Question

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

Answer 1

Answer:

Earth: $t = 498.667\,s$, Mercury: $t = 193\,s$, Pluto: $t = 19700\,s$

Explanation:

The light travels at a constant speed of approximately $3\times 10^{8}$ meters per second. The time ($t$), in seconds, required for light to travel a given distance is:

$t = \frac{x}{v_{l}}$ (1)

Where:

$x$ - Travelled distance, in meters.

$v_{l}$ - Speed of light, in meters per second.

Now, we calculate the time for light to travel to each planet:

Earth ($v_{l} = 3\times 10^{8}\,\frac{m}{s}$, $x = 1.496\times 10^{11}\,m$)

$t = \frac{x}{v_{l}}$

$t = 498.667\,s$

Mercury ($v_{l} = 3\times 10^{8}\,\frac{m}{s}$, $x = 5.79\times 10^{10}\,m$)

$t = \frac{x}{v_{l}}$

$t = 193\,s$

Pluto ($v_{l} = 3\times 10^{8}\,\frac{m}{s}$, $x = 5.91\times 10^{12}\,m$)

$t = \frac{x}{v_{l}}$

$t = 19700\,s$