Chapter 4: Q1E (page 1073)

(a) How much time does it take light to travel from the moon to the earth, a distance of 384,000 km? (b) Light from the star Sirius takes 8.61 years to reach the earth. What is the distance from earth to Sirius in kilometers?

Expert verified

Time taken by light to travel from moon to the earth is 1.28s

The distance between the star sirius and earth is $8.16 * 10^{16} m$

Step by step solution

The speed of light is $3 * 10^{8} m / s$

Distance = speed*time.

The given information is that the distance between earth and the moon is 38400km.

Therefore, Time taken = distance / (speed of light)

Ie.

$t = \frac{3.84 * 10^{8}}{3 * 10^{8}} t = 1.28 s$

The given information is the time taken by light to travel from sirius to earth is 8.61 years.

Therefore, distance = (speed of light) * time

First we need to convert the time taken taken into seconds where $3.154 * 10^{7}$ is the number of seconds in a year..

$8.61 * 3.154 * 10^{7} = 2.72 * 10^{8}$ seconds.

Now the distance between sirius and earth is,

$d = 3 * 10^{8} 2.72 * 10^{8} d = 8.16 * 10^{16} m$

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