The sunlit conditions of the lunar polar regions were estimated by using a digital elevation model made by the laser altimeter data onboard the Japanese lunar orbiter KAGUYA (SELENE). The result shows that i) there are no peaks of eternal light in either north or south polar regions, ii) most continuously lit surfaces are 89% for north and 86% for south, iii) there are permanently shadowed regions. These information will be useful for the long-durable landing experiments on the Moon and possibly for the human activity on the Moon in the near future.
 The Moon is the first destination for the future human activity on the solar system planets, because it is the nearest celestial object to the Earth. However, the Moon has a quite severe environment. Its atmosphere is so tenuous that the temperature of the lunar surface is susceptible directly to the incoming solar light. During the day, the temperature rises to more than 390 K. Once the Sun sets, the surface is quickly cooled by the infrared radiation to less than 110 K [Heiken et al., 1991]. Moreover, the Moon rotates once in a month, which means that the lunar night and day last for up to almost two weeks. As a result, the temperature difference between the days and nights becomes about 280 K, and if we put bare science instruments without any self-power generation equipment such as radioisotope thermoelectric generator (RTG) on the equatorial or midlatitude regions, the heat cycle could damage the instruments. Also, it has long been estimated that in the permanently shadowed regions there could be water ice deposits which would be useful for the in-situ resource utilization (ISRU) for the human activity on the Moon [e.g., Bussey et al., 1999; Margot et al., 1999]. Therefore, the knowledge of the duration of the sunlit period is important to estimate the surface temperature of the Moon. For example, simulation results by Vasavada et al.  showed that the temperature of poles would be 159 K and that in the floor of bowl-like craters would be as low as 40 K [Vasavada et al., 1999, Figure 12]. In simple assumption, because the spin axis of the Moon has an inclination of 1.6 degrees from the ecliptic plane, regions above latitude of 88.4 degrees could enjoy the long summer time, and vice versa on winter. But due to the complicated local topography, illumination condition changes significantly.
 In 1960's the permanently shadowed regions were firstly pointed out to be the possible locations for the water ice deposits on the Moon [Watson et al., 1961; Bussey et al., 1999, and references therein]. The Clementine mission in 1994 collected visible images for both poles, but the data coverage was limited to the summer in the northern hemisphere due to the short mission life. Earth-based radar observations were also carried out for the same purpose [Stacy et al., 1997; Margot et al., 1999], but the visible areas from the Earth are limited due to the synchronous rotation and small librations of the Moon. As a result, until now, we did not have complete data set appropriate for this study.
 Digital elevation models (DEM) are used to estimate the sunlit condition, but accurate lunar DEMs on the polar regions have not been available as stated above. The laser altimeter aboard Clementine satellite had no direct measurements of the topography above 75 degrees of latitude because of its high altitude from the surface [Smith et al., 1997]. The polar orbit of KAGUYA mission [Kato et al., 2008] enables us to obtain data on the polar regions for the first time, based on which we calculated the illumination condition of the polar regions.
2. Data Used and Calculation Setup
 The laser altimeter (LALT) onboard KAGUYA is a ranging instrument which measures distance between the satellite and the lunar surface with repetition rate of 1 Hz by using 1064 nm Cr-doped Nd:YAG laser light. KAGUYA main satellite flies 100 km ± 30 km above the lunar surface with the inclination of 90 ± 1 degrees. The satellite revolves around the Moon in two hours. The footprint size of the laser spot is typically 40 m, and the data spacing is about 1.6 km in along-track direction. The range resolution is 1 m with 5 m accuracy. The specification, the performance and the operation history of the LALT is described elsewhere (H. Araki et al., Lunar global shape and polar topography derived from KAGUYA-LALT laser altimetry, submitted to Science, 2008). Raw altimetric range data are converted to the local topographic altitude data with respect to the sphere whose radius is 1737.4 km by using the satellite orbit data. In addition to the conventional 2-way range and range rate measurement for the satellite positioning, the KAGUYA mission invoked satellite-to-satellite tracking by using a small sub-satellite when the main orbiter is on the far-side of the Moon for gravimetry (N. Namiki et al., Far side gravity field of the Moon from four-way Doppler measurements of SELENE(Kaguya), submitted to Science, 2008). Therefore we have some variety of models and data selections for the precise orbit determination, namely gravity field models and tracking data. In this paper we used orbit data processed with the SELENE Gravity Model version “e” (SGM90e) with 2-way range and Doppler data of Main satellite. The orbit determination and gravity recovery is an ongoing effort leading to more accurate solutions as the data amount increases. The discrepancy in topography at the intersection of two tracks from different orbits, which is called as the crossover difference, gives a measure of the orbit error and thus also of the derived topography. Currently, the root mean square of the crossover difference is about 50 m, among which the radial orbit error that directly affects the error in the topographic altitude is estimated, from an orbit overlap analysis, to be as small as the order of 1 m or at least less than 10 m.
