Lunar Gravity and Rotation Measurements by Japanese Lunar Landing Missions

Trans. JSASS Aerospace Tech. Japan Vol. 10, No. ists28, pp. Tk_33-Tk_36, 2012 Topics

1) 1) 1) 1) 1) 1) By Sho SASAKI , Hideo HANADA , Hirotomo NODA , Fuyuhiko KIKUCHI , Hiroshi ARAKI , Koji MATSUMOTO , 2） 3) 1) 4) 5) Hiroo KUNIMORI , Takahiro IWATA , Sander GOOSSENS , Toshimichi OTSUBO and Ken-ichi FUNAZAKI

1)RISE Project, National Astronomical Observatory of Japan, Oshu, Japan 2)The National Institute of Communication and Technology, Koganei, Japan 3)Institute of Space and Astronautical Science, JAXA, Sagamihara, Japan 4)Faculty of Social Sciences, Hitotsubashi University, Kunitachi, Japan 5)Department of Mechanical Engineering, Iwate University, Morioka, Japan (Received June 27th, 2011)

Measurements of lunar gravity and rotation are important because they provide information of the physical state of the lunar interior. Previously only passive LLR (Lunar Laser Ranging) using CCR (corner cube reflectors) has been applied for the detailed study of lunar librations, rotation variability. As for candidate instruments for SELENE-2 (forthcoming lunar landing mission by JAXA) and future lunar missions, we propose VLBI (inverse-VLBI and differential VLBI) for gravity measurement to constrain tidal Love number, LLR and ILOM (In-situ Lunar Orientation Measurement) for libration measurements.

Key Words: Tidal Love Number, Lunar Libration, Lunar Laser Ranging, VLBI, ILOM

1. Introduction

Precise measurements of gravity and rotation of planets are important methods together with seismic methods to investigate their internal structure. The Moon revolves around the Earth once in a month synchronously with its rotation. It is tidally deformed by the Earth, which would excite irregular motion of the lunar rotation with small amplitude, which is called forced librations. Additionally, free libration would be excited by impacts, fluid core (if exists), and orbital resonance. Dissipation of the libration terms of lunar rotation may depend on the interior structure of the Moon, especially the state of the core and lower mantle1-3). Effect of tidal deformation should also appear on gravity. Long-term

(> a few months) gravity measurements can provide Fig. 1. Degree 2 tidal Love number k2 of the Moon for various 5) information of the lunar tidal deformation. One important solutions . Errors for k2 are based on ten times the formal error.

scale of tidal deformation is degree 2 tidal Love number k2, Data from 1 to 4 are obtained from gravity and LLR observations. which could constrain the state of the core (solid or liquid) and The values of SGM100h and SGM100i are based on KAGUYA data 4) viscosity of the lower mantle of the Moon . without and with VLBI data, respectively 4). Model values (from 5 Figure 1 shows degree 2 tidal Love number k2 estimated to 10) are calculated for various core sizes in the cases of solid core 5) from LLR (Lunar Laser Ranging) and gravity measurements . and liquid core, under 2-week arc length, 12-week mission length, 6 Also shown are model values from numerical simulation hours/day 2-way Doppler observation and S-band same-beam VLBI under a priori lunar interior model. There are discrepancies observation by VERA network as SELENE-VLBI 6). of k2 values between gravity and LLR measurements. The estimated value from LLR is low and solid core is more SELENE-2 is planed as a follow-on mission of KAGUYA preferable, simply from k data. On the other hand, 2 (SELENE). The spacecraft is to be launched in 2010's. estimated values from gravity measurements are higher and SELENE-2 lands on the nearside of the Moon and investigates they prefer liquid core. But as seen in Fig. 1, k depends on 2 the surface and the interior of the moon. SELENE-2 also has the core size. We need to determine the k2 with errors less than a few per cent and compare it with core size value an orbiter for data transmission. As for candidate determined from seismic measurements. instruments for SELENE-2, we propose detailed measurements of lunar rotation by LLR 1,3,7,8) and gravity measurement by iVLBI (inverse-VLBI) 9) and dVLBI

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(differential VLBI). As a complimentary instrument for the determination of core size, a set of seismometers are also proposed for SELENE-2. For a future lunar mission, especially for a lander on the polar region of the Moon, we propose ILOM (In-situ Lunar Orientation Measurement) 2).

