Question
The great astronomer Edwin Hubble discovered that all distant galaxies are receding from our Milky Way Galaxy with velocities proportional to their distances. It appears to an observer on the Earth that we are at the center of an expanding universe. Figure 3.62 illustrates this for five galaxies lying along a straight line, with the Milky Way Galaxy at the center. Using the data from the figure, calculate the velocities: (a) relative to galaxy 2 and (b) relative to galaxy 5. The results mean that observers on all galaxies will see themselves at the center of the expanding universe, and they would likely be aware of relative velocities, concluding that it is not possible to locate the center of expansion with the given information. Figure 3.62: 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.

a) $v_{32} = 2200 \textrm{ km/s}$, $v_{12} = -2300 \textrm{ km/s}$, $v_{42} = 5030 \textrm{ km/s}$, $v_{52} = 8900 \textrm{ km/s}$, $v_{55} = 0$

b) $v_{35} = -6700 \textrm{ km/s}$, $v_{15} = -11200 \textrm{ km/s}$, $v_{25} = -8900 \textrm{ km/s}$, $v_{45} = -3870 \textrm{ km/s}$, $v_{55} = 0$

# OpenStax College Physics, Chapter 3, Problem 63 (Problems & Exercises)  In order to watch this solution you need to have a subscription.

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