Answer:
Earth: [tex]t = 498.667\,s[/tex], Mercury: [tex]t = 193\,s[/tex], Pluto: [tex]t = 19700\,s[/tex]
Explanation:
The light travels at a constant speed of approximately [tex]3\times 10^{8}[/tex] meters per second. The time ([tex]t[/tex]), in seconds, required for light to travel a given distance is:
[tex]t = \frac{x}{v_{l}}[/tex] (1)
Where:
[tex]x[/tex] - Travelled distance, in meters.
[tex]v_{l}[/tex] - Speed of light, in meters per second.
Now, we calculate the time for light to travel to each planet:
Earth ([tex]v_{l} = 3\times 10^{8}\,\frac{m}{s}[/tex], [tex]x = 1.496\times 10^{11}\,m[/tex])
[tex]t = \frac{x}{v_{l}}[/tex]
[tex]t = 498.667\,s[/tex]
Mercury ([tex]v_{l} = 3\times 10^{8}\,\frac{m}{s}[/tex], [tex]x = 5.79\times 10^{10}\,m[/tex])
[tex]t = \frac{x}{v_{l}}[/tex]
[tex]t = 193\,s[/tex]
Pluto ([tex]v_{l} = 3\times 10^{8}\,\frac{m}{s}[/tex], [tex]x = 5.91\times 10^{12}\,m[/tex])
[tex]t = \frac{x}{v_{l}}[/tex]
[tex]t = 19700\,s[/tex]
