Question

3. The observed recession velocity of a galaxy is the sum of its Hubble flow velocity, UH = Hod, and the line-of-sight (LOS) component of its peculiar velocity, vp, due to local gravitational effects. a) Suppose we measure Ho by measuring the distance and redshift for a single galaxy velocity of the galaxy?10 b) At what distance can we measure Ho to 5%? Assume the true value of Ho is 74 kin s-"Mpc-1 and a typical LOS peculiar velocity is up-200 km s-1. [10 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 Ho due to peculiar velocities to 5%? Hint: look up how you calculate the error on a mean if you don't know. [10

Answer 1

ANSWER:

The observed recession velocity of a galaxy is the sum of its Hubble flow velocity, UH = Hod, and the line-of-sight (LOS) component of its peculiar velocity, vp, due to local gravitational effects. a) Suppose we measure Ho by measuring the distance and redshift for a single galaxy velocity of the galaxy?10 b) At what distance can we measure Ho to 5%? Assume the true value of Ho is 74 kin s-Mpc-1 and a typical LOS peculiar velocity is up-200 km s-1. [10 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 Ho due to peculiar velocities to 5%? Hint: look up how you calculate the error on a mean if you dont know.

Given data True value of Hubble constant, Ho 74 km/s/Mpc Typical line of sight of peculiar velocity, v2 200 km/s Let us assume that at a distance of d the Hubble's constant is measured to 5% Consider the Hubble flow velocity at that point Here, Ho' is the measured value of Hubble constant Consider the measured value of Hubble constant for 5% Substitute the value of Ho in the above equation 5%(74) 3.7 Но Substitute the value of Ho in equation (1)

Consider the observed recession velocity Substitute the value of v and v in the above equation. As per the Hubble's law, Substitute the value of v, in equation (2). Substitute the value of Ho in the above equation Hod 3.7d +200 74d 3.7d 200 d 2.845 Mpc 70.3d 200 Hence, the distance at which Ho could be measured to 5%,2.845 Mpc