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    Return the heliocentric radial velocity of a spectroscopic binary


    This function will return the heliocentric radial velocity of a
    spectroscopic binary star at a given heliocentric date
    given its orbit.

Calling Sequence

  Result = HELIO_RV ( JD ,T ,Period ,Gamma , K, [,e ,Omega ] )


  JD - Time of observation
  T - Time of periastron passage (max. +ve velocity
                for circular orbits), same time system as JD
  Period - the period in same units as JD
  Gamma - systemic velocity
  K - velocity semi-amplitude in the same units as Gamma.
  e - eccentricity of the orbit, default is 0.
  Omega - longitude of periastron in degrees. Must be specified for
                eccentric orbits.


  The predicted heliocentric radial velocity in the same units as Gamma
  for the date(s) specified by Reduced_HJD.


  The user should ensure consistency with all time systems being
  used (i.e. JD and T should be in the same units and time system).
  Generally, users should reduce large time values by subtracting
  a large constant offset, which may improve numerical accuracy.
  If using the the routines JULDATE and HELIO_JD, the reduced HJD
  time system must be used throughtout.


  Example 1
  What was the heliocentric radial velocity of the primary component of HU Tau
  at 1730 UT 25 Oct 1994?
  IDL> juldate ,[94,10,25,17,30],JD ;Get Geocentric julian date
  IDL> hjd = helio_jd(jd,ten(04,38,16)*15.,ten(20,41,05)) ; Convert to HJD
  IDL> print, helio_rv(hjd,46487.5303D,2.0563056D,-6.0,59.3)
  NB. 1. The routines JULDATE and HELIO_JD return a reduced HJD (HJD - 2400000)
        and so T and P must be specified in the same fashion.
    2. The user should be careful to use double precision format to specify
        T and P to sufficient precision where necessary.
  Example 2
  Plot two cycles of an eccentric orbit, e=0.6, omega=45 for both
  components of a binary star
  IDL> phi=findgen(100)/50.0 ; Generates 100 phase points
  IDL> plot, phi,helio_rv(phi,0,1,0,100,0.6,45),yrange=[-100,150]
  IDL> oplot, phi,helio_rv(phi,0,1,0,50,0.6,45+180)
  This illustrates both the use of arrays to perform multiple calculations
  and generating radial velocities for a given phase by setting T=0 and P=1.
  Note also that omega has been changed by 180 degrees for the orbit of the
  second component (the same 'trick' can be used for circular orbits).

Modification History

  Written by: Pierre Maxted CUOBS, October, 1994
  Circular orbits handled by setting e=0 and omega=0 to allow
  binary orbits to be handled using omega and omega+180.
                                                      Pierre Maxted,Feb 95
  BUG - omega was altered by the routine - corrected Feb 95,Pierre Maxted
  Iteration for E changed to that given by Reidel , Feb 95,Pierre Maxted
  /SINGLE keyword removed. May 96,Pierre Maxted
  Removed limitation of time system on HJD, C. Markwardt, 2011-04-15
  Change convergence test from relative to absolute precision on E
                                                    Pierre Maxted, Apr 12

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