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Studying of gravitational fields of natural moons


With the support of RFBR grant No. 12-02-31068 (MOL_a, my first grant) works on the study of the field of attraction of nonspherical bodies in the Solar system.

Determination of parameters of gravitational fields of planets is one of the most important tasks in space research. Analysis of the characteristics of the motions of natural satellites and SPACECRAFT that are traded in circumplanetary orbits, serves as a source of information about the parameters of the external gravitational fields and internal structures of planetary bodies. the evolution of the orbital motion of the SPACECRAFT configures the characteristics of a Central gravitational field of the studied celestial bodies.

The project aims to develop methods of representation and calculation of the attraction potential is significantly non-spherical bodies of the solar system directly on its surface, on the example of Phobos.

Expected scientific results, which are expected to receive upon completion of the project:
- algorithm allowing to obtain missing still the idea of variations of potential of attraction of a celestial body at different distances from its surface;
- assessment of the impact of nonspherical global shape of the investigated object in the calculations related to SPACECRAFT maneuvering;
- the calculated potential of attraction on the surface of Phobos.

Research stages:
1. Collection and detailed analysis of available information on existing spatial digital elevation models (Dems) of the surface of Phobos (as most information rich non-spherical celestial bodies).
2. Preparation of models to study.
2. 1 resampling of the irregular structure of the DEM on a regular grid (altitude matrix).
2.2 Evaluation of accuracy of transition to regular dem.
3. Development of an algorithm for computing the potential on the surface of Phobos without the use of approximating polynomials.
3.1 Creating a working model for is described in the article Ogorodova L. V., Nadezhdina I. E. "External attraction potential of a homogeneous model of Phobos" techniques that will ensure the calculation of potential gravity of a truncated pyramid, with spherical bases.
3.2 Calculation of the attraction potential of the proposed method for the sphere and ellipsoid of revolution.
3.3 Critical analysis of the results.
4. Algorithmic method for computing the attraction potential using a matrix of heights.
5. The calculation of potential fields Patagonia according to the Phobos SPACECRAFT "Mars Express" as of 2011.
6. Comparison of the calculated attraction potential with the potential produced by the decomposition of spherical functions for different distances from the surface of Phobos.

During the study completed the first 2 stages of work. Analyzed existing DTM of Phobos - the data that served as the basis for the DEM, and methods of creation. In MIIGAiK DEM was created based on data from the SPACECRAFT Mars Express and Viking Orbiter-1 and 2. Analyzed DTM of Phobos, including those received in MIIGAiK, consolidated in one table (table 1).

The obtained DEM is prepared for further studies - performed recalculation of irregular patterns on a regular DEM grid.

Regular elevation model was derived from vector data with a step of 0.3 degrees in latitude and longitude with physical dimensions 601x1201 cells. The size of each cell is approximately 50 m From the model were excluded blunders, so that the final accuracy of the model can be estimated with RMSE = 32 m. Finally formed the model related to the geometric center of Phobos, the accuracy of which is determined with RMSE = 44 m.

Currently research is ongoing.

Table 1. Terrain model of Phobos

Year Autor The method of creation and brief description of the model
1974 T.C. Duxbury The coordinates of the 38 control points measured on the Mariner 9 images
1978 R. J. Turner - Supporting a network of 260 points on the spacecraft image
- Plaster model on the basis of the network
1989 P.C. Thomas Ellipsoidal model obtained by limb the Mariner 9 definitions
1989
1992
R. M. Batson et al. DEM by interpolation between the reference points. Next, the resulting DEM was used for orthorectification of imagery and mosaicking of Phobos
1993 P.C. Thomas Numerical model is obtained by the images of VO with the control limb on the definitions, using Mariner 9 image
1993
D.P. Simonelli et al. Numerical model with a resolution of 2x2 obtained using limb definitions and reference points. Used for drawing 60 images with a resolution of VO 6-170 m/pixel
1991 T.C. Duxbury For the reference points coordinates were selected coefficients of spherical harmonics up to degree 8 and order. About 315 of the crater (depth-to-diameter 0.1-0.2) were added separately to Refine the model. Using these functions was created numerical model with a step of 0.5 (about 100 m/pixel). The accuracy of this model varies from 100 to 500 m
1994 G.A. Avanesov
Numerical model. Was originally built according to Turner (Turner 1978) and contained 50833 point. Later it was refined through visual comparison with the images of "Viking-1,-2"
2010
2012
K.Willner 
60 MEX HRSC images of different channels (compare the orbit of 110 km) and 16 images of VO (CP altitude orbits 929 km), with resolution from 80 m/pixel.
Dimension of pickets were made in automatic mode. The DEM resolution of 100 m/pixel resolution, high accuracy 10-80 m
2012 MIIGAIK
117 images MEX and VO. Pickets were measured manually in stereo mode in specific parts of the terrain, so the DEM has an irregular structure. The average distance between the points is 0.6. The DEM reflects both global and local relief, due to the content of manually defined structural lines (craters and grooves).

Fig. 1. A DEM in a polar projection of the Northern (left) and southern (right) hemisphere on a sphere of radius 11.1 km

Fig. 2. DTM of Phobos, built on a regular grid with a step of 0.3×0.3°

References:

Аванесов Г.А., Жуков Б.С., Зиман Я.Л. и др. Телевизионные исследования Фобоса // М.: Наука, 1994.-168 с. –ISBN 5-02-000298-4.
Зубарев А.Э., Надеждина И.Е., Конопихин А.А. Проблемы обработки данных дистанционного зондирования для моделирования фигур малых тел Солнечной системы // Современные проблемы дистанционного зондирования Земли из космоса. 2012. Т. 9. № 4. С. 277-285.
Batson R. M., Edwards K., and Duxbury T. C. Geodesy and cartography of the Martian satellites // Mars, 1992. P. 1249-1256.
Duxbury T.C. PHOBOS – Control network analysis // Icarus. 1974. V. 23. P. 290-299.
Duxbury T. C. The figure of PHOBOS // Icarus. 1989. V. 78. P. 169-180.
Duxbury T. C. An analytic model for the PHOBOS surface // Earth Planet Sci. Lett. 1991. V. 39. P. 355–376.
Simonelli D.P., Thomas, P.C., Carcich, B.T., Veverka, J. The generation and use of numerical shape models for irregular solar system objects // Icarus. 1993. V. 103. P. 49–61.
Thomas P.C. The shapes of small satellites // Icarus. 1989. V. 33. P. 116-140.
Turner R. J. A model of PHOBOS // Icarus. January 1978. V. 33. P. 116-140. doi: 10.1016/0019-1035(78)90028-3 .
Willner K., Oberst J., Hussmann H. et al. Phobos Control Point Network, Rotation, and Shape // Earth Planet. Sci. Lett. 2010. V. 294. P. 541–546.

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