*EDIT* It's a bit late now but I've just realised I've been using gammas instead of lambdas for the wavelength
A probe is launched from Earth with velocity . A beacon emits a light with a wavelength of in it's rest frame. After many years, NASA locate the probe using a telescope and measure the light from the beacon to have the wavelength in their rest frame. Is this possible? What is the explanation for this observation.
Essentially the problem states that
so using the doppler shift equation I can solve the relationship between and
From the little I know about redshifting I'd guess that the light should be redshifted as the probe is moving away from us.
But in my notes it says "We know that there is a (small) redshift when . So somewhere between and we must have a situation where , that is where there is no shift at all between the observed and source wavelengths. Under the right conditions (particular relationship between and ) they can exactly balance".
I don't understand why this is the case though... Why do they balance or cancel out? My understanding was any object moving away from the observer will always be redshifted, if only a little bit. I don't get it...

EternalLight
 Follow
 68 followers
 2 badges
 Send a private message to EternalLight
 Thread Starter
Offline2ReputationRep: Follow
 1
 12022017 23:02
Last edited by EternalLight; 16022017 at 21:25. 
Revision help in partnership with Birmingham City University

Pessimisterious
 Follow
 3 followers
 12 badges
 Send a private message to Pessimisterious
Offline12ReputationRep: Follow
 2
 13022017 00:07
(Original post by AishaGirl)
A probe is launched from Earth with velocity . A beacon emits a light with a wavelength of in it's rest frame. After many years, NASA locate the probe using a telescope and measure the light from the beacon to have the wavelength in their rest frame. Is this possible? What is the explanation for this observation.
Essentially the problem states that
so using the doppler shift equation I can solve the relationship between and
From the little I know about redshifting I'd guess that the light should be redshifted as the probe is moving away from us.
But in my notes it says "We know that there is a (small) redshift when . So somewhere between and we must have a situation where , that is where there is no shift at all between the observed and source wavelengths. Under the right conditions (particular relationship between and ) they can exactly balance".
I don't understand why this is the case though... Why do they balance or cancel out? My understanding was any object moving away from the observer will always be redshifted, if only a little bit. I don't get it...
Basically, the earth is moving through space in an orbit around the sun, which means it isn't necessarily going to be in line with the axis of the original direction the beacon was released in. Hence the Doppler effect will be different.
This picture may help (from the wikipedia article):
The left hand image is the reference frame of the beacon. The right hand image is the frame of the observer, so this is the one that explains the question you're dealing with. What it shows is how the wave fronts are actually spherical, so if the observer is at an angle to the motion, the doppler shift will be different.
In the image, the little black dot on the right is the observer. It's pretty obvious that as the beacon passes the observer, the compact wave fronts at the front of the beacon quickly become spread out at the back. It's the same basic concept as when a car zooms by and makes the classed 'nneeeyowwwmmm' noise. The car is constantly moving in that situation but there's still some point at which the doppler effect is zero, at the midpoint where it goes from 'neeee' to 'yooowwwwm'.
So for any situation where the motions is not on the same axis, there's always going to be a variation in redshift as the angle between the observer and the object varies.
So this is how the observation angle can change the amount of doppler shift, and explains why there is some angle where the shift = 1. 
EternalLight
