## Abstract

The ranging instrument aboard the Hayabusa spacecraft measured the surface topography of asteroid 25143 Itokawa and its mass. A typical rough area is similar in roughness to debris located on the interior wall of a large crater on asteroid 433 Eros, which suggests a surface structure on Itokawa similar to crater ejecta on Eros. The mass of Itokawa was estimated as (3.58 ± 0.18) × 10^{10} kilograms, implying a bulk density of (1.95 ± 0.14) grams per cubic centimeter for a volume of (1.84 ± 0.09) × 10^{7} cubic meters and a bulk porosity of ∼40%, which is similar to that of angular sands, when assuming an LL (low iron chondritic) meteorite composition. Combined with surface observations, these data indicate that Itokawa is the first subkilometer-sized small asteroid showing a rubble-pile body rather than a solid monolithic asteroid.

The light detection and ranging instrument (LIDAR) aboard the Hayabusa spacecraft, described in (*1*–*4*), provided information on the shape, surface topography, and mass of the near-Earth asteroid 25143 Itokawa. The LIDAR measures distance by determining the time of flight for laser light to travel from the spacecraft to the asteroid and return. The stop time measured by the LIDAR is obtained by filtering a pulse received from the surface and measuring its time of peak intensity. In this manner, the LIDAR averages the topography within the LIDAR footprint on the surface of the asteroid, which approximates 5 by 12 m at a 7-km altitude for normal incidence. It was found that this pulse-detection technique permits identifying features smaller than the LIDAR footprint.

The LIDAR operated from September 10, 2005, at a distance of 49 km from the target, through November 25; a total of 4,107,104 shots were fired, and 1,665,548 returns were detected. The numbers of returns reduced significantly after October 2 when spacecraft pointing was less accurate because of failures in two of the three on-board reaction wheels.

When the spacecraft arrived at Itokawa, we used two methods to confirm the accuracy of LIDAR ranging obtained from ground calibration of the LIDAR instrument (*3*) (±1 m from a distance of 50 m and ±10 m from 50 km). In one approach, the size of the spacecraft shadow that was cast on the asteroid surface at the center of opposition point in a navigation image equaled that expected given the LIDAR-measured range measured by the spacecraft. In another approach, the height of the largest boulder on Itokawa, namely Yoshinodai, was found to be ∼20 m when using independent measurements obtained from the LIDAR and the narrow angle imager [Asteroid Multiband Imaging Camera (AMICA)].

The LIDAR beamwidth is 0.04° by 0.097°, and the boresight is coaligned with that of the near-infrared spectrometer (NIRS) with its 0.1° by 0.1° field of view. The NIRS alignments relative to the Hayabusa spacecraft, to AMICA, and to the wide-angle optical navigation camera (ONC-W) used for determination of the spacecraft position relative to the asteroid (*2*), were determined from in-flight star field calibrations. The coalignment between the LIDAR and NIRS was confirmed when NIRS detected the reflected 1064-nm yttrium-aluminum-garnet–Nd (YAG-Nd) laser light from LIDAR (Fig. 1) and when changes in LIDAR ranges were found to correspond with expected changes in topography seen in AMICA data.

To measure the mass of Itokawa and its surface topography, the position of the Hayabusa spacecraft relative to Itokawa must be determined. We developed a new method (Fig. 2) to estimate this spacecraft position by combining a shape model (*5*) of the asteroid determined primarily from images, ONC-W information on the direction to the center-of-light from the asteroid, and LIDAR ranging data. With these data, a first guess at the spacecraft trajectory is made. Often, substantial discontinuities are observed that cannot be explained by thrusting. By least-squares fitting of a smooth function to the initial spacecraft trajectory, a more realistic smooth approximation is obtained, from which a cloud of LIDAR points sitting on the Itokawa surface can be determined. Checks with the actual location of the LIDAR spot in simultaneous AMICA images show that this method provides accurate spacecraft locations as well as good surface topography.

An example of the detailed surface topography that can be obtained from the LIDAR using this methodology is shown (Fig. 3) for data obtained from ∼7-km range. In this Tsukuba area (*5*), located on the eastern side of Itokawa and representative of the rough regions on the asteroid, blocks from 3- to 10-m elevation are visible. These data contrast significantly with results obtained from the Muses Sea, which is representative of smooth regions on Itokawa (*6*) where small-scale fluctuations in the elevation are observed that are comparable to the digitization of the LIDAR.

From such topographic data, the fractal roughness of the surface can be measured (*7*, *8*) as the root mean square deviation σ of the height differences along a given baseline. For a 20-m baseline, which exceeds the LIDAR footprint, the Tsukuba region is characterized by a σ value of 2.2 m. This is in contrast to Muses Sea, where σ equals 0.6 m. Comparison of σ on Itokawa and Eros indicates that the rough Tsukuba region of Itokawa has a roughness on 20-m baselines similar to that measured in the interior, near the rim, of the large crater Psyche on Eros (*8*). This region in Psyche primarily consists of disrupted materials, strewn boulders, and coarse talus typical of crater ejecta. The similarity in roughness suggests that the near-surface of Itokawa resembles a rubble pile, which AMICA confirms (*1*, *6*). To investigate the interior structure of Itokawa, we also measured the mass of Itokawa to determine its density. We used the best data available to us that the LIDAR acquired during the rehearsal descent phase on November 11, 2005.

The Hayabusa was designed as a simple spacecraft, with fixed antennas on the upper panel perpendicular to the +*Z* direction and fixed instruments on the base panel faced toward the –*Z* direction (toward the asteroid during in situ observations). On November 11, 2005, the Hayabusa spacecraft made a descent for the asteroid Itokawa along an Earth-Hayabusa-Itokawa line so as to allow both high-rate communication with Earth and in situ observations of the asteroid. The solar phase angle, defined as a Sun-Itokawa-Hayabusa angle, was about 8° during the descent.

