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The observed recession velocity of a galaxy is the sum of its Hubble flow velocity, vH...


The observed recession velocity of a galaxy is the sum of its Hubble flow velocity, vH = H0d, and the line-of-sight (LOS) component of its peculiar velocity, vp, due to local gravitational effects.

a) Suppose we measure H0 by measuring the distance and redshift for a single galaxy. Write an expression for how the error in our measurement depends on the peculiar velocity of the galaxy?

b) At what distance can we measure H0 to 5%? Assume the true value of H0 is 74 km s−1 Mpc−1 and a typical LOS peculiar velocity is vp = 200 km s−1 .

c) The Virgo cluster contains ∼ 1300 galaxies and is at a distance of 16 Mpc. The galaxies have an RMS velocity about their center of mass of 600 km s−1 . How many galaxies do we need to observe in Virgo to reduce the error in H0 due to peculiar velocities to 5%? Hint: look up how you calculate the error on a mean if you don’t know

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