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J/A+AS/110/411      Orbit determination f & g power series          (Bem+, 1995)
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High order f and g power series for orbit determination.
       Bem J., Szczodrowska-Kozar B.
      <Astron. Astrophys. Suppl. Ser. 110, 411 (1995)>
      =1995A&AS..110..411B      (SIMBAD/NED Reference)
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Keywords: celestial mechanics - numerical methods - solar system

Description:
   The table of coefficients and exponents of the power series f and g up
   to derivatives of the 20-th order is the main achievement of this paper.
   The accuracy of the calculation of orbits has been tested by tracing the
   motion of all planets of the solar system.

File Summary:
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  FileName      Lrecl  Records   Explanations
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ReadMe             80        .   This file
table2             41      715   Coefficients and exponents
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Byte-by-byte Description of file: table2
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   Bytes Format  Units   Label    Explanations
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   1-  3  I3     --      n        Order of derivative
   5-  7  I3     ---     L+L'     Number of terms belonging to the derivative
  10- 31  E22.2  ---     R"       Coefficient R" in next L+L' lines (1)
  33- 34  I2     ---     i        Exponent i of each term (1)
  36- 37  I2     ---     j        Exponent j of each term (1)
      39  I1     ---     k        Exponent k of each term (1)
      41  I1     ---     fg       [1-2] Term of the serie, 1 for f, 2 for g
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Note (1):
   To solve the Newtonian equation, d^2^r/dt^2^=-ur, in Taylor's series
   form r={sum(n>=0)}[d^0^r/dt^0^(tau^n^/n!)], and after introducing
   Lagrangian variables u, p and q; the successive terms of Taylor's series
   of order n take the form:
   tau^n^[r_0_{sum(1,L)}(R_L_.u^i^.p^j^.q^k^)
                           + dr_0_/dt{sum(1,L')}(R_L'_.u^i^.p^j^.q^k^)]/n!  (5)
   R are integers numbers, R'=R/n! and R"=R'/(n+1)
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(End)                                           Patricia Bauer [CDS] 12-Dec-1994