(a) Five galaxies, shown in the figure below, are 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. Use the distance and velocity data in the figure below to find the rate of expansion (in km/(s Mly)) as a function of distance. V1 Galaxy 1 325 Mly Galaxy 2 155 Mly -6456 km/s V₂ = -3079 km/s xkm/(s Mly) . Galaxy 3 MW V4 = Galaxy 4 180 Mly Galaxy 5 430 Mly 3576 km/s V5 = 8542 km/s (b) If you extrapolate back in time, how long ago (in Gyr) 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. Gyr

(a) Five galaxies, shown in the figure below, are 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. Use the distance and velocity data in the figure below to find the rate of expansion (in km/(s Mly)) as a function of distance. V1 Galaxy 1 325 Mly Galaxy 2 155 Mly -6456 km/s V₂ = -3079 km/s xkm/(s Mly) . Galaxy 3 MW V4 = Galaxy 4 180 Mly Galaxy 5 430 Mly 3576 km/s V5 = 8542 km/s (b) If you extrapolate back in time, how long ago (in Gyr) 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. Gyr