Abstract
Hotine's (1969) partially nonsingular geopotential formulation is revisited to study its utility for the computation of geopotential acceleration and gradients from high degree and order expansions. This formulation results in the expansion of each Cartesian derivative of the potential in a spherical harmonic series of its own. The spherical harmonic coefficients of any Cartesian derivative of the potential are related in a simple manner to the coefficients of the geopotential. A brief overview of the derivation is provided, along with the fully normalized versions of Hotine's formulae, which is followed by a comparison with other algorithms of spherical harmonic synthesis on a CRAY Y-MP. The elegance and simplicity of Hotine's formulation is seen to lead to superior computational performance in a comparison against other algorithms for spherical harmonic synthesis.
Similar content being viewed by others
References
Baheti, R.S., V.J. Karkhanis, D.R. O'Halloran and M. Wilson (1989), “Fast mapping of gravity equations on a linear array processor,” inReal Time Signal Processing XII, Proceedings of the SPIE, Vol. 1154, Bellingham, Washington.
Bettadpur, S., B.E. Schutz and J.B. Lundberg (1992), “Spherical harmonic synthesis and least squares computations in satellite gravity gradiometry,”Bulletin Geodesique, Vol. 66, No. 2, pp 261–271.
Bettadpur, S. (1991), “Hotine's nonsingular geopotential formulation and its expression in the perifocal frame,” CSR TM 91-04, Center for Space Research, Austin, Texas.
Heitz, S. (1988),Coordinates in Geodesy, Springer Verlag, Berlin.
Hobson, E.W. (1891), “Systems of spherical harmonics,” inProceedings of the London Mathematical Society, Vol. 22, pp 431–449.
Hobson, E.W. (1931),The Theory of Spherical and Ellipsoidal Harmonics, Cambridge, At the University Press.
Hotine, M. (1969),Mathematical Geodesy, ESSA Monograph 2, U.S. Dept. of Commerce, Washington, D.C.
Lord Kelvin and P.G. Tait (1923),Treatise on Natural Philosophy, Volume 1, Cambridge University Press.
Lundberg, J.B. and B.E. Schutz (1988), “Recursion formulas for Legendre functions for use with nonsingular geopotential models,”Jour. of Guidance, Control and Dynamics, Vol. 11, No. 1, p 31.
Maxwell, J.C. (1937),A Treatise on Electricity and Magnetism, Volume I, Oxford University Press.
Morgan, S.H. and H.-J. Paik (1988), “Superconducting gravity gradiometer mission : Volumes 1 and 2,” NASA TM-4091.
Pines, S. (1973), “Uniform representation of the gravity potential and its derivatives,”AIAA Journal, Vol. 11, No. 11, pp 1508–1511.
Rapp, R.H. and N.K. Pavlis (1990), “The development and analysis of geopotential coefficients model to spherical harmonic degree 360,”Jour. of Geophysical Research, Vol. 90, No. B13, pp 21,885–21,911.
Reed, G.B. (1973), “Application of kinematical geodesy for determining short wavelength components of gravity field by satellite gradiometry,” No. 201, Reports of the Department of Geodetic Science and Surveying, Ohio State University, Columbus, Ohio.
Wagner, C.A. and O.L. Colombo (1979), “Gravity spectra from direct measurements,”Jour. of Geophysical Research, Vol. 84, No. B9, p 4699.
Wagner, C.A. (1979), “Gravity spectra from tracking planetary orbiters,”Jour. of Geophysical Research, Vol. 84, No. B12, p 6891.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bettadpur, S.V. Hotine's geopotential formulation: revisited. Bulletin Géodésique 69, 135–142 (1995). https://doi.org/10.1007/BF00815482
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00815482