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Working models for the gravitational field of Phobos

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Abstract

Models for the gravitational field of Mars moon Phobos were developed using the latest shape model and assuming homogeneous density distribution. Three methods were applied in our study. Comparisons were made between these methods and all were shown to yield consistent results. Notably, the most accurate shape model of Phobos to date, complete up to degree and order 17 was used for the first time in our analysis. A set of spherical harmonic coefficients up to degree and order 17 were derived for the gravitational field of Phobos. Also considered was the gravitational field on the surface of Phobos. Typical characteristics as well as some pronounced surface features of this irregular-shaped small body could be conveniently identified. The results are readily applicable for such purposes as spacecraft orbit analysis and assessing the dynamical environment of Phobos.

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References

  1. Burns J A. Contradictory clues as to the origin of the Martian moons. Kieffer H H, Jakosky B M, Snyder C W, et al. eds. Mars. Tuscon: University of Arizona Press, 1992. 1283–1301

    Google Scholar 

  2. Craddock R A. Are Phobos and Deimos the result of a giant impact? Icarus, 2011, 211: 1150–1161

    Article  ADS  Google Scholar 

  3. Duxbury T C. The figure of Phobos. Icarus, 1989, 78: 169–180

    Article  ADS  Google Scholar 

  4. Willner K, Oberst J, Hussmann H, et al. Phobos control point network, rotation, and shape. Earth Planet Sci Lett, 2010, 294: 541–546

    Article  ADS  Google Scholar 

  5. Pang K D, Pollack J B, Veverka J, et al. The composition of Phobos —Evidence for carbonaceous chondrite surface from spectral analysis. Science, 1978, 199: 64–66

    Article  ADS  Google Scholar 

  6. Thomas P. Surface features of Phobos and Deimos. Icarus, 1979, 40: 223–243

    Article  ADS  Google Scholar 

  7. Willner K, Oberst J, Wählisch M, et al. New astrometric observations of Phobos with the SRC on Mars Express. Astron Astrophys, 2008, 488: 361–364

    Article  ADS  Google Scholar 

  8. Andert T P, Rosenblatt P, Pätzold M, et al. Precise mass determination and the nature of Phobos. Geophys Res Lett, 2010, 37: L09202

    Article  Google Scholar 

  9. Andert T P, Rosenblatt P, Pätzold M, et al. The internal structure of Phobos and hints to its origin derived from Mars Express Radio Science observations. European Planetary Science Congress, 2011

  10. Davis D R, Housen K R, Greenberg R. The unusual dynamical environment of Phobos and Deimos. Icarus, 1981, 47: 220–233

    Article  ADS  Google Scholar 

  11. Thomas P C. Gravity, tides, and topography on small satellites and asteroids — Application to surface features of the Martian satellites. Icarus, 1993, 105: 326–344

    Article  ADS  Google Scholar 

  12. Chao B F, Rubincam D P. The gravitational field of Phobos. Geophys Res Lett, 1989, 16: 859–862

    Article  ADS  MATH  Google Scholar 

  13. Martinec Z, Pec K, Bursa M. The Phobos gravitational field modeled on the basis of its topography. Earth Moon Planets, 1989, 45: 219–235

    Article  ADS  Google Scholar 

  14. Balmino G. Gravitational potential harmonics from the shape of an homogeneous body. Celest Mech Dyn Astron, 1994, 60: 331–364

    Article  ADS  MATH  Google Scholar 

  15. Seidelmann P K, Archinal B A, A’Hearn M F, et al. Report of the IAU/IAG working group on cartographic coordinates and rotational elements: 2006. Celest Mech Dyn Astron, 2006, 98: 155–1

    Google Scholar 

  16. Kaula W. Theory of satellite geodesy: Applications of satellites to geodesy. New York: Dover Publications, 2000. 1–8

    MATH  Google Scholar 

  17. Turner R J. A model of Phobos. Icarus, 1978, 33: 116–140

    Article  ADS  Google Scholar 

  18. Werner R A, Scheeres D J. Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celest Mech Dyn Astron, 1997, 65: 313–344

    Article  ADS  MATH  Google Scholar 

  19. Miller J K, Konopliv A S, Antreasian P G, et al. Determination of shape, gravity, and rotational state of asteroid 433 Eros. Icarus, 2002, 155: 3–17

    Article  ADS  Google Scholar 

  20. Chao B F, Gross R S. Changes in the earth’s rotation and low-degree gravitational field induced by earthquakes. Geophys J, 1987, 91: 569–596

    Article  ADS  Google Scholar 

  21. Garmier R, Barriot J Konopliv, A K, et al. Modeling of the Eros gravity field as an ellipsoidal harmonic expansion from the NEAR Doppler tracking data. Geophys Res Lett, 2002, 29: 1231–1233

    Article  ADS  Google Scholar 

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Correspondence to Xian Shi.

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Recommended by ZHAO Ming (Editorial Board Member)

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Shi, X., Willner, K., Oberst, J. et al. Working models for the gravitational field of Phobos. Sci. China Phys. Mech. Astron. 55, 358–364 (2012). https://doi.org/10.1007/s11433-011-4606-4

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  • DOI: https://doi.org/10.1007/s11433-011-4606-4

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