Rate of Expansion. Use the figure below to answer the following questions: Betwe

Question

Rate of Expansion.

Use the figure below to answer the following questions: Between 1 and 2 Mpc from Earth (that is, ~1.5 Mpc), how fast (v1=?) are galaxies moving away from us? Between 2 and 3 Mpc from Earth (that is, ~2.5 Mpc), how fast (v2=?) are galaxies moving away from us? Extrapolating from v1 and v2, how fast (v3=?) are galaxies between 3 and 4 Mpc (that is, ~3.5 Mpc) moving away from us? Express your answers in units of km/s. From these numbers, do galaxies move at the same speed, faster, or slower the further they are from us? (Hint: Assume that Hubble's original figure which is shown below is correct. Use the data in this figure to formulate your answer.)

Please round the answers to two significant digits.

v1 =  km/s.

v2 =  km/s.

v3 =  km/s.

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Explanation / Answer

From Hubbles law,

v1 = Ho * d1 (Ho = 70 km/s /Mpc)

or, v1 = 70 km/s/Mpc * 1.5 Mpc = 105 km/s

Similarly, v2= Ho * d2

or, v2= 70km/s/Mpc * 2.5 Mpc =175 km/s

From extrapolation, we get-

(v-v1 )= m * ( d - d1) where m = (v2 - v1)/ (d2 - d1) = 70

or, v - 105 = 70 *( d - 1.5)

or, v = 70d

So, v3 = 70 * d3 = 70 * 3.5 km/s = 245km/s

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