 For calculation of sunlit conditions, we used a gridded topography data above the latitude of 85 degrees for both north and south polar regions, which is made by using first three-month (1 Jan. 2008 – 31 Mar. 2008) regular operation of the LALT. At first we selected data above latitude of 85 degrees at north and south polar regions, which are gridded by the nearest neighbor method within a 15 km search radius with weight proportional to the distance from the search center so that each bin dimension becomes 470 m by 470 m square at 85 degree latitude, which corresponds to 1/64 degree resolution in latitudinal direction. We drew maps to check the data quality by visual inspection, and we ruled out suspicious data whose orbits seem to be ill-determined. These data correspond to particular orbits in an edge-on geometry (where the normal of the orbital plane is perpendicular to the line from the Earth to the Moon). The data numbers used above 85 degrees latitude at both north/south regions are 173766 and 142655 points respectively. Because of this data selection, small parts near latitude of 85 degrees are lost which originally existed before the data selection. Basically it does not affect the context of this paper, because the region of interest is mainly well over latitude of 86 degrees, especially over 89 degrees. These data gaps should be filled with more accurate topography data, but it is not until after the whole KAGUYA mission complete in the middle of the year 2009 and much more precise gravity field model and orbit are determined.
 Firstly, we calculate the direction of the Sun from the Moon center by using the DE403 ephemeris file at 00:00 UTC for every 24 hours from 1 January 2000 to 31 December 2019 to cover the lunar precession period. We take the apparent radius of the Sun into account when we calculate the solar direction vector, since the apparent radius of the Sun from the Moon is approximately 0.26 degrees while the maximum elevation angle of the Sun from the lunar surface at the poles is 1.6 degrees and this is not negligible. Then we judged the illumination condition by a ray-tracing method for 2000 days (about 5.5 years) due to the limitation of the computing time. We also calculated for 19 years for certain well-illuminated parts to cover the whole lunar precession period, which as a result gave less than 0.5 percent difference between results of 2000 days and 19 years. Here we adopted the lunar-fixed, lunar-centered coordinate system, so that the surface curvature is automatically taken into account. We select one cell and extend the solar direction vector from this cell toward the Sun until we find the Z component of the vector exceeds the altitude of other grid points. If every grid point is under the vector within the calculation area, then this cell is judged as the sunlit region for this particular solar direction. The calculation was done for every grid above latitude of 85 degrees, and we iterated the calculation for each solar direction until the end of the calculation period. It is noted that the illumination condition in the marginal zone is overestimated. Because there are no data beyond the boundary (85 degrees), even if there are higher topography these parts are judged as sunlit regions depending on the solar direction.
 To evaluate the DEM and calculation code, we computed the same period (a month from the end of February 1994) when Bussey et al.  composed the illumination map of the north polar region. Figure 1 shows a comparison with the Clementine mosaic image appeared in their paper and our calculation. The features of illuminated areas in the simulation seem to correspond to those of the mosaic. Partly our result shows overestimation of the illumination, and one of the reasons is that regions where less sunlight comes are counted as illuminated. We also composed an illumination map for the same period of the first mapping phase of the Clementine (not shown). The 100 percent illumination areas near the north pole given by Bussey et al.  are almost retrieved, though our result sometimes show a slightly higher percentage. There can be several reasons for this overestimation: a possibility that high topography at lower than 85 degrees would cast the shadow well above 85 degrees area, or smoothing by means of interpolation when computing the topography grid. Nevertheless, even if there are indications of overestimation of the sunlit areas, if no 100% sunlit area is found in this analysis, it means that one of the aims of this paper, to place an upperbound on the sunlit areas, would not be affected.
Figure 2 shows the topography in both regions above latitude of 85 degrees. The projections are stereographic. The altitude is shown in the color bar, which ranges from −9 to 11 km as color changes from purple to red. For deeper discussion of the topographic results, see Araki et al. (submitted manuscript, 2008).
Figure 3 shows the illumination rate in the same projection as in Figure 2. The color scale corresponds to the illumination rate from 0.01 to 99 percent, with 0 percent in black. As stated above, data are lacking in the small area near (85N, 0E) and (85S, 180E). Also, it should be noted that data on the exact poles are also missing and therefore the data values (nearly zero percent illumination) are artificial, because we applied what is called “the pixel registration” for the expression of grid data for calculation in which the value of each bin is located at the center of the bin, not on the grid. Therefore the pole is not a data point but a boundary between bins. Figure 4 is a close-up figure above latitude of 88 degrees. In Figure 4, areas with rates between 60 and 70, 70 to 80 and those with over 80 percents are added as light blue, green and red dots, respectively. The topography is expressed as contours with 0.5 km level. Zero percent area are expressed as blue so that contours can be visible.
