Question

Be sure to show all calculations clearly and state your final answers in complete sentences. Distances by Light. Just as a light-year is the distance that light can travel in 1 year, we define a light-second as the distance that light can travel in 1 second, a light-minute as the distance that light can travel in 1 minute, and so on. Calculate the distance in both kilometers and miles represented by each of the following: a. 1 light-second b. 1 light-minute c. 1 light-hour d. 1 light-day

Short answer

1 light-second = 299,792 km / 186,282 mi; 1 light-minute = 17,987,520 km / 11,176,920 mi; 1 light-hour = 1,079,251,200 km / 670,615,200 mi; 1 light-day = 25,902,068,800 km / 16,091,044,800 mi.

Step-by-step solution

Define Speed of Light

The speed of light in a vacuum is approximately \( 299,792 \) kilometers per second (km/s) or about \( 186,282 \) miles per second (mi/s). This will be used to calculate the distance traveled in the given time periods.

Calculate Distance for Light-Second

A light-second is the distance light travels in one second. In kilometers, this is calculated as follows: \[ 1 \text{ light-second} = 299,792 \text{ km/s} \times 1 \text{ s} = 299,792 \text{ km} \]In miles:\[ 1 \text{ light-second} = 186,282 \text{ mi/s} \times 1 \text{ s} = 186,282 \text{ mi} \]

Calculate Distance for Light-Minute

A light-minute is the distance light travels in one minute. First, calculate the time in seconds (1 minute = 60 seconds) and then use the speed of light:In kilometers:\[ 1 \text{ light-minute} = 299,792 \text{ km/s} \times 60 \text{ s} = 17,987,520 \text{ km} \]In miles:\[ 1 \text{ light-minute} = 186,282 \text{ mi/s} \times 60 \text{ s} = 11,176,920 \text{ mi} \]

Calculate Distance for Light-Hour

A light-hour is the distance light travels in one hour. First, convert hours to seconds (1 hour = 3600 seconds):In kilometers:\[ 1 \text{ light-hour} = 299,792 \text{ km/s} \times 3600 \text{ s} = 1,079,251,200 \text{ km} \]In miles:\[ 1 \text{ light-hour} = 186,282 \text{ mi/s} \times 3600 \text{ s} = 670,615,200 \text{ mi} \]

Calculate Distance for Light-Day

A light-day is the distance light travels in one day. Convert days to seconds (1 day = 86,400 seconds):In kilometers:\[ 1 \text{ light-day} = 299,792 \text{ km/s} \times 86,400 \text{ s} = 25,902,068,800 \text{ km} \]In miles:\[ 1 \text{ light-day} = 186,282 \text{ mi/s} \times 86,400 \text{ s} = 16,091,044,800 \text{ mi} \]

Key concepts

Light-Second

A light-second is a measure of the distance that light can travel in just one second. To put it simply, if you could ride on a beam of light, you'd cover a massive distance in that brief moment of time. The speed of light is absolutely astounding at approximately 299,792 kilometers per second (km/s) or about 186,282 miles per second (mi/s).

When you think about how fast light travels, just one light-second is already quite a distance. It means that in the time it takes you to blink an eye, light has traveled nearly 300 thousand kilometers or about 186 thousand miles.

- The distance light travels in one second is:

• 299,792 kilometers
• 186,282 miles

Light-Minute

A light-minute takes the speed of light over the span of one minute, offering a more extended imagination of distance. Since there are 60 seconds in a minute, we simply multiply the distance light travels in one second by 60.

Using the speed of light, we can calculate that light journeys 17,987,520 kilometers or 11,176,920 miles in the space of just one minute. It's incredible to think that every minute, light can circumnavigate the Earth nearly 7500 times!

- The distances light travels in one minute are:

• 17,987,520 kilometers
• 11,176,920 miles

Light-Hour

Envisioning a light-hour extends our understanding of light travel across an hour. To find out how far light travels in an hour, consider that an hour has 3600 seconds. By continuing to use the defined speed of light, we see that light will cover a staggering distance indeed.

This calculation shows that light can travel 1,079,251,200 kilometers or 670,615,200 miles in one hour. Such enormous distances are perfect for understanding celestial distances like those within our solar system.

- A light-hour equates to traveling:

• 1,079,251,200 kilometers
• 670,615,200 miles

Light-Day

Picturing a light-day involves seeing light as it perpetually moves through the universe for an entire day or 86,400 seconds. Over this period, light covers a distance that truly captivates the imagination, underlying just how minuscule earthly voyages are by comparison.

In one day, light zips through 25,902,068,800 kilometers or 16,091,044,800 miles. Imagining such distances helps us understand why light-years become a more practical measure for space distances, as even a light-day spans an unimaginably large span of space!

- The distance covered in one light-day:

• 25,902,068,800 kilometers
• 16,091,044,800 miles