We estimated the acceleration term *F* of the spacecraft motion by using the descent data from 17:51:17 to 19:35:49 UT on November 11 (Fig. 4A) at distances from the center of Itokawa from 1427 to 825 m. We subtracted the effects of solar radiation pressure and thruster forces from the acceleration to estimate asteroid gravity. The thruster forces depend on injector temperature, and this contribution is presented as a function of thruster-injection rate when the maneuver uses only ±*Z* thrusters. The following relationship was derived from maneuver data obtained in mid-October about 10 km from Itokawa: *F*_{10} (cm/s^{2}) = 0.1603 × (thruster ratio) + 1.5695 × 10^{–5}, where thruster ratio is defined as a ratio of an integrated time of thruster burn to the total time of interest, and the acceleration due to solar radiation is calculated as 1.3303 × 10^{–5} cm/s^{2}.

During the above period of the descent, the thrusters were operated in only ±*Z* directions with a constant temperature of 35°C, and the total number of thruster injections was 136. Because the duration time of each thruster is 19.53 msec, the thruster ratio becomes 4.2348 × 10^{–4}, and the resulting *F*_{10} value is 8.3594 × 10^{–5} cm/s^{2}. We assumed that the acceleration caused by solar radiation force and thruster effect is constant during the descent. As an initial condition, we subtract the above *F*_{10} value from the total acceleration term. Then, to investigate the gravity potential, we adopted a polyhedron method that was well suited to evaluate the gravitational field of an irregularly shaped body such as Itokawa (*9*), where we assumed a constant-density interior of the asteroid.

By least-squares fitting of the spacecraft orbit during descent to calculated orbits obtained with the Itokawa's polyhedron model, we estimate the gravitational potential *GM* of Itokawa, where *G* is the gravitational constant and *M* denotes the mass of the asteroid (Fig. 4B). The resulting value of *GM* leads to the gravitational acceleration at a 10-km altitude, which is then also subtracted from the initial *F*_{10} to obtain an improved estimate of the solar radiation and thruster force. We then iterated the trajectory fit to the descent data to derive a revised value of *GM* using the modified *F*_{10} value and find a best estimate of *GM* equal to (2.39 ± 0.12) × 10^{–9} km^{3}/s^{2}. The gravitational acceleration at the distance of 10 km from Itokawa is ∼0.2392 × 10^{–5} cm/s^{2}, and it is about 3% of the acceleration term there.

Our *GM* value finds the mass of Itokawa to be 3.58 × 10^{10} kg with an uncertainty of 5%. The shape model of Itokawa constructed with AMICA images indicates that the volume is 1.84 × 10^{7} m^{3} within 5% uncertainty (*1*). Consequently, the bulk density of asteroid Itokawa measures 1.95 g/cm^{3} with 7% uncertainty. Our error in mass estimation is significantly larger than that obtained by the laser rangefinder aboard the Near Earth Asteroid Rendezvous mission (*10*), because Hayabusa did not orbit the asteroid, and the mass of Eros is 190,000 times that of Itokawa, producing greater uncertainty in the determination of spacecraft position.

Hayabusa NIRS reported that the Itokawa spectrum near the 1-μm absorption band is similar to those of LL-type chondrites (*11*). Considering the bulk density of LL ordinary chondrites of 3.19 g/cm^{3} (*12*), our bulk density of asteroid Itokawa indicates a high porosity of about 40%, similar to that found for freshly formed coarse angular sands. Such a high porosity of Itokawa is noted in (*1*). It is known that the porosity of five S-type asteroids studied to date does not exceed about 20% (*12*), whereas two M-type asteroids have larger porosity of about 70%, and the average porosity of four C-type asteroids is about 28%. Our porosity for Itokawa is consistent with identification as a “loosely consolidated (rubble-pile) asteroid” (*13*). Itokawa is the first S-type asteroid showing such high porosity, and the first subkilometer-sized small asteroid showing a rubble-pile structure rather than a solid monolithic structure.

Two distinct types of terrain are found on Itokawa, rough terrain with numerous boulders and smooth terrain covered with regolith layer (*6*), which suggests a complex history but does not predicate a heterogeneous composition. In addition, no clear regional difference in the normalized x-ray intensity ratios of Mg/Si and Al/Si has been found on the surface of asteroid Itokawa (*14*), indicating homogeneous composition. NIRS reported olivine-rich mineral assemblages similar to LL5 and LL6 chondrites, with variations in albedo and absorption band depth more than 10%, but this diversity may be consistent with differences in freshness and/or particle size (*11*), and it does not suggest the presence of unusual inhomogeneous materials.

As noted in (*15*, *16*), the size of the asteroid, 150 to 1000 m in radius, may be a transition size between monolithic structure and rubble-pile structure. The large porosity of ∼40% and the roughness of the surface found on Itokawa strongly suggest a rubble-pile structure. The 12.1324-hour spin period of Itokawa (*1*) is far above the critical value of 2 hours, where a rubble-pile structure cannot withstand centrifugal forces [e.g., (*17*)], and is also consistent with a rubble-pile structure.

The internal structure of the asteroid Itokawa gives us a hint of its origin. It is predicted, on the basis of the numerical simulation of orbital evolution of asteroid Itokawa, that the most probable source region of asteroid Itokawa is the inner part of the main belt (*18*). High porosity in asteroid Itokawa may be the result of gravitational aggregation of the collision fragments.