# Hubble and doppler

jakrabb
I am trying to understand how the doppler effect was used when determining that the other stars were moving away from us. I get that the spectral lines observed are shifted and by examining that data we can calculate how fast its moving and if it is towards or away from us. could anyone elaborate on this? can we actually tell a direction; is the margin of error large or small? ... i guess i just need more info to comprehend it all..

## Answers and Replies

Greetings !

Welcome to PF jakrabb !

If the object moves away the frequency of the emmited
electromagnetic waves (light) will decrease (Doppler Effect),
if it moves towards us the frequency will increase.
The whole EM frequency range is called the electromagnetic
spectrum.

When we observe a star or some other distant object we take
the emission pattern that we would normally expect from such
an object and search for it along the observed EM spectrum.

Live long and prosper.

Originally posted by drag
Greetings !

Welcome to PF jakrabb !

If the object moves away the frequency of the emmited
electromagnetic waves (light) will decrease (Doppler Effect),
if it moves towards us the frequency will increase.
The whole EM frequency range is called the electromagnetic
spectrum.

When we observe a star or some other distant object we take
the emission pattern that we would normally expect from such
an object and search for it along the observed EM spectrum.

Live long and prosper.
Greetings also!

To add to what drag correctly stated, it must be remembered that the "velocity" change we see, toward or away from us, is radial velocity only. That is, straight-line toward or away from us. Any proper motion (sideways or at any angle) can't be determined. But, when the tilt angle of a particular galaxy is known, we can use the radial velocity and the tilt to get an actual velocity, for example star velocity around the galactic center. The Massive black hole in the center of M87, a giant elliptical galaxy, was determined (required) by this method of measuring the velocity of stars orbiting near the core.

Also, the "correct" velocity of distant objects depends greatly on the value of the Hubble Parameter used at the time. For years, a value of Hv was used at 55km/sec./Mpc. Then, everyone was using any value between 55 and 75. Now, with new discoveries and new data, the figure of Hv is settled on at 71km/sec./Mpc. I don't doubt that this figure will change also, but it seems to fit observations for now.

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Originally posted by jakrabb
I am trying to understand how the doppler effect was used when determining that the other stars were moving away from us. I get that the spectral lines observed are shifted and by examining that data we can calculate how fast its moving and if it is towards or away from us. could anyone elaborate on this? can we actually tell a direction; is the margin of error large or small? ... i guess i just need more info to comprehend it all..

lines are shifted by two effects----ordinary doppler due to relative motion (visible e.g. in spectra of nearby stars) and cosmological redshift due to expansion of space (visible e.g. in spectra of distant galaxies)

the rate space is expanding has changed over the course of time and so the cosmological redshift cannot be ascribed to anyone particular radial velocity but must be related to how much space has expanded during all the time the light has been in transit

it may help to think of a distant galaxy as sitting still in the space around it---but that neighborhood of space is getting farther away from us

the standard formula for the cosmological redshift (as opposed to doppler) is in terms of a(temit) and a(trec) the scale-factor (indicating "size of universe" or "average distance between galaxies") at the time the light was emitted and at the time it was received.

1 + z = a(trec)/a(temit)

(see Eric Linder's online "cosmology overview" for this, or any of a bunch of other sources findable on google)

DOPPLER shift formula on the other hand is primarily for things in the same coordinate chart---same local coordinates----so that there is a well-defined radial velocity.
For things in the same locale, Special Relativity applies and we have the SR Doppler formula

1 + z = sqrt ((1 + beta)/(1 - beta))

here beta = v/c, the radial velocity expressed a fraction of light

this SR Doppler formula is approximately the same as a much simpler one without the square root:

1 + z = 1 + v/c

z = v/c

The approximation is fine as long as v/c is small, like 0.01 or less.

The sideways component of velocity (as contrasted with the radial component which Doppler indicates) has to be determined by different means, like noting a star's change in position over the course of years.

Any of this what you wanted?

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jakrabb
thanks guys, that gets me started. and yes you were Very helpful marcus that is exactly the type of stuff i am looking for... i was trying to figure out if takeing different doppler readings from opposite sides of the sun might give different 'vectors' and give an idea of the true direction of a star

thanks

Originally posted by marcus
lines are shifted by two effects----ordinary doppler due to relative motion (visible e.g. in spectra of nearby stars) and cosmological redshift due to expansion of space

Gravity itself causes redshifting as well.

Originally posted by marcus
DOPPLER shift formula on the other hand is primarily for things in the same coordinate chart---same local coordinates

Doppler formulae can breakdown over distances covered within the same coordinate chart.

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