Consider a hypothetical cluster of galaxies distributed in space as shown in the top part of Figure P31.28, where each galaxy is positioned on a grid with a spacing of two million lightyears. Four billion years later, the universe has expanded such that the grid spacing is now three million light-years as seen in the bottom part of Figure P31.28. 

(a) Assume your planet is in galaxy A. Calculate the change in distance to galaxies B, C, D, and E as seen from A over the 4.0-billion-year period. 

(b) Which galaxy moves the most with respect to galaxy A? 

(c) Now assume your planet is in galaxy D. Find the change in distance to galaxies C, B, A, and F. 

(d) Which galaxy moves the most with respect to galaxy D over this period of time? 

(e) Find the velocities of galaxies B, C, D, and E that would be measured if your planet were in galaxy A. 

(f) Find the velocities of galaxies C, B, A, and F as seen from a planet in galaxy D.