Present status of ILOM, VLBI and LLR for future lunar missions *

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1 Deep Space Exploration Vol.*, No.*, **-** P u b l i s h e d O n l i n e * * * * in****** DOI: * * * * * Present status of ILOM, VLBI and LLR for future lunar missions * H. Hanada 1,2, S. Tsuruta 1, K. Asari 1, H. Araki 1,2, H. Noda 1,2, S. Kashima 1, K. Funazaki 3, F. Kikuchi 1, K. Matsumoto 1,2, Y. Kono 4,2, H. Kunimori 5, S. Sasaki 6 1 RISE Project, National Astronomical Observatory, Oshu, Japan 2 Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI), Mitaka, Japan 3 Faculty of Engineering, Iwate University, Morioka, Japan 4 Mizusawa VLBI Observatory, National Astronomical Observatory, Mitaka, Japan 5 Wireless Network Research Institute, National Institute of Information and Communications Technology, Koganei, Japan 6 Department of Earth and Space Science, Osaka University, Toyonaka, Japan hideo.hanada@nao.ac.jp Received Month Day, Year (2014). We investigated basic characteristics of the telescope for In-situ Lunar Orientation Measurement (ILOM), such as the centroid accuracy and the effects of temperature change, tilt and ground vibrations, by laboratory experiments using a Bread Board Model and by simulations. We have a prospect to observe the lunar rotation on the lunar surface with the accuracy of 1 milliarcsecond. We will make test observations on the ground in order to evaluate overall characteristics with the target accuracy of better than 0.1 arcseconds. Keywords: Moon, Rotation, ILOM, Telescope, PZT, Mercury pool Introduction Geodetic observation of the Moon, such as the lunar rotation, the gravitational fields and tidal deformation, is one of the essential and basic observations for investigating the interior of the Moon. We are developing instruments for study of internal structure of the Moon in SELENE-2 and future missions., They are radio sources for differential VLBI (Very Long Baseline Interferometer), a retro-reflector for Lunar Laser Ranging (LLR), and a telescope for In-situ Lunar Orientation Measurement (ILOM). VLBI is effective and promising method for orbit determination of artificial satellites. Kaguya mission employed the differential VLBI for orbit determination and gravity study, and attained the accuracy of 1 ps in the differential phase delay of the X-band signal, which resulted in the orbit accuracy of around 10 m (Kikuchi et al., 2009). We can expect that the differential VLBI between artificial radio sources on a lunar lander and a lunar orbiter will measure the doubly-differenced ranges more accurately than Kaguya because there is more chance of the same beam observations (Kikuchi et al., 2014). An S/X-band two-beam system on a ground station can increase the chance for simultaneous observations of the two spacecraft, and we are developing a phase array system using self-complementary antennas. We have also developed an antenna which has a gain of -5 dbi for beam-width of 60 degrees and for bandwidth of 140 MHz in temperature range of -200 to +120 degrees for future landing mission (Kikuchi et al., 2014). We are proposing to put a new retro-reflector on the Moon in order to expand the network of retro-reflectors and to make it possible for many ground stations to participate in the observations, and thus to improve the accuracy of LLR (Sasaki et al., 2012). The reflector on the Moon of not in an array but of a single large one will improve the ranging accuracy up to 1mm order because it will not be affected by the shift of the optical center due to change of the incident angle. We should set dihedral angles which are the angles created by two intersecting surfaces with the accuracy of better than 0.1 arcseconds in order to receive return energy effectively (Otsubo et al., 2011). Therefore Manufacturing method is under development and bonding of three mirrors or integral molding are two alternatives. We are developing also a small telescope like Photographic Zenith Tube (PZT) for observations of the lunar rotation through positioning of stars on the Moon with a target accuracy of 1 milliarcsecond (mas) as an ILOM project. Since the observation is not affected by orbital motion of the Moon and the rotation of the Earth, the observed data are independent to observations by LLR. Observations for longer than one year have a potential to detect small components of the physical librations and the lunar free librations which are related to the lunar interior (Heki, 2000; Petrova & Hanada, 2013). We have already made a bread board model (BBM) and are in a stage of test observations on the ground as the basis for a future lunar telescope. Development of mainly a telescope for ILOM is presented in this paper. Development of a Telescope for ILOM Bread Board Model Copyright 2013 SciRes. 1

