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Celestial Mechanics and Dynamical Astronomy

, Volume 65, Issue 3, pp 313–344 | Cite as

Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia

  • Robert A. Werner
  • Daniel J. Scheeres
Article

Abstract

The exterior gravitation of a constant-density polyhedron is derived analytically in closed form. Expressions for potential, attraction, and gravity gradient matrix involve one logarithm term per edge and one arctangent term per face, The Laplacian can be used to determine whether a field point is inside or outside the polyhedron, This polyhedral method is well suited to evaluating the gravitational field of an irregularly shaped body such as an asteroid or comet, Conventional harmonic and mascon potential and attraction expressions suffer large errors when evaluated close to a polyhedral model of asteroid 4769 Castalia.

Key words

gravitational potential polyhedron mascon asteroid 4769 Castalia 

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References

  1. Bannerjee, B. and Gupta, S.P.D.: 1977, Geophysics 42, 1053.Google Scholar
  2. Barnett, C.T.: 1976, Geophysics 41(6), 1353.Google Scholar
  3. Broucke, R.A.: 1995, ‘Closed Form Expressions for Some Gravitational Potentials: Triangle, Rectangle, Pyramid and Polyhedron’, AAS/AIAA Spaceflight Mechanics Meeting, Albuquerque, New Mexico, February 13–16, paper AAS 95–190.Google Scholar
  4. Cady, J.W.: 1980, Geophysics 45(10), 1507.Google Scholar
  5. Geissler, P., Petit, J.-M., Durda, D., Greenberg, R., Bottke, W., Nolan, M. and Moore, J.: 1996, Icarus 120, 140.Google Scholar
  6. Goldstein, H.: 1980, Classical Mechanics (second edition), Reading, Mass: Addison-Wesley.Google Scholar
  7. Golizdra, G.Ya.: 1981, Izvestiya, Physics of the Solid Earth 17(8), 625.Google Scholar
  8. Go\`zdziewski, K. and Maciejewski, A.J.: 1981, ‘On the Gravitational Fields of Pandora and Prometheus’ (preprint).Google Scholar
  9. Grafarend, E. and Engles, J.: 1994, Manuscripta Geodaetica 19, 18.Google Scholar
  10. Greenberg, M.D.: 1978, Foundations of Applied Mathematics, Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
  11. Greenwood, D.T.: 1988, Principles of Dynamics (second edition), Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
  12. Heiskanen, W.A. and Moritz, H.: 1967, Physical Geodesy, San Francisco: W.H. Freeman and Co.Google Scholar
  13. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. and Stuetzle, W.: 1992, ‘Surface Reconstruction from Unorganized Points’, Proceedings of SIGGRAPH `92(Chicago, Illinois, July 26–31, 1992), in: Computer Graphics 26(2), 71–78 New York: ACM SIGGRAPH.Google Scholar
  14. Hudson, R.S. and Ostro, S.J.: 1994, Science 263, 940.Google Scholar
  15. Kaula, W.M.: 1966, Theory of Satellite Geodesy, Waltham, Mass.: Blaisdell.Google Scholar
  16. Kwok, Y-K.: 1991, Geophysical Prospecting (Netherlands) 39(3), 435.Google Scholar
  17. MacMillan, W.D.: 1930, The Theory of the Potential, New York: McGraw-Hill, Republished by Dover, New York (1958).Google Scholar
  18. MacMillan, W.D.: 1936, Dynamics of Rigid Bodies, New York: McGraw-HillGoogle Scholar
  19. Malovichko, Al.K.: 1963, ‘Hundred-year anniversary of the work of F.A. Sludskiy on the attraction of homogeneous polyhedra’, Questions in the Processing and Interpretation of Geophysical Observations. Perm*, No. 4.Google Scholar
  20. Miller, J.K., Williams, B.G., Bollmann, W.E., Davis, R.P., Helfrich, C.E., Scheeres, D.J., Synnott, S.P., Wang, T.C. and Yeomans, D.K.: 1995, Journal of the Astronautical Sciences 43(4), 453.Google Scholar
  21. Montana, C.J., Mickus, K.L. and Peeples, W.J.: 1992, Computers and Geosciences (UK) 18(5), 587.Google Scholar
  22. Moritz, H.: 1980, Advanced Physical Geodesy, Abacus Press.Google Scholar
  23. Nagy, D.: 1966, Geophysics 31(2), 362.Google Scholar
  24. Okabe, M.: 1979, Geophysics 44(4), 730–741.Google Scholar
  25. Plouff, D.: 1976, Geophysics 41, 727–741.Google Scholar
  26. Pohánka, V.: 1988, Geophysical Prospecting 36, 733.Google Scholar
  27. Scheeres, D.J., Ostro, S.J., Hudson, R.S. and Werner, R.A.: 1996, Icarus 121, 67.Google Scholar
  28. Selby, S.M. (ed.): 1965, CRC Standard Mathematical Tables, Cleveland, Ohio: The Chemical Rubber Co.Google Scholar
  29. Simonelli, D.P., Thomas, P.C., Carcich, B.T. and Veverka, J.: 1993, Icarus 103, 49.Google Scholar
  30. Strakhov, V.N. and Lapina, M.I.: 1990, Geophysical Journal (UK) 8(6), 740.Google Scholar
  31. Telford, W.M., Geldart, L.P., Sheriff, R.E. and Keys, D.A.: 1976, Applied Geophysics, New York: Cambridge University Press.Google Scholar
  32. Thomas, P., Veverka, J. and Dermott, S.: 1986, ‘17 Small Satellites’, in Satellites, J.A. Burns and M.S. Matthews (eds.), Tucson: University of Arizona Press, pp. 802–835.Google Scholar
  33. Thomas, P.C.: 1993, Icarus 105, 326.Google Scholar
  34. Thomas, P.C., Veverka, J., Simonelli, D., Helfenstein, P., Carcich, B., Belton, M.J.S., Davies, M.E. and Chapman, C.,: 1994, Icarus 107, 23.Google Scholar
  35. Thomas, P.C., Belton, M.J.S., Carcich, B., Chapman, C., Davies, M.E., Sullivan, R. and Veverka, J.: 1995, ‘The Shape of Ida’ (preprint).Google Scholar
  36. Waldvogel, J.: 1976, Journal of Applied Mathematics and Physics (ZAMP) 27, 867.Google Scholar
  37. Waldvogel, J.: 1979, Journal of Applied Mathematics and Physics (ZAMP) 30, 388.Google Scholar
  38. Werner, R.A.: 1994, Celestial Mechanics and Dynamical Astronomy 59, 253.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Robert A. Werner
    • 1
  • Daniel J. Scheeres
    • 1
  1. 1.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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