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.
Similar content being viewed by others
References
Bannerjee, B. and Gupta, S.P.D.: 1977, Geophysics 42, 1053.
Barnett, C.T.: 1976, Geophysics 41(6), 1353.
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.
Cady, J.W.: 1980, Geophysics 45(10), 1507.
Geissler, P., Petit, J.-M., Durda, D., Greenberg, R., Bottke, W., Nolan, M. and Moore, J.: 1996, Icarus 120, 140.
Goldstein, H.: 1980, Classical Mechanics (second edition), Reading, Mass: Addison-Wesley.
Golizdra, G.Ya.: 1981, Izvestiya, Physics of the Solid Earth 17(8), 625.
Go\`zdziewski, K. and Maciejewski, A.J.: 1981, ‘On the Gravitational Fields of Pandora and Prometheus’ (preprint).
Grafarend, E. and Engles, J.: 1994, Manuscripta Geodaetica 19, 18.
Greenberg, M.D.: 1978, Foundations of Applied Mathematics, Englewood Cliffs, N.J.: Prentice-Hall.
Greenwood, D.T.: 1988, Principles of Dynamics (second edition), Englewood Cliffs, N.J.: Prentice-Hall.
Heiskanen, W.A. and Moritz, H.: 1967, Physical Geodesy, San Francisco: W.H. Freeman and Co.
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.
Hudson, R.S. and Ostro, S.J.: 1994, Science 263, 940.
Kaula, W.M.: 1966, Theory of Satellite Geodesy, Waltham, Mass.: Blaisdell.
Kwok, Y-K.: 1991, Geophysical Prospecting (Netherlands) 39(3), 435.
MacMillan, W.D.: 1930, The Theory of the Potential, New York: McGraw-Hill, Republished by Dover, New York (1958).
MacMillan, W.D.: 1936, Dynamics of Rigid Bodies, New York: McGraw-Hill
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.
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.
Montana, C.J., Mickus, K.L. and Peeples, W.J.: 1992, Computers and Geosciences (UK) 18(5), 587.
Moritz, H.: 1980, Advanced Physical Geodesy, Abacus Press.
Nagy, D.: 1966, Geophysics 31(2), 362.
Okabe, M.: 1979, Geophysics 44(4), 730–741.
Plouff, D.: 1976, Geophysics 41, 727–741.
Pohánka, V.: 1988, Geophysical Prospecting 36, 733.
Scheeres, D.J., Ostro, S.J., Hudson, R.S. and Werner, R.A.: 1996, Icarus 121, 67.
Selby, S.M. (ed.): 1965, CRC Standard Mathematical Tables, Cleveland, Ohio: The Chemical Rubber Co.
Simonelli, D.P., Thomas, P.C., Carcich, B.T. and Veverka, J.: 1993, Icarus 103, 49.
Strakhov, V.N. and Lapina, M.I.: 1990, Geophysical Journal (UK) 8(6), 740.
Telford, W.M., Geldart, L.P., Sheriff, R.E. and Keys, D.A.: 1976, Applied Geophysics, New York: Cambridge University Press.
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.
Thomas, P.C.: 1993, Icarus 105, 326.
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.
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).
Waldvogel, J.: 1976, Journal of Applied Mathematics and Physics (ZAMP) 27, 867.
Waldvogel, J.: 1979, Journal of Applied Mathematics and Physics (ZAMP) 30, 388.
Werner, R.A.: 1994, Celestial Mechanics and Dynamical Astronomy 59, 253.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Werner, R.A., Scheeres, D.J. Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celestial Mech Dyn Astr 65, 313–344 (1996). https://doi.org/10.1007/BF00053511
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00053511