Understanding Sunlight Travel Time to Earth

This question asks us to determine how long it takes for sunlight, traveling at the speed of light, to cover the vast distance between the Sun and Earth. We are given the average distance and the speed of light to perform this calculation.

Analyzing the Given Data for Sunlight Travel

To solve this, we need to consider the two crucial pieces of information provided:

• The average distance between the Sun and Earth: This is given as approximately $1 \text{ AU}$, which translates to $149.6 \times 10^6 \text{ km}$.
• The speed of light in a vacuum: This is given as $c \approx 2.998 \times 10^5 \text{ km/s}$.

Understanding these values is key to calculating the time it takes for light to travel from the Sun to Earth.

Calculating the Sunlight Travel Time Step-by-Step

We can find the time it takes for sunlight to reach our planet using a basic physics formula relating distance, speed, and time.

1. Identify the Formula: The relationship between distance, speed, and time is:

   $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$

2. Substitute the Given Values: Now, we plug the provided distance and speed of light into the formula:

   $$ \text{Time} = \frac{149.6 \times 10^6 \text{ km}}{2.998 \times 10^5 \text{ km/s}} $$

3. Perform the Calculation: Dividing the distance by the speed gives us the time in seconds:

   $$ \text{Time} \approx 498.999 \text{ seconds} $$

4. Convert Seconds to Minutes and Seconds: To make this time more understandable, we convert it into minutes and seconds. There are 60 seconds in a minute.
   • Calculate the number of whole minutes:

     $$ \text{Minutes} = \left\lfloor \frac{498.999}{60} \right\rfloor = \lfloor 8.3166... \rfloor = 8 \text{ minutes} $$

   • Calculate the remaining seconds:

     $$ \text{Seconds} = 498.999 \text{ seconds} - (8 \times 60 \text{ seconds}) $$

     $$ \text{Seconds} = 498.999 - 480 = 18.999 \text{ seconds} $$

   • Rounding the seconds to the nearest whole number, we get approximately 19 seconds.
5. Final Time: Therefore, the total time is approximately 8 minutes and 19 seconds.

Relating Calculation to Options

Our calculated time for sunlight to reach Earth is approximately 8 minutes and 19 seconds. Comparing this result with the given options, we find that it matches one of them precisely.

The calculation shows that the journey of sunlight from the Sun to our planet takes about 8 minutes and 19 seconds.