2. Inverse and differential VLBI

Very long baseline interferometry (VLBI) is conventionally Fig. 4. The principle of inverse VLBI in the case of landers. The used for precise positioning of radio source. Radio signal differential range (T2-T4)*c is used to estimate rotation variability. transmitted from a radio source, such as a radio star, a quasar or spacecraft, is received at two separate ground VLBI In SELENE-2 mission, we will have VLBI radio (VRAD) stations (Figure 2). These signals are cross-correlated and sources both in the lander and the orbiter. Then, using VLBI, difference of signal arrival times, so-called delay time, is we will determine the orbit of the orbiter precisely to have measured. In the spacecraft navigation, delay time of VLBI is sensitive to motion of spacecraft in a direction perpendicular very accurate low degree gravity coefficients. The to line of sight (LOS) in contrast to range and Doppler which same-beam VLBI observation is only possible when the are sensitive to LOS direction. Using both Doppler and VLBI, separation angle between the two radio sources is smaller than precise orbit determination can be possible. the beamwidth of the ground antennas. The relatively large In KAGUYA (SELENE) mission, multi-frequency VLBI shape of Rstar’s orbit (perilune 100 km x apolune 2400 km) observations (S/X bands) are used for the precise did not allow the same-beam observation all the time. But the determination of orbits of satellites leading to increase in the situation can be improved by adequately setting the orbit such accuracy of lunar gravity field6). Using differential VLBI as lowering the apolune. For example, the Vstar-like orbit (dVLBI) between subsatellites Rstar and Vstar, when both the (100 km x 800 km) will almost always keep the separation radio sources were within a beam of the ground antenna angle smaller than the S-band beamwidth of domestic VERA (so-called same-beam), atmospheric and ionospheric stations since one of the radio sources is fixed on the near-side disturbances are almost cancelled out by the simultaneous lunar surface. observation. Using Doppler tracking data and same-beam In the case of inverse VLBI, radio signals transmitted from differential VLBI data, an improved lunar gravity field model radio sources both on the lander and the orbiter are received at SGM100i was obtained 4) a ground station 9). These signals are cross-correlated and the difference of propagation times from the sources to the ground station is measured. The desired accuracy of the measurement is predicted to several to several tens picosecond. Figure 3 is a configuration of inverse VLBI for the estimation of the gravity field The difference of the propagation times between orbiter to ground station and lander to ground station T1-T3 is measured. Here, 2-way ranging is carried out to compensate for the propagation time between orbiter and lander T2. The differential range (T1-T3)*c is used to estimate gravity field through precise orbit determination of the orbiter. Fig. 2. The principle of VLBI observation. Combination of dVLBI and iVLBI should improve the orbital information greatly, which would precisely determine the change of low degree gravity coefficient and constrain tidal

Love number k2. A crucial issue for VLBI radio sources is the survival of lunar night of the lander. In SELENE-2 mission, the lander radio source is installed within the survival unit of thermal blanket using stored heat in regolith. If we can use radio signals from another lander (Fig. 4), combination of dVLBI and iVLBI for landers can provide information of rotation variability especially librations, which are discussed in Fig. 3. The principle of inverse VLBI in the case of an orbiter and a following sections. Therefore, we should seek a possibility lander. of simultaneous observation between SELENE-2 lander and another lander in the framework of recently discussed ILN

