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eraFk524

ERFA.fk524(r2000, d2000, dr2000, dd2000, p2000, v2000)

Convert J2000.0 FK5 star catalog data to B1950.0 FK4.

Given: (all J2000.0, FK5) r2000,d2000 double J2000.0 RA,Dec (rad) dr2000,dd2000 double J2000.0 proper motions (rad/Jul.yr) p2000 double parallax (arcsec) v2000 double radial velocity (km/s, +ve = moving away)

Returned: (all B1950.0, FK4) r1950,d1950 double B1950.0 RA,Dec (rad) dr1950,dd1950 double B1950.0 proper motions (rad/trop.yr) p1950 double parallax (arcsec) v1950 double radial velocity (km/s, +ve = moving away)

Notes:

  1. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, and are per year rather than per century.

  2. The conversion is somewhat complicated, for several reasons:

   . Change of standard epoch from J2000.0 to B1950.0.

. An intermediate transition date of 1984 January 1.0 TT.

. A change of precession model.

. Change of time unit for proper motion (Julian to tropical).

. FK4 positions include the E-terms of aberration, to simplify the hand computation of annual aberration. FK5 positions assume a rigorous aberration computation based on the Earth's barycentric velocity.

. The E-terms also affect proper motions, and in particular cause objects at large distances to exhibit fictitious proper motions.

The algorithm is based on Smith et al. (1989) and Yallop et al. (1989), which presented a matrix method due to Standish (1982) as developed by Aoki et al. (1983), using Kinoshita's development of Andoyer's post-Newcomb precession. The numerical constants from Seidelmann (1992) are used canonically.

  1. In the FK4 catalog the proper motions of stars within 10 degrees of the poles do not embody differential E-terms effects and should, strictly speaking, be handled in a different manner from stars outside these regions. However, given the general lack of homogeneity of the star data available for routine astrometry, the difficulties of handling positions that may have been determined from astrometric fields spanning the polar and non- polar regions, the likelihood that the differential E-terms effect was not taken into account when allowing for proper motion in past astrometry, and the undesirability of a discontinuity in the algorithm, the decision has been made in this ERFA algorithm to include the effects of differential E-terms on the proper motions for all stars, whether polar or not. At epoch J2000.0, and measuring "on the sky" rather than in terms of RA change, the errors resulting from this simplification are less than 1 milliarcsecond in position and 1 milliarcsecond per century in proper motion.

Called:

   eraAnp       normalize angle into range 0 to 2pi
   eraPdp       scalar product of two p-vectors
   eraPm        modulus of p-vector
   eraPmp       p-vector minus p-vector
   eraPpp       p-vector pluus p-vector
   eraPv2s      pv-vector to spherical coordinates
   eraS2pv      spherical coordinates to pv-vector
   eraSxp       multiply p-vector by scalar

References:

Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0 FK4-based positions of stars to epoch J2000.0 positions in accordance with the new IAU resolutions". Astron.Astrophys. 128, 263-267.

Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the Astronomical Almanac", ISBN 0-935702-68-7.

Smith, C.A. et al., 1989, "The transformation of astrometric catalog systems to the equinox J2000.0". Astron.J. 97, 265.

Standish, E.M., 1982, "Conversion of positions and proper motions from B1950.0 to the IAU system at J2000.0". Astron.Astrophys., 115, 1, 20-22.

Yallop, B.D. et al., 1989, "Transformation of mean star places from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space". Astron.J. 97, 274.

This revision: 2021 February 24

Copyright (C) 2013-2021, NumFOCUS Foundation. Derived, with permission, from the SOFA library.