Chapter 33, Problem 22P

Solution

The distance of galaxy from a person.

  $d=1.26\times {10}^{12}$ meter

Given:

A galaxy is travelling away from us at 1.0% of the speed of light

Formula used:

Hubble’s law $v=H_{0}d$

Here, v is speed of light , H₀ is Hubble’s constant and d is distance

Calculation:

Speed of light is equal to $3\times {10}^8\text{m}/\text{s}$

1% of speed of light is $\frac{3\times {10}^8\times 1}{100}=3\times {10}^6\text{m}/\text{s}$

Value of H₀ is $73.8\text{km/sec/Mpc}$

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 $v=H_{0}d$

  $d=\frac{v}{H_0}$

  $d=\frac{3\times {10}^6}{23.88\times {10}^{-19}}=0.126\times {10}^{13}$ meter

  $d=1.26\times {10}^{12}$ meter