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HELIO_RV

HELIO_RV

## Purpose

Return the heliocentric radial velocity of a spectroscopic binary

## Explanation

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 ] )

## Input

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.

## Output

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

## Restrictions

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.

## Examples

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)
-62.965569
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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