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Laplace Series for the Gravity Potential Gradient of the Earth

Transactions of IAA RAS, issue 20, 481–483 (2009)

Keywords: радиоинтерферометрия со сверхдлинными базами, ряд Лапласа, алгоритма Л. Каннингема, градиент гравитационного потенциала Земли, производная сферической функции порядка n, сферическая функция порядка n + 1, коэффициент производной, линейная комбинация коэффициентов функции, шаровые функции, высшие производные

Abstract

It is well known that the derivative of a solid spherical harmonic of degree n is a solid spherical harmonic of degree n+1. Using the algorithm by L. Cunningham [1] we succeed to expand the derivative's coefficients as linear combinations of the original function's coefficients. It seems to be the best expression for the gradient of the gravitational potential of any celestial body represented by Laplace series in spherical harmonics. It is important that the Stokes coefficients of any derivative of the geopotential depend on 2 or even 1 Stokes coefficients of the geopotential itself. Note, that the form of the final formulas depends on the normalization rule of the elementary spherical harmonics.

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K. V. Kholshevnikov . Laplace Series for the Gravity Potential Gradient of the Earth // Transactions of IAA RAS. — 2009. — Issue 20. — P. 481–483.

@article{kholshevnikov2009,
  abstract = {It is well known that the derivative of a solid spherical harmonic of degree n is a solid spherical harmonic of degree n+1. Using the algorithm by L. Cunningham [1] we succeed to expand the derivative's coefficients as linear combinations of the original function's coefficients. It seems to be the best expression for the gradient of the gravitational potential of any celestial body represented by Laplace series in spherical harmonics. It is important that the Stokes coefficients of any derivative of the geopotential depend on 2 or even 1 Stokes coefficients of the geopotential itself. Note, that the form of the final formulas depends on the normalization rule of the elementary spherical harmonics.},
  author = {K.~V. Kholshevnikov},
  issue = {20},
  journal = {Transactions of IAA RAS},
  keyword = {радиоинтерферометрия со сверхдлинными базами, ряд Лапласа, алгоритма Л. Каннингема, градиент гравитационного потенциала Земли, производная сферической функции порядка n, сферическая функция порядка n + 1, коэффициент производной, линейная комбинация коэффициентов функции, шаровые функции, высшие производные},
  pages = {481--483},
  title = {Laplace Series for the Gravity Potential Gradient of the Earth},
  url = {http://iaaras.ru/en/library/paper/681/},
  year = {2009}
}

TY  - JOUR
TI  - Laplace Series for the Gravity Potential Gradient of the Earth
AU  - Kholshevnikov, K. V.
PY  - 2009
T2  - Transactions of IAA RAS
IS  - 20
SP  - 481
AB  - It is well known that the derivative of a solid spherical harmonic of
degree n is a solid spherical harmonic of degree n+1. Using the
algorithm by L. Cunningham [1] we succeed to expand the derivative's
coefficients as linear combinations of the original function's
coefficients. It seems to be the best expression for the gradient of
the gravitational potential of any celestial body represented by
Laplace series in spherical harmonics. It is important that the
Stokes coefficients of any derivative of the geopotential depend on 2
or even 1 Stokes coefficients of the geopotential itself. Note, that
the form of the final formulas depends on the normalization rule of
the elementary spherical harmonics.
UR  - http://iaaras.ru/en/library/paper/681/
ER  -