Question

(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?

Short answer

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

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

Step-by-step solution

The speed of light and distance and time formula.

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

Distance = speed*time.

Time taken by light to travel from moon to the earth.

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

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

Ie.

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

Distance between sirius and earth.

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,

$$\begin{gathered} d=3*{10}^{8}2.72*{10}^8 \\ d=8.16*{10}^{16}m \end{gathered}$$