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SRVDOPP

SRVDOPP

Name


  SRVDOPP

Author


  Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
  craigm@lheamail.gsfc.nasa.gov
  UPDATED VERSIONs can be found on my WEB PAGE:
      http://cow.physics.wisc.edu/~craigm/idl/idl.html

Purpose


  Compute relativistic doppler shift (arbitrary velocity & photon dir.)

Major Topics


  Physics, Geometry

Calling Sequence


  NU1_NU0 = SRVDOPP(U0, V)

Description



  The function SRVDOPP computes the relativistic doppler shift
  between two inertial reference frames.
  Consider two inertial coordinate frames. Frame "0" is a "lab" or
  rest frame. Frame "1" is a "rocket" or moving frame, moving at
  velocity V with respect to the lab frame. The velocity V is
  allowed to be an arbitrary 3-vector.
    * An observer in the lab frame sees a photon of frequency NU0
      propagating in the direction U0. (U0 is a unit 3-vector)
    * An observer in the rocket frame observes the same photon with
      frequency NU1.
    * This function computes the ratio NU1 / NU0.
  U0 and V are allowed to be 3xN arrays, which means more than one
  set of values can be computed in a single call. If the dimensions
  of either U0 or V are 3x1, then it will be expanded to match the
  dimensions of the other vector.
  NOTE: Velocities passed to SRVDOPP are measured as a *fraction of
        the speed of light*.
  The formula for computing the relativistic doppler shift is:
             
    NU1_NU0 = (1 - U0 . V) * GAMMA
             
  where
    GAMMA is the Lorentz factor = 1/SQRT(1 - |V|^2)
    "." is the vector dot product
  [ IDL notation is not strictly adhered to in this formula, for
  clarity of presentation. ]

Inputs



  U0 - 3-vector or 3xN array, the unit vector of the photon
        propagation direction, as seen in the lab frame.
  V - 3-vector or 3xN array, the velocity of the rocket frame as
      seen by an observer in the lab. The velocity is normalized
      such that the speed of light is 1.

Returns



  A N-vector giving the ratio, NU1/NU0, which is the ratio of the
  frequency observed in the rocket frame to the frequency seen in
  the lab frame.

Keyword Parameters



  CLASSICAL - if set, then classical Doppler shift is performed,
              and the relativistic form is disabled.
              Default: not set (i.e., relativity is applied)

Example



  IDL> RATIO = SRVDOPP([-1d,0,0], [0.1d,0,0])
  A photon of frequency NU0 is moving along the -x axis in the lab
  frame; a rocket observer is moving with speed 0.1 c along the +x
  axis. NU0 * RATIO is the frequency seen by the rocket observer.
  IDL> RATIO = SRVDOPP([0,-1d,0], [0.1,0,0])
  The observer is the same, but the photon is moving along the -y
  axis. NU0 * RATIO is the frequency seen by the rocket observer.
  This is the relativistic transverse doppler shift.

Modification History


  Written, 05 May 2002, CM
  Documentation, 12 May 2002, CM
  Add CLASSICAL keyword, 29 Jul 2002, CM
  $Id: srvdopp.pro,v 1.3 2002/07/29 23:16:47 craigm Exp $



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