Question

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 is 300,000 km or about 186,400 miles. 1 light-minute is 18 million km or about 11,180,000 miles. 1 light-hour is 1.08 billion km or about 671,100,000 miles. 1 light-day is 25.92 billion km or about 16,110,000,000 miles.

Step-by-step solution

Understanding the Concept of Light-Distance

A light-distance is the distance that light can travel in a specific amount of time. Light travels at a speed of approximately \( 3 \times 10^8 \) meters per second. To find the distance a light can travel, we multiply this value by the total seconds for each time period.

How to Convert Meters to Kilometers and Miles

To convert the distance from meters to kilometers, divide the distance in meters by 1000 since there are 1000 meters in a kilometer. To convert meters to miles, use the factor by dividing by approximately 1609 since there are 1609 meters in a mile.

Calculate 1 Light-Second Distance

A light-second is the distance light travels in one second. Using the speed of light \( 3 \times 10^8 \) m/s: Distance in meters for 1 second: \( 3 \times 10^8 \) meters Distance in kilometers: \( \frac{3 \times 10^8}{1000} = 3 \times 10^5 \) km Distance in miles: \( \frac{3 \times 10^8}{1609} \approx 1.864 \times 10^5 \) miles.

Calculate 1 Light-Minute Distance

A light-minute is the distance light travels in sixty seconds: Distance in meters for 60 seconds: \( 60 \times 3 \times 10^8 = 1.8 \times 10^{10} \) meters Distance in kilometers: \( \frac{1.8 \times 10^{10}}{1000} = 1.8 \times 10^7 \) km Distance in miles: \( \frac{1.8 \times 10^{10}}{1609} \approx 1.118 \times 10^7 \) miles.

Calculate 1 Light-Hour Distance

A light-hour is the distance light travels in 3600 seconds (60 minutes):Distance in meters for 3600 seconds: \( 3600 \times 3 \times 10^8 = 1.08 \times 10^{12} \) meters Distance in kilometers: \( \frac{1.08 \times 10^{12}}{1000} = 1.08 \times 10^9 \) km Distance in miles: \( \frac{1.08 \times 10^{12}}{1609} \approx 6.711 \times 10^8 \) miles.

Calculate 1 Light-Day Distance

A light-day is the distance light travels in 86400 seconds (24 hours):Distance in meters for 86400 seconds: \( 86400 \times 3 \times 10^8 = 2.592 \times 10^{13} \) meters Distance in kilometers: \( \frac{2.592 \times 10^{13}}{1000} = 2.592 \times 10^{10} \) km Distance in miles: \( \frac{2.592 \times 10^{13}}{1609} \approx 1.611 \times 10^{10} \) miles.

Key concepts

Light-Speed

Understanding the speed of light is fundamental in physics, especially when it relates to light-distance calculations. Light travels incredibly fast at approximately \(3 \times 10^8\) meters per second. This mere fact showcases the staggering distances light can cover in short periods. When we talk about a light-second, light-minute, or light-hour, we're essentially considering the distance light will travel in those specific time intervals.

Because of the speed of light, we can calculate how far light travels and express it in larger time segments:

• A light-second means how far light goes in one second.
• A light-minute translates to sixty times the distance light travels in a second.
• A light-hour computes the distance light travels in an hour.

Comprehending the speed of light also bridges concepts between astronomical calculations and everyday physics applications, affirming its central role in understanding universal laws.

Unit Conversion

Unit conversion is a crucial aspect of physics that allows different measurements to be translated into understandable units, like kilometers and miles from meters. This process ensures clarity and uniformity across different systems of measurement, especially essential when dealing with light distances.

For light-distance calculations, it's typical to convert meters (SI units) to more practical distances such as kilometers or miles. The conversions are especially straightforward but pivotal:

• To convert from meters to kilometers, divide the number of meters by 1,000. This conversion is due to 1 kilometer equaling 1,000 meters.
• To convert from meters to miles, divide by approximately 1,609 because there are 1,609 meters in a mile.

These conversions facilitate understanding and application across various scientific and practical disciplines, ensuring that distances like those traveled by light are more accessible and comprehensible.
This approach is especially beneficial in educational contexts, where clear and simple conversions can anchor students' understanding in real-world terms.

Physics Education

In physics education, comprehending concepts like the speed of light and unit conversions serves as a foundation for broader scientific learning. These principles empower students to tackle more advanced topics with confidence and precision.

Physics problems often involve real-world applications, such as calculating astronomical distances or understanding how signals travel. Teaching strategies that emphasize practical examples, like using light-distances to calculate how far light can travel in seconds, minutes, or hours, can make abstract concepts tangible.

• Breaking down the speed of light into smaller segments helps students visualize these distances with more relatability.
• Incorporating unit conversion in solving these problems transforms complex tasks into manageable steps. This builds logical thinking skills by moving from the known (meters) to the more relatable (kilometers and miles).

Utilizing such hands-on approaches advances both critical thinking and problem-solving skills, enriching the educational experience and equipping learners with essential tools for their academic journeys.