Question

How long does it take for light (in minutes) to reach Saturn from the Sun, at a distance of $1.532\times {{10}^{9}}Km$?

Answer 1

Sun is the biggest natural source of light, sunlight. The time taken by light to travel from the Sun to the different planets of the solar system depends on the distance between the planet and the Sun. The farther away will be the planet, the more time it will take for light to reach that planet. This can be calculated by the simple formula of speed in physics.

Complete step-by-step solution:
Saturn orbits the sun at a distance of 1.532 billion kilometer and the light travels at a speed of $3\times {{10}^{8}}m{{s}^{-1}}$. Dividing the two quantities as speed is equal to distance divided by time.
Hence,
$\begin{aligned} & speed=\dfrac{\text{distance}}{time} \\\ & \Rightarrow time=\dfrac{\text{distance}}{speed} \\\ \end{aligned}$

Distance of Saturn from Sun = 1.532 billion km = $1.532\times {{10}^{12}}m$ \left\\{ \because 1km=1000m \right\\}
$\Rightarrow time=\dfrac{1.532\times {{10}^{12}}m}{3\times {{10}^{8}}m{{s}^{-1}}}=5106.66s$

Also, 1 hour = 3600 seconds
$\begin{aligned} & \Rightarrow time=51066.66s\times \dfrac{1h}{60\times 60s} \\\ & \Rightarrow time=1.418hours \\\ \end{aligned}$
$\begin{aligned} & \Rightarrow time=1.418hours \\\ & \Rightarrow time=1.418hours\times \dfrac{60\min }{1hour} \\\ & \Rightarrow time=85.08\min \\\ \end{aligned}$

Therefore, light approximately takes 1.418 hours or 85.08 minutes to reach Saturn.

However, this light generated by the Sun is tens of thousands of years old. This is because for this long duration of time, the photons inside the sun light striking each other and then emitted the light finally from the surface of the Sun.

Note:
The Sun is a yellow dwarf star, a hot ball of glowing gases at the center of the solar system. It emits light due to the hydrogen and helium gases burning in it by the process called gamma decay or gamma radiation. To carry out this process, the temperature of the Sun is about 5,800 Kelvin and it emits gamma rays from solar flares.