 From Figures 3 and 4, it is evident for both regions that crater rims record higher rate than other parts. Especially, parts of the rim of Peary and Shackleton craters which locates very near to both poles have more than 80 percent illumination (shown in red points in Figure 4). In the north, the highest rate is 89 percent at (88.1N, −117.6E). The area at (89.4N, 127.3E), which is a part of the rim of the Peary crater located at (88.6N, 33.0E), also has high rate as 87 percent. The most illuminated area at south occurs at (88.8S, 124.1E) with 86 percent. A part of the rim of Shackleton at (89.8S, 207.5E) also receives 84% sunlight of the whole period.
 There are more shaded regions in the south than in the north, because there are three large deep craters (Faustini (87.3S, 77.0E), Shoemaker (88.1S, 44.9E) and an unnamed one at (86.5S, 0E)) in the south. In contrast, there is no large crater in the north which results in less long-durable shadow regions. Summarizing the illumination rates, areas with more than 80 percent sunlit regions are 1 and 5 km2 for north and south, respectively. 0 percent illumination areas are 1236 and 4466 km2 for north and south, respectively. For comparison with previous results, if we use data only above 87.5 degrees, these values become 844 and 2751 km2, respectively. These values are comparable to those described by Margot et al.  (1030 for north and 2550 for south), but differs significantly from 530(north) and 6361(south) by Nozette et al.  by Clementine bistatic radar data. These values are summarized in Table 1.
Table 1. Comparison of the Zero Percent Illumination Area With Previous Results Over the Latitude of 87.5 Degrees
 The Shackleton crater is one of the main targets as the landing site for next generation of the lunar exploration. It is located almost at the south pole, with a diameter of 20 km. The peak height is 1.7 km whose illumination rate is about 84%, and the bottom height is −2.8 km. In this crater, areas with an altitude deeper than 0.5 km are almost shaded regions (Figure 4), where water ice deposit is expected to be detected. Parts of regions above 1.5 km have more than 70 percent illumination and these will be suitable for the observation by science instruments or robotic activity. 10 km from this crater in 210E direction, there is a mountain whose peak is 1.9 km, higher than surrounding area by a few hundred meters and enjoys nearly 79 percent illumination. This site is also appropriate for landing because the solar light is available for a long time.
4. Summary and Concluding Remarks
 In this paper, we calculated the illumination rate at the polar regions above latitudes of 85 degrees of the Moon by using LALT data aboard KAGUYA main satellite. The main results are as follows: i) there are no peaks of eternal light in both regions, ii) parts of both regions receive nearly or more than 85% sunlight of the lunar year, iii) there are permanent night places in both regions, and the area for these places is much larger in the south pole. Our data give the best estimate for the illumination condition up to now, since the LALT data cover the whole region with dense data distribution especially near the pole.
 Basically these results do not modify previous extensive works by Clementine images [Bussey et al., 1999, 2005] and radar-based DEM data [Margot et al., 1999; Zuber and Garrick-Bethell, 2005], but it is worth emphasizing that there is no 100 percent illumination area. This information will be useful for the lunar landing experiments for the next decade in which solar power and passive thermal control are of great importance due to the long day and night on the Moon.
 In this paper, we used the orbit of Main satellite which is determined with 2-way range and Doppler data, using SGM90e as gravity field model. In the near future, we need to include four-way Doppler data in the orbit determination process to constrain the orbit over the far side. Orbit determination errors arising from including the relay satellite will need to be assessed. Also, we used the nearest neighbor method for making grid data with a spatial resolution of 470 m at latitude of 85 degrees, but the local topography should be more complicated with smaller-scale variations. Grid data with higher spatial resolution, such as the digital terrain model made by the optical imager (Terrain Camera) aboard KAGUYA, are useful to narrow the candidate of most illuminated area.
 The effect of secondary reflected light is not taken into account in this paper. The reflected light which penetrates into the permanently shaded regions could raise the temperature and the volatile with lower boiling point could sublimate [Vasavada et al., 1999]. Detailed study should be needed with the image data in this respect.
 We are grateful for all the SELENE project team. We thank the LALT development team at the NEC co. Ltd. for development and support for operation of the LALT. We used the Generic Mapping Tool (GMT) software [Wessel and Smith, 1991] for data interpolation and drawing topographic maps.