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SRVDOPP

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

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