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 3.64 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.

Question Image

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

Solution Video