SHAP2 versions of the 67P/Churyumov-Gerasimenko nucleus shape model The SPC versions of the dataset represent the shape models of the nucleus of comet 67P/Churyumov-Gerasimenko as derived using photoclinometry techniques. Images obtained with the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) instrument (including both the Narrow Angle Camera and the Wide Angle Camera) were used in constructing these models The shape models presented here were developed by Laurent Jorda et al. (LAM, Marseille, France) and Robert Gaskell (PSI, Tucson, USA) from two different techniques: Stereophotoclinometry (SPC) and Multi-resolution stereophotoclinometry by deformation (MSPCD). Details about the SPC technique can be found in Gaskell et al., 'Characterizing and navigating small bodies with imaging data', Meteoritics and Planet. Sci. 43, 1049-1061, 2008 [GASKELLETAL2008]. The MSPCD technique has been described in details by Capanna et al., 'Three-dimensional 3D reconstruction using multiresolution photoclinometry by deformation', The Visual Computer 29, 825-835, 2013 [CAPANNAETAL2013]. Both techniques allowed modeling of the areas of the surface illuminated and visible in the Rosetta images. Additional information about the nucleus of 67P can be found in Sierks et al., 'On the nucleus structure and activity of comet 67P/Churyumov-Gerasimenko', Science 347, aaa1044, 2014 [SIERKSETAL2014]. SHAP2 Version of the model --------------------------- The SHAP2 models represent the first archived versions of the 67P nucleus, and were used for the first series of publications. These models were produced using images obtained up through 3 August 2014. This was before the south pole had become illuminated, so there are regions on the surface that are not constrained by observations. These unconstrained areas of the surface appear smooth in the models. OSIRIS obtained body-resolved images during the approach phase to comet 67P/Churyumov-Gerasimenko, before the spacecraft started orbiting the nucleus on August 6, 2014. Four sets of images were used during the model construction. The acquisition dates are as follows: (1) between July 14, 14:24 UTC and July 15, 02:04 UTC, (ii) between July 21, 14:34 UTC and July 22, 00:44 UTC, (iii) on August 1, between 11:49 UTC and 21:24 UTC, and (iv) on August 3, between 11:04 UTC and 21:39 UTC. The images covered about 75 % of the surface, with a spatial scale up to 4.9 m/pix. Reference Frame and Coordinate System --------------------------------------- The spin axis orientation was derived from a stereophotogrammetric analysis of OSIRIS images acquired in between August and early September 2014. The orientation of the models in the J2000 Equatorial frame (EME2000) is described in Scholten, F. et al., 'Reference Frames and Mapping Schemes of Comet 67P/C-G' in the PDF document CHEOPS_REF_FRAME_V1.PDF in the DOCUMENTS directory. The SPC technique led to a spin axis such that the North (positive) pole points to a right ascension of 69.4+/-0.2 deg and a declination of +64.1+/-0.2 deg (J2000), compatible with the more accurate definition given in the above document. The body's coordinate system was defined with the +Z axis in the direction of the spin axis and the prime meridian (+X axis) is defined such that the center of the large boulder named Cheops is at a longitude +142.35 degrees, following the IAU definition presented in the document CHEOPS_REF_FRAME_V1.PDF. The +Y axis completes the right-hand coordinate system. The body center is not exactly coincident with its center of gravity, but the offset is within the uncertainties derived for the surface positions. Data Formats -------------- The models are presented in the standard PDSSBN vertex/triangular plate format (see PDSSBN_PLATE_SHAPE_DEF.ASC in the documents directory) with dimensions of km in cartesian coordinates. The files are presented with VRML wrappers that allow the model to be displayed with existing VRML viewers that are freely available (e.g., INSTANT PLAYER, OCTAGA, CORTONA, etc.). In addition to the PDS formatted files, the models have also been converted to DSK kernels that can be used with the SPICE utilities. For the complex shape of 67P, spherical coordinates (lat/long/radius) result in multiple values in some regions of the nucleus, so the model is not presented in this form. Model Resolutions ------------------- Two different SPC-derived models are included, known as SPC and MSPCD. Each of these models is presented in its highest resolution form, with additional versions degraded in resolution (in steps of ~2). The different resolutions are included to allow calculations to be optimized for a given problem, when the highest resolution is not needed. Additional information on how the high-resolution shape model was degraded into lower resolution versions can be found in H. Hoppe, 'Progressive meshes', Conference SIGGRAPH 96; 23rd International Conference on Computer Graphics and Interactive Techniques. New Orleans, LA, USA — August 04 - 09, 1996, pp. 99-108. DOI: 10.1145/237170.237216 Information contained in the filenames: CG_MSPCD_SHAP2_006K_CART.WRL ^ ^ ^ ^ ^ ^---- File format (VRML, SPICE DSK) | | | | |-------- Cartesian coordinates | | | |-------------- Resolution (# triangular plates) | | |------------------- Shape model generation (currently only SHAP2) | |------------------------- Production Technique (SPC, MPSCD) |------------------------------ Comet C-G Details about the MSPCD SHAP2 files CG_MSPCD_SHAP2_006K_CART.WRL - 2894 vertices forming 5784 triang. plates CG_MSPCD_SHAP2_012K_CART.WRL - 5958 vertices forming 11912 triang. plates CG_MSPCD_SHAP2_024K_CART.WRL - 12225 vertices forming 24446 triang. plates CG_MSPCD_SHAP2_048K_CART.WRL - 23780 vertices forming 47556 triang. plates CG_MSPCD_SHAP2_098K_CART.WRL - 48893 vertices forming 97782 triang. plates CG_MSPCD_SHAP2_191K_CART.WRL - 95268 vertices forming 190532 triang. plates CG_MSPCD_SHAP2_391K_CART.WRL - 195743 vertices forming 391482 triang. plates CG_MSPCD_SHAP2_760K_CART.WRL - 379794 vertices forming 759584 triang. plates CG_MSPCD_SHAP2_001M_CART.WRL - 655000 vertices forming 1309996 triang. plates Details about the SPC SHAP2 files CG_SPC_SHAP2_006K_CART.WRL - 2860 vertices forming 5716 triang. plates CG_SPC_SHAP2_012K_CART.WRL - 5928 vertices forming 11852 triang. plates CG_SPC_SHAP2_024K_CART.WRL - 12176 vertices forming 24348 triang. plates CG_SPC_SHAP2_047K_CART.WRL - 23656 vertices forming 47308 triang. plates CG_SPC_SHAP2_096K_CART.WRL - 47932 vertices forming 95860 triang. plates CG_SPC_SHAP2_195K_CART.WRL - 97347 vertices forming 194690 triang. plates CG_SPC_SHAP2_399K_CART.WRL - 199434 vertices forming 398864 triang. plates CG_SPC_SHAP2_786K_CART.WRL - 392942 vertices forming 785880 triang. plates TABLE: Shape Model Characteristics (for the MSPCD model) Surface Area: 46.2 km^2 Volume: 21.4 +/- 3.6 km^3 Mean diameter: 3.4 +/- 0.2 km (diameter of sphere of equivalent vol.) Dimensions along the principal axes of inertia: A: (4.6 +/- 0.1) km B: (2.6 +/- 0.1) km C: (2.2 +/- 0.4) km Axis orientation: RA: 69.4 +/- 0.2 deg Dec: +64.1 +/- 0.2 deg Rotation Period: 12.4041 +/- 0.0001 hr