 Follow
 68 followers
 2 badges
 Send a private message to EternalLight
 Thread Starter
Offline2ReputationRep: Follow
 3
 13022017 00:18
(Original post by Pessimisterious)
I never studied this, but a quick look at the Transverse Doppler Effect on wikipedia shows what's going on.
Basically, the earth is moving through space in an orbit around the sun, which means it isn't necessarily going to be in line with the axis of the original direction the beacon was released in. Hence the Doppler effect will be different.
This picture may help (from the wikipedia article):
The left hand image is the reference frame of the beacon. The right hand image is the frame of the observer, so this is the one that explains the question you're dealing with. What it shows is how the wave fronts are actually spherical, so if the observer is at an angle to the motion, the doppler shift will be different.
In the image, the little black dot on the right is the observer. It's pretty obvious that as the beacon passes the observer, the compact wave fronts at the front of the beacon quickly become spread out at the back. It's the same basic concept as when a car zooms by and makes the classed 'nneeeyowwwmmm' noise. The car is constantly moving in that situation but there's still some point at which the doppler effect is zero, at the midpoint where it goes from 'neeee' to 'yooowwwwm'.
So for any situation where the motions is not on the same axis, there's always going to be a variation in redshift as the angle between the observer and the object varies.
So this is how the observation angle can change the amount of doppler shift, and explains why there is some angle where the shift = 1.
Does this mean that at some specific time a galaxy will not appear to be redshifted even though it is technically?Last edited by EternalLight; 13022017 at 00:43. 
Pessimisterious
 Follow
 3 followers
 12 badges
 Send a private message to Pessimisterious
Offline12ReputationRep: Follow
 4
 13022017 11:26
(Original post by AishaGirl)
But the probe is moving at 0.8c, even if Earth was moving toward the probe, the probe would still be moving away at a faster rate and therefore still be redshifted? I understand that Earth is in orbit but I don't see a time when Earths position cancels out the probe moving at 0.8c. If the prove was moving at the same velocity as Earth then sure.
Does this mean that at some specific time a galaxy will not appear to be redshifted even though it is technically?
Maybe the beacon also ends up orbiting something?
I think the point of the question is just to somehow demonstrate the transverse doppler effect and how things can change with the angle. This is the only thing I can guess from it, given the fact that the equation you're working with deals with , which only happens in that context.
And yeah, I guess it's possible for a galaxy to not redshift even though it actually is moving. This is definitely something for astrophysics people though! Haven't studied a jot of that for about 4 years now, ha. 
EternalLight
 Follow
 68 followers
 2 badges
 Send a private message to EternalLight
 Thread Starter
Offline2ReputationRep: Follow
 5
 13022017 11:54
(Original post by Pessimisterious)
But it's not just about the earth moving towards or away from it. It's about the relative alignment of the two velocity vectors.
Maybe the beacon also ends up orbiting something?
I think the point of the question is just to somehow demonstrate the transverse doppler effect and how things can change with the angle. This is the only thing I can guess from it, given the fact that the equation you're working with deals with , which only happens in that context.
And yeah, I guess it's possible for a galaxy to not redshift even though it actually is moving. This is definitely something for astrophysics people though! Haven't studied a jot of that for about 4 years now, ha. 
 Follow
 6
 14022017 19:10
Does any of this apply to GCSE?
please... 
EternalLight
 Follow
 68 followers
 2 badges
 Send a private message to EternalLight
 Thread Starter
Offline2ReputationRep: Follow
 7
 14022017 19:12

