How many minutes does it take light from the sun to reach Earth? (The distance from the sun to Earth is 93 million \(\mathrm{mi} ;\) the speed of light \(=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\).)

Understanding how to convert units of distance is a vital skill in physics and everyday situations alike. In the context of light travel from the Sun to the Earth, converting the distance from miles to meters is necessary because the speed of light is commonly expressed in meters per second (\( m/s \)).

To perform this conversion, we use the fact that 1 mile is approximately equal to 1609.34 meters. Consequently, if we have a distance in miles, we multiply by this conversion factor to find the equivalent distance in meters. For example, if the Sun is 93 million miles away, the calculation would look like this: \( 93,000,000 \text{ miles} \times 1609.34 \text{ m/mile} \). The result is a much larger number in meters, because meters are a smaller unit than miles, which reflects the incredible vastness of space that light can travel.

The relationship between speed, distance, and time is a foundational concept in physics, commonly known as the speed-distance-time formula. This relationship is given by the equation \( \text{speed} = \frac{\text{distance}}{\text{time}} \).

However, when we need to find the time it takes for something to happen, like how long it takes light to travel from the Sun to the Earth, we rearrange the formula to \( \text{time} = \frac{\text{distance}}{\text{speed}} \). By plugging in the distance in meters and the speed of light in meters per second, we can calculate the time it takes for light to cover that distance. This equation helps us understand that the higher the speed or the shorter the distance, the less time it will take for an object to travel. Conversely, the greater the distance or the slower the speed, the more time it will take.

The travel time calculation for light is a fascinating application of the speed-distance-time formula. Light moves at an incredibly fast, constant speed of approximately \(3.00 \times 10^8 m/s\) in a vacuum, like space. To determine how long it takes for light to travel a given distance, we divide the distance the light has to travel by its speed.

After calculating the travel time in seconds, we often convert it into more understandable units, such as minutes or hours. For instance, by dividing the time in seconds by 60, we convert it to minutes. This allows us to appreciate the astronomical distances in our universe on a more human scale, such as understanding that light from the Sun takes just over eight minutes to reach Earth – an astounding fact that illustrates both the vastness of space and the incredible speed at which light travels.