## 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