n this problem we are going to explore the evidence for the expansion of the uni
ID: 1408759 • Letter: N
Question
n this problem we are going to explore the evidence for the expansion of the universe that was first discovered by Edwin Hubble. In the 1920s, Hubble discovered that far-off galaxies were all redshifted by an amount that increased with their distance from us. In other words, it appeared that the further away a galaxy was, the faster it was receding from us. This became known as Hubble's law. Suppose that you attempt to measure the hydrogen spectral lines from three distant galaxies. You get the following values for what corresponds to the 656.46-nm hydrogen line. For galaxy 1 you get a line at 656.50 nm, for galaxy 2 the line is at 656.57 nm, and for galaxy 3 the line is at 656.64 nm. Using a few independent techniques (which we will not go into here) you are able to pin down the distances to these three galaxies. Galaxy 1 is determined to be approximately 106 light years away (or 1Mly), galaxy 2 is 2.5Mly away, and galaxy 3 is 4Mly away. Recall that a light year is the distance that light travels in a year or roughly 9.46×1015m. For this problem we can use the standard special relativistic Doppler shift to determine the galaxies' recessional velocities. One should note that this is not strictly correct because, unlike velocities of objects passing through space, Hubble's law is due to the expansion of space itself, which requires the more complicated theory of general relativity. For cases in which the galaxies are relatively close to earth (such as this problem) and thus have recessional speeds vc, the Doppler shift equations from general relativity become the same as those from special relativity. What is the recessional velocity v1 of the first galaxy? What is the recessional velocity v2 of the second galaxy? What is the recessional velocity v3 of the third galaxy? Let's first determine the relationship between the recessional velocity of a galaxy and the distance to it. It might help to use some graph paper to plot the velocity (calculated from the Doppler shift) versus distance. Which of the following statements is correct? Let's first determine the relationship between the recessional velocity of a galaxy and the distance to it. It might help to use some graph paper to plot the velocity (calculated from the Doppler shift) versus distance. Which of the following statements is correct? The recessional velocity varies as the square of the distance. The recessional velocity varies linearly with the distance. The recessional velocity varies as the square root of the distance. The recessional velocity varies as the inverse of the distance. Use the given information and the answers to Parts A to D to determine the Hubble constant H0. What is the relation between the Hubble constant H0 and the age of the universe t? Assume that the Hubble constant has not changed over the history of the universe. Use the information from the previous part to estimate the age of the universe tage.
Explanation / Answer
The equation is :
V = Ho D
'V' is velocity
'Ho' is the Hubble Constant (73.8 km/sec/Mpc = 20 Km/sec/Mly)
A megaparsec (Mpc) = 3,261,688.071 light years
Galaxy 1: V= 20 km/sec/Mly * 1 Million light years = 20 km/s
Galaxy 2: V= 20 km/sec/Mly * 2.5 Million light years = 50 km/s
Galaxy 3: V= 20 km/sec/Mly * 4 Million light years = 80 km/s
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