Callicious
 Follow
 16 followers
 18 badges
 Send a private message to Callicious
Offline18ReputationRep: Follow
 8
 14022017 20:22
Also, with regard to the question, the reason the redshift may be small is that at the angle pi/2 or 90 degrees, the beacon is moving perpendicular to our line of sight, thus the relativistic velocity we consider is to be thought of as negligible, at least for this case.
The ships velocity isn't along the line of sight, thus any sort of beaming from the ship along the line of sight wont be redshifted by the factor that 0.8c seems to imply. That's my guess.
Quick Edit : Gotta add this on.
The reason they may balance out is that at some point, the lineofsight velocity will cancel out with the velocity of the earth or whatever place you are at with NASA, and as such there is no relative velocity that should be considered for the calculations with regard to the frames that the beacon and earth are in, thus there shouldn't be any redshift.
Also one last edit kicking in my head :
The reason it may be travelling orthogonal to the field of sight is that nothing will travel purely straight through space unless the forces on it superpose to be zero. If it is shot off from earth and travels for some time as the question implies, much less at 0.8c, it's going to end up being attracted by other large bodies, etc.Last edited by Callicious; 14022017 at 20:35. 
EternalLight
 Follow
 68 followers
 2 badges
 Send a private message to EternalLight
 Thread Starter
Offline2ReputationRep: Follow
 9
 14022017 20:45
(Original post by Callicious)
If you're with OCR, you may have to deal with out. Our old teacher made a habit of having us go through calculations and lots of details on relativistic redshift :;
Also, with regard to the question, the reason the redshift may be small is that at the angle pi/2 or 90 degrees, the beacon is moving perpendicular to our line of sight, thus the relativistic velocity we consider is to be thought of as negligible, at least for this case.
The ships velocity isn't along the line of sight, thus any sort of beaming from the ship along the line of sight wont be redshifted by the factor that 0.8c seems to imply. That's my guess.
Quick Edit : Gotta add this on.
The reason they may balance out is that at some point, the lineofsight velocity will cancel out with the velocity of the earth or whatever place you are at with NASA, and as such there is no relative velocity that should be considered for the calculations with regard to the frames that the beacon and earth are in, thus there shouldn't be any redshift.
Using the doppler shift equation we can say that
It's clear that the square root term will always be less than or equal to 1 and so the right side will always be negative given that for
Then using the taylor expansion it becomes
So you are right and there is a time when the probe travels nearly perpendicular to pi/2. If we just plug in we get .
All well and good but I still fail to see where the speed of the probe is taken into account... As I mentioned earlier even if the probe was moving directly away from earth with it should still be redshifted due to the sheer speed of the probe compared to Earths orbit. 
Callicious
 Follow
 16 followers
 18 badges
 Send a private message to Callicious
Offline18ReputationRep: Follow
 10
 14022017 20:56
(Original post by AishaGirl)
Well let's work it through.
Using the doppler shift equation we can say that
It's clear that the square root term will always be less than or equal to 1 and so the right side will always be negative given that for
Then using the taylor expansion it becomes
So you are right and there is a time when the probe travels nearly perpendicular to pi/2. If we just plug in we get .
All well and good but I still fail to see where the speed of the probe is taken into account... As I mentioned earlier even if the probe was moving directly away from earth with it should still be redshifted due to the sheer speed of the probe compared to Earths orbit.
My best guess would be that the folks on Earth are accelerating, at some point they will be accelerating relative to the probe, thus this acceleration may cancel out the relativistic doppler shift. That's true to some extent but on the scale of 0.8c, no idea.
My only notion would be as I mentioned earlier with the probe being at 90 degrees to the line of sight, but ignoring any external influence, i.e. just considering the probe heading straight away and the folks on earth not orbiting just sitting there, I don't know. 
EternalLight
 Follow
 68 followers
 2 badges
 Send a private message to EternalLight
 Thread Starter
Offline2ReputationRep: Follow
 11
 14022017 21:00
(Original post by Callicious)
Ya, to be honest that part has me in a loop too.
My best guess would be that the folks on Earth are accelerating, at some point they will be accelerating relative to the probe, thus this acceleration may cancel out the relativistic doppler shift. That's true to some extent but on the scale of 0.8c, no idea.
My only notion would be as I mentioned earlier with the probe being at 90 degrees to the line of sight, but ignoring any external influence, i.e. just considering the probe heading straight away and the folks on earth not orbiting just sitting there, I don't know. 
 Follow
 12
 16022017 19:07
(Original post by AishaGirl)
Yeah I dunno, going to ask the physics teacher at school see if he can explain it better .
i didnt mean to spark of a whole lecture
thanks anyways tho
Related discussions
 redshift and doppler effect help
 Edexcel GCSE Physics P1 June 2014 (19/05/2014)
 Edexcel cosmology/red shift question?
 revision HELP AS physics Edexcel
 AQA GCSE PHYSICS UNIT 1 (P1): Friday 12th June 2015
 I have no idea what Red Shift is or the difference between ...
 Red Shift??
 Red shift and orbital speed
 Astrophysics and calculation of red shift?
 Astrophysics Doppler Wobble
Related university courses

Physics with Particle Physics & Cosmology
Swansea University

Physics
University of York

Physics
HeriotWatt University

Physics
University of Hull

Environmental Science and Physics
Keele University

Mathematics and Theoretical Physics
University of St Andrews

Physics with Astrophysics with Professional and Research Placements
University of Bath

Physics with Astrophysics with Science Foundation Year
Keele University

Physics with Nuclear Technology BSc Hons (Sandwich)
University of the West of Scotland

Theoretical Physics (4 years)
University of Birmingham
We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.
 charco
 Mr M
 Changing Skies
 F1's Finest
 rayquaza17
 Notnek
 RDKGames
 davros
 Gingerbread101
 Kvothe the Arcane
 TeeEff
 The Empire Odyssey
 Protostar
 TheConfusedMedic
 nisha.sri
 claireestelle
 Doonesbury
 furryface12
 Amefish
 harryleavey
 Lemur14
 brainzistheword
 Rexar
 Sonechka
 TheAnxiousSloth
 EstelOfTheEyrie
 CoffeeAndPolitics
 an_atheist
 Labrador99
 EmilySarah00
 thekidwhogames
 entertainmyfaith
 Eimmanuel