2 A. NAME (an abbreviation of the first author s name) ET AL. from the vertical (Hanada et al., 2012). The attitude control system can make the tube vertical within an error of degrees (or about 20 arcseconds) (Funazaki et al., 2008). Ray tracing simulations showed that the effect of temperature change, which is expected to be about 3 mas per degree for an objective with conventional lenses, can be reduced to about 0.1 mas per degree by adopting a diffractive element (DOE) in the objective (Kashima et al., 2012; Kashima et al., 2013). We made laboratory experiments by using the BBM and an artificial light source in order to know the effect of ground vibrations upon the stellar position on the focal plane. It is anticipated that the mercury surface as a reflector may magnify the effect through the surface vibrations. Three copper vessels of 84 mm diameter with a conical bottom surface of different depth, 0.25 mm, 0.5mm and 1mm, were used for the experiments. Copper amalgam is formed inside of the vessel for reducing the effect of surface tension of mercury (Tsuruta et al., 2014). Ground Experiment Model Figure 1. Optical system of PZT. 1: objective, 2: plain parallel, 3: prism, 4: CCD, 5: mercury surface. The PZT is a kind of zenith telescope with a mercury pool as a reflector at the middle point of the focal length of the objective. Stellar images on the focal plane at the nodal-plane of the objective does not shift in principle even if the tube inclines a little except the effect of aberration, since the optical path reflected at the mercury surface does not change by the tilt. We have already developed a bread board model (BBM) of a telescope for basic experiments of ILOM. Technical development for improvement of accuracy, environmental test of key elements were made by using the BBM in cooperation with JASMINE project of National Astronomical Observatory of Japan (NAOJ) and Iwate University. The optical system of PZT is shown in Figure 1 and the specification is shown in Table 1. We improved the BBM for aiming at observations on the ground and developed so called Ground Experiment Model or Ground Model in short as shown in Figure 2. A new tripod makes it possible to set the telescope on the slope of less than 30 degrees. PZT has a potential to observe deflection of the vertical (DOV) with an accuracy better than 0.1 arcsecond (Hirt & Bürki, 2002; Li et al., 2005). It is not always possible, however, to observe DOV with such a high accuracy on the ground since the environments such as the atmosphere, ground vibrations and the air temperature can perturb the images of stars. It is important to confirm how accurately we can observe DOV under the condition on the ground. Spacial resolution of a telescope generally depends on astronomical seeing, diffraction limit and pixel size of CCD. The latter two factors are inherent in the optical system and detectors and do not depend on environments. The diffraction limit, which is represented as the radius of the Airy disk, is the best focused spot of light through a perfect lens with a circular aperture, limited by the diffraction of light. The diffraction limit θ [rad] is expressed as θ = 1.22λ/D with λ of Table 1. Specification of the telescope Aperture 0.1m Focal Length 1m Type PZT Detector CCD Pixel Size 7.4μm 7.4μm ( ) Number of Pixels Angle of View rad (12 12 ) We succeeded in determination of star position with the accuracy of about 1/300 pixel, which corresponds to about 3 mas for the PZT with 1m focal length and CCD with pixels of 5μm 5μm (Yano et al., 2004). Effect of tilt is compensated according to the principle of Photographic Zenith Tube (PZT). The error of the compensation is less than 1 mas if the tilt is within about 80 arcseconds Figure 2. The Ground Experiment Model. 2 Copyright 2013 SciRes.

3 A. NAME (an abbreviation of the first author s name) ET AL. wavelength and D aperture. It becomes (1.5 arcseconds) when D = 0.1m and λ = 600nm. It is possible to determine stellar position better than the diffraction limit by centroid estimation which fits the stellar image to a point spread function. We assume the centroid estimation as well as the pixel size of CCD in setting the target accuracy of ILOM of 1 mas. The diffraction limit and the pixel size of CCD are not important in comparison between the observations on the lunar surface and those on the ground. The astronomical seeing or the seeing in short, on the other hand, is an index how much the Earth's atmosphere perturbs the images of stars as seen through a telescope, and depends on the place, season and time of the day. The seeing is normally about 1 even under a good condition on the ground, and the seeing of 0.4 was attained at the top of a high mountain such as Mauna Kea in Hawaii which is one of the best places for astronomical observations. There are two alternatives; to increase integration time or to adopt the adaptive optics, for reducing the effect of the atmosphere. The adaptive optics, however, is not adequate for astrometry such as ILOM since it can shift the stellar position in the course of compensation using a tip tilt mirror and deformable mirrors. We can reduce the effect of atmospheric turbulence by lengthen the integration time if we suppose the flickers are random phenomena. Roughly speaking, the standard error of the mean will be 1/10 of the standard deviation if we get 100 data during the integration time. Long integration time contribute also to improve the signal to noise ratio (SNR), which results in improvement of the accuracy in determination of stellar position. There is a limit, however, in the integration time for observations using PZT since it does not track the stars. Stars move in the field of view according to the rotation of the Earth. Time when a star is within a field of view corresponds to the maximum integration time in this case. The maximum integration time depends on the rotation rate of the Earth. It is estimated that the maximum integration time is 48 s from the angular velocity of the rotation of the Earth of 7.3 rad/s and the angle of view