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(International Lunar Network). provide information on various components of the physical librations, and possibly that on the lunar free librations in 3. LLR (Lunar Laser Ranging) order to investigate the lunar mantle and the liquid core. A photographic zenith tube (PZT) telescope, which is similar to The Lunar Laser Ranging (LLR) is the method to measure ones used for the international latitude observations of the the distance between the Earth and the Moon using laser beam Earth, is applied to ILOM. Although ILOM optical telescope from the ground station. For more than 40 years since the is small in size (20 cm in diameter), it can be stated as a Apollo and the Lunokhod mission placed retroreflectors on precursor for the future larger telescope. the Moon, LLR produced data on the lunar rotation as well as the lunar orbital evolution. A strong advantage of LLR over the other methods is the capability of long-term observation, since the retroreflectors need no electric power. On the basis of LLR data, the state of lunar interior is discussed. Williams et al.1) discussed the dissipation between the solid mantle and a fluid core from LLR data. LLR observation has also provided information of moment of inertia and tidal Love number of the Moon. Discussion on the tidal Love number was already introduced in Section 1. A new LLR should be on board SELENE-2. Instead of conventional corner cube reflector (CCR) array, we are planning to use a larger single reflector. This has an advantage over the conventional CCR array, because a single cube should have smaller distance variation within the reflector upon monthly libration of the lunar rotation. The new reflector should be somewhere in the southern hemisphere on the nearside Moon. Then in combination Fig. 5. BBM of ILOM model. Attitude control system is attached to with pre-existed reflectors, latitudinal component of lunar the outside of the telescope tube. Optical tests with CCD and light libration and its dissipation can be measured precisely. sources are performed using this model. Apollo and the Lunokhod settled 6 retroreflectors on the surface of the Moon. With newly found Lunokhod 1 The observed stellar trajectories should be decomposed to reflector, 5 reflectors are useful. Since then, more than 40 librations, polar motion, and the precession, where the years, lunar rotation data have been accumulated. After the amplitude and phase of each component are estimated. start of Apache-point station in 2006, the precision of distance Thermal and mechanical perturbations during observation determination has improved to mm level. With a new should be suppressed. Simulated standard deviation of the reflector by SELENE-2 possibly on the southern hemisphere parameter estimation becomes nearly 1 milli-arcsecond, which of the Moon, more decadal observations should increase the accuracy of parameters controlling lunar rotation variability. will be better than the Lunar Laser Ranging observation. The results would constrain the size, density, state of the core (and lower mantle) through the moment of inertia and tidal 4. ILOM (In-situ Lunar Orientation Measurement) Love number. More theoretical study in relation to the interior structure is being developed by Petrova et al.10). The ILOM (In-situ Lunar Orientation Measurement) is an We have developed a BBM model of ILOM at Iwate experiment to measure the lunar physical librations in situ on University (Fig. 5). This BBM was made for the tests of the Moon with a small telescope, which tracks stars 2). Since controllability and optical characteristics. Since the lunar ILOM on the Moon does not use the distance between the surface is covered with regolith, the precise attitude control of Earth and the Moon, the effect of orbital motion is clearly ILOM PZT telescope is inevitable after its deployment on the separated from the observed data of lunar rotation. This is lunar surface. The crucial issue that should be overcome is the survival of the advantage of ILOM over the ground-based methods such lunar night and thermal effect of solar illumination on the as LLR and VLBI. zenith tube. The thermal effect should affect the optical The ILOM will observe the lunar physical and free pointing. If ILOM telescope is put on the lunar polar region librations from the lunar surface with an accuracy of 1 and can use stable electric power, those can be overcome. If millisecond of arc. If ILOM telescope is put on the lunar a telescope is put on mid-to-low latitude (as currently polar region, it can detect spiral trajectories of the stars. If a suggested by SELENE-II), the lander should have a battery to telescope is put on mid-to-low latitude on the moon, it can still keep telescope electronics alive during the lunar night for the derive information of lunar rotation from the motion of the survival and stellar observation might be limited during stars. Long-term (possibly longer than a half year) data will daytime when enough electric power can be used.

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Orientation Measurement (ILOM), Proc. Int. Ass. Geod. (2005), Springer, pp.163-168. 3) Boggs, D. and Williams, J. G.: Lunar core and mantle. What does 5. Conclusion LLR see ? Proc. 18th Int’l Workshop on Laser Ranging, (2009), pp.101-128. 4) Goossens, S. et al.: Lunar gravity field determination using Precise measurements of lunar gravity rotation are SELENE same-beam differential VLBI tracking data, Journal of important for the study of lunar interior, especially the state of Geodesy, 85 (2011), pp. 205-228 the core and lower mantle. To measure very small change of 5) Matsumoto, K. et al.: VLBI radio sources on a lander and an orbiter for study of lunar internal structure proposed for SELENE-2 direction and/or distance, instruments on board lunar lander mission, Geophysical Research Abstracts 13, EGU2011-2032-1, are desirable. As for candidate instruments for SELENE-2 (2011) (forthcoming lunar landing mission by JAXA) and future 6) Currie, D. G. et al.: A Lunar Laser Ranging RetroReflector Array for the 21st Century, NLSI Lunar Science Conference (2008), lunar missions, we propose VLBI (inverse-VLBI and #2145. differential VLBI), LLR (Lunar Laser Ranging) and ILOM 7) Murphy, T. W. Jr. et al.: The Apache Point Observatory Lunar (In-situ Lunar Orientation Measurement). Laser-ranging Operation: Instrument Description and First Detections, Publications of the Astronomical Society of the Pacific, 120, (2008), pp. 20-37. 8) Battat, J. B. R. et al.: The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO): Two Years of Acknowledgments Millimeter-precision Measurements of the Earth-Moon Range, Publications of the Astronomical Society of the Pacific, 121, The authors acknowledge SELENE-2 team of JAXA for the (2009) , pp. 29-40. 9) Kawano, N., Hosokawa, M., Hanada, H. and Imae, M.: Inverse stimulus discussion and support for the development. VLBI Method for Planetodesy, J. Geodetic. Soc. Japan 45 (1999), Thoughtful review by a referee is acknowledged. (in Japanese). 10) Petrova, N., Gusev, A., Kawano, N. and Hanada, H.: Free Librations of the Two-Layer Moon and the Possibilities of Their Detection, Adv. Space Res. 42 (2008), 1398-1404. References

1) Williams, J. G., Boggs, D., Yoder, Ch., Ratcliff, J. and Dickey, J.: Lunar Rotational Dissipation in Solid Body and Molten Core, J. Geophys. Res. 106 (2001), pp.27933-27968. 2) Hanada, H. et al.: Application of a PZT Telescope to In Situ Lunar

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