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The orbital radius of the Earth (the average Earth-Sun distance) is 1.496 × 1011 m. Mercury’s orbital radius is 5.79 × 1010 m and Pluto’s is 5.91 × 1012 m. Calculate the time required for light to travel from the Sun to each of the three celestial bodies

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xero099

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]

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