of rad. Considering the integration time of longer than 100 s assumed in ILOM (Hanada et al., 2012), we cannot expect to attain the accuracy of the observation on the ground comparable to that on the Moon by lengthening the integration time far longer than 100s. Eventually, it will be possible to reduce the effect of atmospheric turbulence to be smaller than 0.1 although further improvement is difficult in this situation. Preliminary Experiment Ground vibration is also the factor which can affect the accuracy of astronomical observations as has pointed out above, and it is inevitable if we carry out the observations on the ground. We must pay special attention to the mercury pool in the telescope relating to the ground vibrations (Tsuruta et al., 2014). We investigated how CCD image of a star moves by ground vibration through vibration of the mercury surface as a preliminary experiment to observations on the ground. We recorded Figure 3 Variations of stellar position observed by the Ground Model with the mercury pool of 0.5mm depth. Upper : X-component, Lower : Y-component. Time : 2013/12/3 15:51:30 15:52:30 Figure 5 Power Spectra of the variation of stellar position in the case with a mercury pool of 5mm depth (upper), and that with a mirror instead of it (lower). Figure 4 Variations of stellar position observed by the Ground Model without a mercury pool. Upper : X-component, Lower : Y-component. Time : 2013/12/3 14:55:16 14:56:16 Figure 6 Power Spectra of ground vibrations for the period corresponding to the experiment with the mercury pool (upper) and that with a mirror instead of it (lower). Copyright 2014 DeepSpace. 3

4 A. NAME (an abbreviation of the first author s name) ET AL. the variation of the centroid of artificial stellar images fitted to Gaussians for 60 s with 30 Hz sampling frequency. Ground vibrations were observed by 3 components of velocity seismometers with a natural frequency of 1 Hz. Figure 3 shows the variation of the centroids when the mercury pool of 0.5 mm depth was used. We also observed the variation of the centroids in the case when the mercury pool was not used but a plane mirror was used as a reference (Figure 4). There is no big difference between the two sets of records. Then, we compared them in power spectra as shown in Figure 5. There is also no big difference between them except that the power between 0.5 and 1 Hz are relatively larger in the case with the mercury pool. Further, there are no strong peaks at around 0.5, 1.0 and 2.0 Hz as been seen before (Hanada et al., 2014). The possible causes for the no noticeable difference are that the amplitude of ground vibrations is not big enough to excite the mercury surface, that there is no power in the ground vibrations near the resonance frequency of the mercury surface, and that we made a stronger frame for a mirror which guides the beam from a light source (artificial star) to the telescope. The ground vibrations, on the other hand, are almost similar in both cases (Figure 6). With respect to the amplitude of the variation of the centroid, it exceed m in the frequency range lower than 0.5 Hz. This large amplitude seems to be related to the ground vibrations since the spectra of the centroid and ground vibrations are similar in this range. More specifically, the peaks at about 0.06, 0.16, 0.35, 0.45, 0.48, 0.65 and 0.74 are seen both in the centroid and ground vibrations. We can confirm the similarity also from time series data. Figure 7 shows the comparison between the centroid data and vibration data for 20 s in which the variations are larger and more remarkable. There are long period variations with the periods of a few seconds in both data. There are stronger correlations between (x, y) components of the centroid data and (NS, EW) components of the vibration data, respectively. It seems to be possible to reduce the effect of the ground vibrations to be less than m if we correct for the variation of the centroid by using vibration data. The relation between the centroid variation and the ground vibrations, however, can be different for the future observations on the ground since the Figure 7 Comparison of the viriation of the centgroid and the ground vibrations for the period from 15;52:00 to 15:52:20) configuration for the preliminary experiment in a laboratory using an artificial star and that for the observation on the ground outside are different. The effective method for the correction is future issues. Concluding Remarks We will perform observations on the ground by using the Ground Model in order to check the total system of the telescope and the software. It is also important to evaluate the effect of the ground vibrations and temperature change upon the stellar position on CCD. The goal of the observations on the ground is to attain the accuracy of better than 0.1 arcseconds. There are important targets for the observations, such as the variation of DOV caused by seismic or volcanic activity. Verification of 1 mas on the Moon will be possible in a specially equipped laboratory in the future. Acknowledgements The experiments in this work were supported by Advanced Technology Center (No ). This work was supported by Grant-in-Aid for Scientific Research (A) (No ) from Japan Society for the Promotion of Science. This research was also supported by JSPS Bilateral Joint Research Projects between Japan and Russia ( ). 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