Asteroid Itokawa model

The Hayabusa spacecraft sent by Japan Aerospace Exploration Agency (JAXA) ob-served the near-Earth asteroid 25143 Itokawa (Itokawa from now on) during the in-terval from September through early December 2005. The onboard instruments measured a variety of data to determine the shape, mass, and surface topography, as well as the spectral properties of the asteroid. On 20 and 26 November 2005, the spacecraft landed on the Muses-C region of the asteroid to capture dust parti-cles from the surface. The sample capsule landed back to Earth in Woomera, South Australia, on 13 June 2010. The analysis of the sampled dust particles confirmed the earlier terrestrial remote sensing classification[11]and the remote sensing observa-tion of Hayabusa[1]of Itokawa being an S-type asteroid composed of ordinary LL4 to LL6 chondrites, and indicated that the particles had suffered from long-term ther-mal annealing and subsequent impact shock, suggesting that Itokawa is a rubble-pile asteroid made of reassembled pieces of the interior portions of a once larger asteroid [55].

The shape of Itokawa resembles a potato or a sea otter. It has a clear ”head” re-gion and a ”body” rere-gion separated by a ”neck”. The Muses-C rere-gion, where the dust samples were collected, is located in the concave part, close to the neck of the asteroid. The surface is smoother in that region, whereas in other parts the terrain is significantly rougher, consisting mainly of numerous boulders. Based on remote sensing spectral analysis[1], there is no substantial difference in the mineralogical composition over the asteroid’s surface although the roughness of the terrain varies.

Figure 3.1 shows the high-resolution surface model[37]of the asteroid in three di-rections rotated around the x axis, and the corresponding smoothed surfaces, which

Orientation Detailed surface Smoothed surface

Figure 3.1 The detailed the smoothed model surfaces of the asteroid Itokawa from different views. The smoothed surface was used as the surface for the FE model. The smooth Muses-C region is clearly visible in the bottom views of the asteroid. The data for depicting the high-resolution surface has been obtained from [37].

are used here as a basis for the numerical asteroid model, and the 3D-printed asteroid analogue.

During the rendezvous with Itokawa, the instruments on Hayabusa determined the basic physical characteristics of the asteroid. The orthogonal axes of Itokawa are 535, 294, and 209 meters in the x, y, and z directions, respectively, and the rotational period 12.1 hours[33]. The mass of the asteroid was measured as(3.58±0.18)·10¹⁰ kilograms, and the volume approximately(1.84±0.09)·10⁷m³[1]. The estimated bulk density of the asteroid was hence 1.95±0.14 g/cm³, which is significantly less than that of S-type asteroids on average[16], suggesting a significant level of macro-porosity of up to approximately 40 % of the total volume[33].

To enable a creation of a conforming tetrahedral finite element mesh, the smoothed Itokawa surface (Figure 3.1, right column) was used. The interior structure of the model was based on the physical measurements by Hayabusa on Itokawa[1, 33, 55, 66], and impact simulations, which suggest that the internal porosity of the asteroid

Figure 3.2 The structural FE model of the Detail Model (DM) target domain based on asteroid Itokawa’s surface model, showing the different structural compartment surfaces in the ellipsoidal void structure.

varies, and that it increases towards the centre implying a slightly more porous sur-face[20, 24, 41]. Therefore, the target asteroid domainD for the three-dimensional Detail Model (DM) based on Itokawa’s surface model was constructed to include an interior structure where there is a surface layer (mantle), and a deep interior com-partment containing interior details such as an ellipsoidal void. The surfaces of each of the finite element model compartments were meshed with triangular elements providing the nodes and edges for volumetric tetrahedral meshing. The triangular surface mesh structure of the asteroid containing a mantle and an ellipsoidal void is shown in Figure 3.2. The Homogeneous Model (HM), which was used as the background permittivity distribution in the computations, only includes the outer surface of the target domainD, and a homogeneous permittivity distribution within the interior.

The dielectric permittivity of the model was chosen based on the data on the porosity and mineralogical composition of the model asteroid. The permittivity val-ues of rocky materials found on Earth exhibit some correlation with density. Com-pact rocks with little porosity usually have relative permittivity values between 3.0 and 10.0[3]while highly porous materials are found in the lower end of the range.

For S-type asteroids, the real part of the electric permittivity is between 7.0 and 10.0 for solid, non-porous material, and the value decreased as the porosity increases, be-ing between 3.7 and 4.8 when the porosity is 40 %[38]. The loss tangent ranges for the solid and 40 % porous materials are 0.010 and 0.007, respectively[38]. Consid-ering that the analysis of the CONCERT signal revealed that the overall real part of the permittivity of the comet 67P/Churyumov-Gerasimenko was 1.27±0.05, and that the permittivity of dust including 30 percent porosity was less than 2.9[39], the relative permittivity values for the Itokawa model used here were chosen

accord-ingly thus producing a complex-shaped, high-contrast target for radar tomographic investigations.

The mantle of the asteroid model based on the Itokawa shape was thus assigned the real permittivity value of 3.0, and the interior compartment the value of 4.0. The permittivity of the deep interior ellipsoidal void detail was that of free space, 1.0.

These values were used as the target references when constructing the 3D-printed analogue object using the finite element mesh and choosing the appropriate dielectric plastic materials for model printing purposes.