Chapter 1, Problem 22P

Solution

a.

Total meters in 1 light year.

  $9.45\times {10}^{15} \text{m}$

Given:

A light year is the distance light travels in one year at speed 2.998×10⁸m/sec

Formula used:

  $d=v\times t$ here d is distance, v is velocity and t is time

Calculation:

One year =365 days = $365\times 24\times 60\times 60$ Second

So one light year = $v\times t$ meters

One light year = $2.998\times {10}^8\times 365\times 24\times 60\times 60\text{meter}$

One light year = $9.45\times {10}^{15} \text{m}$

Conclusion:

Therefore, in 1 light year there are $9.45\times {10}^{15} \text{m}$

b.

Total AU in 1 light year.

One light year $=6.3\times {10}^4$ AU.

Given information:

A light year is the distance light travels in one year at speed 2.998×10⁸m/sec. An astronomical unit (AU) is the average distance from sun to earth , 1.5×10⁸km.

Formula used:

  $\begin{array}{l}1\text{AU}=1.5\times {10}^8\text{km}\\ 1\text{AU}=1.5\times {10}^{11}\text{m}\end{array}$

Calculation:

One light year is equal to $9.45\times {10}^{15}$

So, number of AU in 1.00 light year=

  $\frac{9.45\times {10}^{15}}{1.5\times {10}^{11}}=6.3\times {10}^4$

Conclusion:

Therefore, number of AU in 1 light year is $6.3\times {10}^4$

c.

The speed of light in AU/h.

7.20AU/hour

Given:

A light year is the distance light travels in one year at speed 2.998×10⁸m/sec

Formula used:

  $1\text{km}=1000\text{m}$

  $1\text{hour}=3600\sec$

Calculation:

The speed of light in meter/sec is $2.998\times {10}^8$

In km/sec the speed of light $=\frac{2.998\times {10}^8}{1000}=2.998\times {10}^5$ km/sec

In km/hour Speed of light

  $=2.998\times {10}^5\times 3600$ km/hour

One AU is equal to $1.5\times {10}^8\text{km}$

So the speed of light in AU/h

  $=\frac{2.998\times {10}^5\times 3600}{1.5\times {10}^8}=\frac{1.07928\times {10}^9}{1.5\times {10}^8}=7.20$ AU/hour

Conclusion:

Therefore, speed of light is 7.2 AU/hour.