4) Hubble\'s Law, which is the relationship between the distance to a galaxy and

Question

4) Hubble's Law, which is the relationship between the distance to a galaxy and its recessional velocity, helped determine that the universe is expanding, and, once calibrated, gave us a new way to determine distances to distant galaxies. Use this information to answer the questions below. a) How do you measure the recessional velocities of galaxies? If you quote a formula, be sure to explain it. (1 pt) b) Assuming a modern value for the Hubble constant of 67.8 km/s/Mpc, calculate an estimate for the age of the universe. Be sure to show your work, and put your answer in terms of gigayears (Gyr or Byr) with the proper number of sig figs. (4 pts) c) For a very high redshift galaxy, will the look-back time be large or small? Was the d) Are the galaxies within the Local Group affected by the expansion of the universe e) Imagine aliens in a distant galaxy are making observations of the universe on large universe older or younger than it is now when that galaxy's light was emitted? (2 pts) relative to one another? Why or why not? (3 pts) scales at the same time that we are making these same kinds of observations from Earth. Will they come to completely different conclusions about the expansion of the universe than we do? Why or why not? (3 pts) f Distant galaxies are moving away from us, which causes their spectral lines to be redshifted. What causes them to move away from us, and thus what is the root cause of their redshifts? (2pts)

Explanation / Answer

Problem 4(e):

If distant aliens were also making observations regarding universe simultaneously with us from their respective planet, they would come up with very different conclusion. And the reasons for this are listed below:

1) universe expand faster than the speed of light, and, perhaps some of the galaxies we are seeing right now are currently moving away from us faster than the speed of light. Same thing will be happening at distant galaxy as well to their respective reference frame. As a consequence of their great speeds, these galaxies will likely not be visible to us forever; some of them are right now emitting their last bit of light that will ever be able to make it all the way across space and reach us.

2) Most useful method to measure universe's expansion is Hubble constant, which is approximately equal to 71, measured in units of "kilometers per second per megaparsec." It means, the Hubble constant is approximately equal to 0.007% per million years -it's meaning is that every million years, all the distances in the universe stretch by 0.007%. (This interpretation assumes that the Hubble "constant" actually stays constant over those million years, which it doesn't, but given that a million years is extremely short on cosmic timescales, this is a pretty good approximation. It also assumes that when we talk about the "distance" between two galaxies, we are referring to the distance between them right now.

3) Redshift and motion: If an object that emits light moves away from you, the light from it gets redshifted. This is the same exact effect — the doppler shift — that causes police sirens to sound lower pitched when they move away from you. As light travels through space and space expands, it causes the wavelength of that very light to expand, too. And that’s cosmic expansion in our Universe.

So, the gist of the matter is galaxies are not really moving through space away from each other. Instead, the space between them is expanding (just like the rubber band expanded, separating the dots fixed to it from each other). As the universe expands, the galaxies get farther from each other, and the apparent velocity will appear to be larger for the more distant galaxies. So, all the observations which we are observing here in earth are also keeps changing with time, similarly when aliens observing that too, they will also get different conclusion.

According to Chegg guidelines I can answer one question at a time so please post other questions separately. Please rate my answer if you find it helpful, good luck...

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