Speed Of Stars.

[NebulaBilly]

Hi, when doing some studies I have come up with a problem I was wondering if anybody could help.

The spectra of stars at one edge of the galaxy are observed at a wavelength of 492.2nm while the same line seen in the spectra of stars at the opposite edge of the galaxy are observed at a wavelength of 494.2nm. Given the rest wavelength is 486.1nm calculate the speed of the stars at the two edges with respect to a observer from Earth.

Now I understand Doppler shift, redshift and blueshift, I am just not sure how to put them into practice to calculate the speed here. 

 

Any help would be appreciated

[saac]

For a simple treatment the red shift ratio (Z) is calculated first  where Z = λobserved – λrest/ λrest.    This ratio in turn equates to V/C  where V is the velocity of the galaxy or star with respect to Earth. So in effect the percentage red/blue shift equates to the percentage velocity with respect to the speed of light.

For a more involved interpretation see the link below:

Red Shift Ratio

Jim

 

 

[mikeyj1]

confirmed, that was just what i wanted to write but couldn't find the delta symbols

so one is coming toward you, the other going away, so you can tell the direction of rotation..

[saac]

2 minutes ago, mikeyj1 said:

confirmed, that was just what i wanted to write but couldn't find the delta symbols

so one is coming toward you, the other going away, so you can tell the direction of rotation..

Mikey I picked it from the symbol editor in word - it comes in handy for Greek letters    I don't really have much experience of the second interpretation (Hyperphysics) I think it accounts for relativistic effects, the simpler form is the equation we use in school.

 

Jim 

[mikeyj1]

2 minutes ago, saac said:

Mikey I picked it from the symbol editor in word - it comes in handy for Greek letters

thanks Jim, yes i just learnt it as: Change in wavelength/original = velocity of star/speed of light, so you transpose to find the speed

shorter wavelength = blue shift = coming toward us

cheers

Mike

[NebulaBilly]

Thanks so much for replies this I what I had before I posted 

 

My thoughts were, as the rest wavelength is 486.1nm and both observed wavelengths were 492.6nm and 494.2nm this shows the stars moving away so (Red Shift). So this took me to using the equation vr = c(1 − λ/λ_r) 

so to substitute the numbers into that would give me vr = (300000 km/s)*(1-486.1/494.2) this equals vr = 300000*(1-0.98)km/s = and here is where I get 6000km/s and this does not seem correct  

 

I noticed a mistake so I made an edit to this

 

[mikeyj1]

the whole galaxy is receding, the difference is the rotation speed,

taking the formula above (mine) and transpose (6.1x300,000)/486.1 = 3,764 km/s 

and the other is 4999km/s

at least thats how i see it...

[NebulaBilly]

8 minutes ago, mikeyj1 said:

the whole galaxy is receding, the difference is the rotation speed,

taking the formula above (mine) and transpose (6.1x300,000)/486.1 = 3,764 km/s 

and the other is 4999km/s

at least thats how i see it...

Thanks mikey with the risk of sounded silly, where did the 6.1 come from? and your way you would not come across a negative value such as I have when calculating the 494.2nm 

[mikeyj1]

5 minutes ago, NebulaBilly said:

where did the 6.1 come from?

no worries, the difference between the resting wavelength and the new one, (492.2 - 486.1) 8.1 for the other

you're right about the negative, but because it's a longer wavelength than the resting one, you know it's receding rather than coming toward us.

[mikeyj1]

found this, hopefully it helps not confuses..

[NebulaBilly]

So put into practice its is Vr = (λobs-λrest)*300000/λrest = speed

Just want to make sure I get the formula written down correctly 

 

That is great thanks mikey I appreciate the help

[mikeyj1]

yup

[robin_astro]

Strictly speaking this is not the speed of the star it is the radial velocity (The component of the speed in the direction of the observer)

Interestingly measurement of galaxy rotation is within the capability of amateurs eg as here by Christian Buil and Valerie Desnoux

Robin

[Demonperformer]

Fascinating read. Thanks for starting the thread, Billy, and for all the contributions that have explained it so well.

[NebulaBilly]

Hey this has been really good, id like to add a little more to the discussion and that would be how from the redshift data obtained  we can determine the apparent recession speed, was just something my friend said to me earlier but we was not sure, as we need that recession speed to calculate the distance to the galaxy. We thought that maybe redshift is used the determine the recession speed. Redshift = (λobs-λrest)/λrest.

But we were both a little unsure how we would calculate the speed from this

 

[robin_astro]

You already have an estimate of the recession velocity for the galaxy. (The average radial velocity calculated from the redshifts of the two stars)  You can then use Hubble's law to estimate the distance. This is only an estimate though as it assumes the recessional velocity is only due to cosmological expansion. In practise galaxies also move due to local gravitation effects and this can give significant errors in distances to nearby galaxies calculated  this way  (for example the Andromeda galaxy is actually moving towards us!)

Robin