(a) Use the distance and velocity data in Figure 3.64 to find the rate of expansion as a function of distance. (b) If you extrapolate back in time, how long ago would all of the galaxies have been at approximately the same position? The two parts of this problem give you some idea of how the Hubble constant for universal expansion and the time back to the Big Bang are determined, respectively.
Figure 3.64 Five galaxies on a straight line, showing their distances and velocities relative to the Milky Way (MW) Galaxy. The distances are in millions of light years (Mly), where a light year is the distance light travels in one year. The velocities are nearly proportional to the distances. The sizes of the galaxies are greatly exaggerated; an average galaxy is about 0.1 Mly across.
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In the given problem, relative velocities and distances are given for five different galaxies as shown in the figure below. The given velocities of the galaxies are relative to milky way galaxy whereas the the given distances are the distances of the other galaxies from milky way galaxy.
Here we need to calculate the average rate of expansion as a function of distance and also we need to find how long back does the galaxies were at the same position.
The relative velocity is the velocity of an object measured from a particular reference frame and it will vary as the reference frame changes.