Chapter 33, Problem 24P

Solution

The speed of the galaxy relative to a person on Earth.

  $v=2.72\times {10}^8\text{m}/\text{s}$

Given:

Galaxy is 12 billion light years away

Formula used:

Hubble’s Law

  $v=H_{0}d$

Here,

v is speed of light

H₀ is Hubble’s constant

d is distanceCalculation:

Here d is equal to 12 billion light year= $12\times {10}^9$ light year

1 light year = $3\times {10}^8\times 365\times 24\times 60\times 60=9.5\times {10}^{15}\text{m}$

So $12\times {10}^9$ light year= $12\times {10}^9\times 9.5\times {10}^{15}=114\times {10}^{24}$ meter Value of H₀ is 73.8km/sec/Mpc

Number of km in Mpc is $3.09\times {10}^{19}$

For converting Hubble’s constant in the unit of per second , we divide the value of hubble’s constant (km/sec/Mpc )by $3.09\times {10}^{19}$

So Hubble’s constant in sec-1 is $\frac{73.8}{3.09\times {10}^{19}}=23.88\times {10}^{-19}$

From $v=H_{0}d$

  $v=23.88\times {10}^{-19}\times 114\times {10}^{24}=2722.32\times {10}^5$

  $v=2.72\times {10}^8\text{m}/\text{s}$