## Function `epochPropErr( tYr, astrom22 )`

Description:
  Propagates the astrometry parameters and their associated errors and correlations, supplied as a 22-element array, to a different epoch.

  The input and output astrometry parameters with associated error and correlation information are each represented by a 22-element array, with the following elements:

       index  gaia_source name      unit    description
       -----  ----------------      ----    -----------
         0:   ra                    deg     right ascension
         1:   dec                   deg     declination
         2:   parallax              mas     parallax
         3:   pmra                  mas/yr  proper motion in RA * cos(dec)
         4:   pmdec                 mas/yr  proper motion in Declination
         5:   radial_velocity       km/s    barycentric radial velocity
         6:   ra_error              mas     error in right ascension
         7:   dec_error             mas     error in declination
         8:   parallax_error        mas     error in parallax
         9:   pmra_error            mas/yr  error in RA proper motion * cos(dec)
        10:   pmdec_error           mas/yr  error in Declination proper motion
        11:   radial_velocity_error km/s    error in barycentric radial velocity
        12:   ra_dec_corr                   correlation between ra and dec
        13:   ra_parallax_corr              correlation between ra and parallax
        14:   ra_pmra_corr                  correlation between ra and pmra
        15:   ra_pmdec_corr                 correlation between ra and pmdec
        16:   dec_parallax_corr             correlation between dec and parallax
        17:   dec_pmra_corr                 correlation between dec and pmra
        18:   dec_pmdec_corr                correlation between dec and pmdec
        19:   parallax_pmra_corr            correlation between parallax and pmra
        20:   parallax_pmdec_corr           correlation between parallax and pmdec
        21:   pmra_pmdec_corr               correlation between pmra and pmdec

  Note the correlation coefficients, always in the range -1..1, are dimensionless.

  Null values for `parallax`, `pmra`, `pmdec` and `radial_velocity` are treated as if zero for the purposes of propagation. The documentation of the equivalent function in the Gaia archive comments "This is a reasonable choice for most stars because those quantities would be either small (parallax and proper motion) or irrelevant (radial velocity). However, this is not true for stars very close to the Sun, where appropriate values need to be taken from the literature (e.g. average velocity field in the solar neighbourhood)."

  The effect is that the output represents the best estimates available for propagated astrometry; proper motions, parallax and RV are applied if present, but if not the output values are calculated or simply copied across as if those quantities were zero.

  This transformation is only applicable for radial velocities determined independently of the astrometry, such as those obtained with a spectrometer. It is not applicable for the back-transformation of data already propagated to another epoch.

  This is clearly an unwieldy function to invoke, but if you are using it with the gaia_source catalogue itself, or other similar catalogues with the same column names and units, you can invoke it by just copying and pasting the example shown in this documentation.

Parameters:
  `tYr` (floating point)
    epoch difference in years
  `astrom22` (array of floating point)
    astrometry at time t0, represented by a 22-element array as above

Return Value (array of floating point):
  astrometry at time t0+tYr, represented by a 22-element array as above

Example:
  `epochPropErr(-15.5, array( ra,dec,parallax,pmra,pmdec,radial_velocity, ra_error,dec_error,parallax_error,pmra_error,pmdec_error,radial_velocity_error, ra_dec_corr,ra_parallax_corr,ra_pmra_corr,ra_pmdec_corr, dec_parallax_corr,dec_pmra_corr,dec_pmdec_corr, parallax_pmra_corr,parallax_pmdec_corr, pmra_pmdec_corr))` - calculates the astrometry with all errors and correlations at 2000.0 for gaia_source values that were observed at 2015.5.

Signature:
  `double[] epochPropErr(double, double[])`