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(Q002) For a galaxy with a redshift of z = 6, the radius of theobservable Universe would have been what fraction of its currentvalue?...

Question

(Q002) For a galaxy with a redshift of z = 6, the radius of theobservable Universe would have been what fraction of its currentvalue?

(Q002) For a galaxy with a redshift of z = 6, the radius of the observable Universe would have been what fraction of its current value?



Answers

How much has the universe expanded since light was emitted from a galaxy with a redshift of $z=8 ?$

Everybody. So we need to find a, um, the distance. And we have distance equals velocity of the Hubble. And they gave us the glossy as 28,700 killing meters per second. And he gave us Hubble as 70 feeling meters per second m he see which equals 4100 m p. C. Okay, get that. See, There now be is asking us about the time. And it says that assuming is looking back at the time of this galaxy, How old was it? So we have 2/3 okay and times 13.8 billion. And we don't need to worry about the billions, and it's not gonna change. Okay, so this is gonna be 9.2 1,000,000,000 years. Okay, Now we need to find expansion and find expansion using this equation 1/1 plus z. So we got one a plus, and it gave us 5.8 to the red shift, so it's gonna be 1/6 point Eat too. So expansion expanded, Um, six point 82 times. Okay. Thank you, guys.

The distance to this galaxy D is 10. Make up our sex. So to find the velocity of recession, we're gonna use Hubble's law, which says the velocity of resection V is equal to Hubble's constant H, not times the distance d. So Hubble's constant is equal to 70 kilometers per second times. Make a parsecs or 70 times 10 to the third meters per second times made a parsecs again. D is 10 mega parsecs. So if we use the 70 kilometers per second time to make a parsecs for each, not we get a recession velocity V equal to 700 kilometers per second Chloe comme boxes and as their solution for part A for part B, it says that it wants us to figure out what fraction of the Starlight and the galaxy is red shifted. That is, what is the Z value? Okay, so the Z value is equal to, um, the swear it of one plus the velocity divided by the speed of light divided by one minus velocity, divided by the speed of light. In that value, we're going to subtract one from it. So since the velocity V is in kilometers per second, We also want to use the kilometers per second version of the speed of light. So C is three times 10 to the eight meters per second or three times 10 to the fifth kilometers per second. So we want to use the kilometers per second version so our units will cancel out properly plugging these values in. We find that Z is equal to 0.0 25 which you could also write as a percent by multiplying it by 100%. This is equal to 0.25%. So the red shift of the Z values approximately 0.25%. So it is a small amount of red shift, but it is there and this is because V is a small fraction of the speed of light. The larger value the V is, the more the red shipped is going to be. Weaken boxes in as our solution for B

So we know that one plus Z is the quality of their frame wavelike over restroom we went. So observe, frame wavelength will just be one plus 7.6 its 1.6 times the rest frame wavelength of 656.28 nanometers. Um, and that's equal to 56 44 nanometers. Um, And so whereas the rest frame and the rest room, this is ah, optical line. Remember, the optical goes from about 400 to buck 700. Um, this eyes is a lot greater. It's beyond the optical, and it's in the infrared. So this is actually in the infrared. Um, in fact, the mid infrared on. And so the inference starts has about 1000 nanometers. Um and so this is which is equal to, ah, about which is equal to one micro meter. So that's about 5.6 micrometers. So that is very much in the infrared. Made him Fred

All right. So purport a, um we're already given him a session velocity. So the velocity will be recalled. Each not times D, um and so d semi Hubble's law as applicable is just velocity over each. Not since is 2.87 times 10 to the five kilometers per second h, not 70 kilometers for a second per mega parsecs. So this kilometre prince second drops out and you get 4100 mega parsecs or about R 4.1 giga parsecs, Um, part fealty and part of you, you're assuming Hubble Ah, Hubble time of 13.7 billion years. How old was universe? And look back home galaxy. So for that, all you need to do is convert this distance to ah which is currently in mega parsecs to a lecture. So you multiply that by 2.26 to get the conversion between millions of light years on duh mega parsecs. Ah, so this is 13.2 B seven 1,000,000,000 light years are 3 13,070 million light years. Uh, and so the look back times is just the number of years, and, um, that is encoded in this. So look back time, we'll just be a 13.37 1,000,000,000 years. Ah, And finally, for a scale factor A That is just equal to 1/1 plus the red shift. So this is one over one plus hopes 5.82 So that's 1/6 0.82 since his 0.147 Remember that scale factor? The present day is one. So, uh, this red shift skehf of the universe was about 14% besides the nah present universe.


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