Ejemplo n.º 1
0
double eraEe00b(double date1, double date2)
/*
**  - - - - - - - - -
**   e r a E e 0 0 b
**  - - - - - - - - -
**
**  Equation of the equinoxes, compatible with IAU 2000 resolutions but
**  using the truncated nutation model IAU 2000B.
**
**  Given:
**     date1,date2  double    TT as a 2-part Julian Date (Note 1)
**
**  Returned (function value):
**                  double    equation of the equinoxes (Note 2)
**
**  Notes:
**
**  1) The TT date date1+date2 is a Julian Date, apportioned in any
**     convenient way between the two arguments.  For example,
**     JD(TT)=2450123.7 could be expressed in any of these ways,
**     among others:
**
**            date1          date2
**
**         2450123.7           0.0       (JD method)
**         2451545.0       -1421.3       (J2000 method)
**         2400000.5       50123.2       (MJD method)
**         2450123.5           0.2       (date & time method)
**
**     The JD method is the most natural and convenient to use in
**     cases where the loss of several decimal digits of resolution
**     is acceptable.  The J2000 method is best matched to the way
**     the argument is handled internally and will deliver the
**     optimum resolution.  The MJD method and the date & time methods
**     are both good compromises between resolution and convenience.
**
**  2) The result, which is in radians, operates in the following sense:
**
**        Greenwich apparent ST = GMST + equation of the equinoxes
**
**  3) The result is compatible with the IAU 2000 resolutions except
**     that accuracy has been compromised for the sake of speed.  For
**     further details, see McCarthy & Luzum (2001), IERS Conventions
**     2003 and Capitaine et al. (2003).
**
**  Called:
**     eraPr00      IAU 2000 precession adjustments
**     eraObl80     mean obliquity, IAU 1980
**     eraNut00b    nutation, IAU 2000B
**     eraEe00      equation of the equinoxes, IAU 2000
**
**  References:
**
**     Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
**     implement the IAU 2000 definition of UT1", Astronomy &
**     Astrophysics, 406, 1135-1149 (2003)
**
**     McCarthy, D.D. & Luzum, B.J., "An abridged model of the
**     precession-nutation of the celestial pole", Celestial Mechanics &
**     Dynamical Astronomy, 85, 37-49 (2003)
**
**     McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
**     IERS Technical Note No. 32, BKG (2004)
**
**  Copyright (C) 2013-2015, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
   double dpsipr, depspr, epsa, dpsi, deps, ee;

/* IAU 2000 precession-rate adjustments. */
   eraPr00(date1, date2, &dpsipr, &depspr);

/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
   epsa = eraObl80(date1, date2) + depspr;

/* Nutation in longitude. */
   eraNut00b(date1, date2, &dpsi, &deps);

/* Equation of the equinoxes. */
   ee = eraEe00(date1, date2, epsa, dpsi);

   return ee;

}
Ejemplo n.º 2
0
void eraBp00(double date1, double date2,
             double rb[3][3], double rp[3][3], double rbp[3][3])
/*
**  - - - - - - - -
**   e r a B p 0 0
**  - - - - - - - -
**
**  Frame bias and precession, IAU 2000.
**
**  Given:
**     date1,date2  double         TT as a 2-part Julian Date (Note 1)
**
**  Returned:
**     rb           double[3][3]   frame bias matrix (Note 2)
**     rp           double[3][3]   precession matrix (Note 3)
**     rbp          double[3][3]   bias-precession matrix (Note 4)
**
**  Notes:
**
**  1) The TT date date1+date2 is a Julian Date, apportioned in any
**     convenient way between the two arguments.  For example,
**     JD(TT)=2450123.7 could be expressed in any of these ways,
**     among others:
**
**             date1         date2
**
**         2450123.7           0.0       (JD method)
**         2451545.0       -1421.3       (J2000 method)
**         2400000.5       50123.2       (MJD method)
**         2450123.5           0.2       (date & time method)
**
**     The JD method is the most natural and convenient to use in
**     cases where the loss of several decimal digits of resolution
**     is acceptable.  The J2000 method is best matched to the way
**     the argument is handled internally and will deliver the
**     optimum resolution.  The MJD method and the date & time methods
**     are both good compromises between resolution and convenience.
**
**  2) The matrix rb transforms vectors from GCRS to mean J2000.0 by
**     applying frame bias.
**
**  3) The matrix rp transforms vectors from J2000.0 mean equator and
**     equinox to mean equator and equinox of date by applying
**     precession.
**
**  4) The matrix rbp transforms vectors from GCRS to mean equator and
**     equinox of date by applying frame bias then precession.  It is
**     the product rp x rb.
**
**  5) It is permissible to re-use the same array in the returned
**     arguments.  The arrays are filled in the order given.
**
**  Called:
**     eraBi00      frame bias components, IAU 2000
**     eraPr00      IAU 2000 precession adjustments
**     eraIr        initialize r-matrix to identity
**     eraRx        rotate around X-axis
**     eraRy        rotate around Y-axis
**     eraRz        rotate around Z-axis
**     eraCr        copy r-matrix
**     eraRxr       product of two r-matrices
**
**  Reference:
**     "Expressions for the Celestial Intermediate Pole and Celestial
**     Ephemeris Origin consistent with the IAU 2000A precession-
**     nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
**     n.b. The celestial ephemeris origin (CEO) was renamed "celestial
**          intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
**  Copyright (C) 2013-2017, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
/* J2000.0 obliquity (Lieske et al. 1977) */
   const double EPS0 = 84381.448 * ERFA_DAS2R;

   double t, dpsibi, depsbi, dra0, psia77, oma77, chia,
          dpsipr, depspr, psia, oma, rbw[3][3];


/* Interval between fundamental epoch J2000.0 and current date (JC). */
   t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;

/* Frame bias. */
   eraBi00(&dpsibi, &depsbi, &dra0);

/* Precession angles (Lieske et al. 1977) */
   psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * ERFA_DAS2R;
   oma77  =       EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * ERFA_DAS2R;
   chia   = (  10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * ERFA_DAS2R;

/* Apply IAU 2000 precession corrections. */
   eraPr00(date1, date2, &dpsipr, &depspr);
   psia = psia77 + dpsipr;
   oma  = oma77  + depspr;

/* Frame bias matrix: GCRS to J2000.0. */
   eraIr(rbw);
   eraRz(dra0, rbw);
   eraRy(dpsibi*sin(EPS0), rbw);
   eraRx(-depsbi, rbw);
   eraCr(rbw, rb);

/* Precession matrix: J2000.0 to mean of date. */
   eraIr(rp);
   eraRx(EPS0, rp);
   eraRz(-psia, rp);
   eraRx(-oma, rp);
   eraRz(chia, rp);

/* Bias-precession matrix: GCRS to mean of date. */
   eraRxr(rp, rbw, rbp);

   return;

}