moon. As for the instrument, the transmitter that deals with the new transmission modes is designed. The power consumption is 9.6 W when three S-band and one X-band signals are transmitted (multi-frequency case) and 7.6 W when one S-band and X-band signals are transmitted (dual-frequency case). The standby power consumption is 1 W. In these cases the signals are transmitted continuously. When the intermittent transmission mode is introduced, in which the percentage of the transmission time is 16.7 % for example, the average power consumption decreases to 2.4 W in the multi-frequency case and 2.1 W in the dual-frequency case. The critical value of 2 W is almost achieved. Consequently, the introduction of the new transmission mode is acceptable. The S-band survival antenna to be installed on the lander is also designed. The computational simulation using the analytic model shows that the required performances are confirmed at the temperature range between -200 Υ and

Pk_18 F. KIKUCHI et al.: Recent Status of SELENE-2/VLBI Instrument

+120 Υ. The beam width of the conical beam, which satisfies Observations of Lunar Orbiters in SELENE (Kaguya) for Precise the gain of -5 dBi, is 60 degrees from the antenna boresight. Orbit Determination and Lunar Gravity Field Study, Space Sci. Rev, 154 (2010), pp.123-144. The bandwidth is 140 MHz that covers the frequency of three 14) Kikuchi, F., Liu, Q., Matsumoto, K., Hanada, H. and Kawano, N.: S-band signals and its temperature change. In the future, these Simulation study of differential phase delay estimation by same performances will be confirmed by the breadboard model of beam VLBI method, Earth Planets Space, 60 (2008), pp.391-406. the antenna. 15) Pavlis, D. E., Poulose, S., Rowton, S. C. and McCathy, J. J.: GEODYN II system documentation, Raytheon ITSS Contractor rep, Greenbelt, MD, 2001. References 16) Cremers, C. J., Birkebak, R. C. and White, J. E.: Lunar surface temperatures from apollo 12, The Moon, 3, Issue 3 (1971), pp. 346-351. 1) Wieczorek, M., Jolliff, B., Khan, A., Pritchard, M., Weiss, B., Williams, J., Hood, L., Righter, K., Neal, C., Shearer, C., McCallum, I., Tompkins, S., Hawke, B., Peterson, C., Gillis, J. and Bussey, B.: The constitution and structure of the lunar interior. In: Joliff, B., Wieczorek, M., Shearer, C., Neal, C. (Eds.), New views of the moon. Vol. 60 of Reviews in mineralogy & geochemistry. Mineralogical society of America and the geochemical society, 2006, pp.221-364. 2) Konopliv, A. S., Binder, A. B., Hood, L. L., Kucinskas, A. B. and Williams, J. G.: Improved gravity field of the Moon from Lunar Prospector, Science, 281 (1998), pp.1476-1480. 3) Hood, L. L., Mitchell, D. L., Lin, R.P., Acuna, M. H. and Binder, A. B.: Initial measurements of the lunar induced magnetic dipole moment using Lunar Prospector magnetometer data, Geophys. Res. Lett., 26 (1999), pp.2327-2330. 4) Williams, J. G., Boggs, D. H. and Ratcliff, J. T.: Lunar fluid core and solid-body tides, Proceedings of the Lunar and Planetary Science Conference XXXVI, 2005. 5) Goossens, S., Matsumoto, K., Liu, Q., Kikuchi, F., Sato, K., Hanada, H., Ishihara, Y., Noda, H., Kawano, N., Namiki, N., Iwata, T., Lemoine, F. G., Rowlands, D. D., Harada, Y. and Chen, M.: Lunar gravity field determination using SELENE same-beam differential VLBI tracking data, J. Geod., 85 (2011), pp. 487-504. 6) Williams, J. G., D. H. Boggs and J. T. Ratcliff (2012), Lunar moment inertia, Love number and core, Abstract #2230 of the Lunar and Planetary Science Conference XXXXIII. 7) Yamada, R., Matsumoto, K., Kikuchi, F. and Sasaki, S.: Error determination of lunar interior structure by lunar geodetic data on seismic restriction, submitted to Physics of the Earth and Planetary Interiors. 8) Thornton, C. L. and Border, J. S. (2003), Radiometric Tracking Techniques for Deep Space Navigation, JPL Deep Space Communication and Navigation Series, Wiley and Sons Inc., US, 2003, pp. 85. 9) Kikuchi, F., Liu, Q., Hanada, H., Kawano, N., Matsumoto, K., Iwata, T., Goossens, S., Asari, K., Ishihara, Y., Tsuruta, S., Ishikawa, T., Noda, H., Namiki, N., Petrova, N., Harada, Y., Ping J. and Sasaki, S.: Pico-second accuracy VLBI of the two subsatellites of SELENE (KAGUYA) using multifrequency and same beam methods, Radio Science, 44 (2009), pp. 1-7. 10) Kono, Y., Hanada, H., Ping, J., Koyama, Y., Fukuzaki, Y. and Kawano, N.: Precise positioning of spacecrafts by multi-frequency VLBI, Earth Planets Space, 55 (2003), pp. 581-589. 11) Kobayashi, H., Sasao, T., Kawaguchi, N., Manabe, S., Omodaka, T., Kameya, O., Shibata, M., Miyaji, T., Honma, M., Tamura, Y., Hirota, T., Kuji, S., Horiai, K., Sakai, S., Sato, K., Iwadate, K., Kanya, H. Ujihara, T. Jike, T. Fujii, T. Oyama, H. Kurayama, H. Suda, Y., Sakakibara, S., Kamohara, R. and Kasuga, T.: VERA Project, ASP Conference Series 306, 2003, pp.36. 12) Jike, T.: private communication. 13) Hanada, H., Iwata, T., Liu, Q., Kikuchi, F., Matsumoto, K., Goossens, S., Harada, Y., Asari, K., Ishikawa, T., Ishihara, Y., Noda, H., Tsuruta, S., Petrova, N., Kawano, N., Sasaki, S., Sato, K., Namiki, N., Kono, Y., Iwadate, K., Kameya, O., Shibata, K.M., Tamura, Y., Kamata, S., Yahagi, Y., Masui, W., Tanaka, K., Maejima, H., Hong, X., Ping, J., Shi, X., Huang, Q., Aili, Y., Ellingsen, S., and Schlüter, W.: Overview of Differential VLBI

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