Question

A light year is the distance light travels in 1.00 year. Given the velocity of light, \(1.86 \times 10^{5} \mathrm{mi} / \mathrm{s}\), how many miles does light travel in a light year?

Short answer

Light travels \(5.86536 \times 10^{12}\) miles in a light year.

Step-by-step solution

Understand the Problem

We need to calculate the total distance that light travels in one year. We are given the velocity of light as \(1.86 \times 10^{5}\) miles per second.

Calculate Seconds in a Year

First, calculate the number of seconds in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year: \[60 \text{ sec/min} \times 60 \text{ min/hr} \times 24 \text{ hr/day} \times 365 \text{ day/year} = 31,536,000 \text{ sec/year}.\]

Calculate Distance Light Travels in a Year

Using the formula \( \text{distance} = \text{velocity} \times \text{time} \), multiply the velocity of light by the number of seconds in a year to find the distance light travels:\[(1.86 \times 10^5 \text{ mi/s}) \times 31,536,000 \text{ s/year} = 5.86536 \times 10^{12} \text{ miles}.\]

Express the Result

The distance that light travels in one year, or one light year, is \(5.86536 \times 10^{12}\) miles.

Key concepts

Velocity of Light

The velocity of light refers to how fast light travels through space. It’s a universal constant, meaning it doesn't change regardless of the conditions around it. In this exercise, the velocity of light is given as \(1.86 \times 10^5\) miles per second. This value is crucial for any calculations involving distances in space.
Understanding the velocity of light helps us grasp how far light can travel over time. Unlike our everyday velocities, such as the speed of a car, the speed of light is incredibly fast. This rapid speed allows light to cover vast distances across the universe in relatively short amounts of time.
In the context of this exercise, knowing the velocity helps in determining how far light travels in one year, essentially calculating a distance measured in light years. By understanding this concept, you can appreciate the enormity of distances in space and time.

Distance Calculation

Calculating distance using the speed of light involves multiplying its velocity by time, which is expressed through the formula: \[ \text{distance} = \text{velocity} \times \text{time} \]The question asks us to find the distance light travels in one year. Given the velocity of light as \(1.86 \times 10^5\) miles per second, we need to use this to find out the distance.
To calculate how many miles light travels in a year, you must first determine how many seconds are in that year. For this, convert the units of time to seconds per year, which will be covered in the next section. Once you have that number, multiply by the given velocity.
The end result, \( 5.86536 \times 10^{12} \) miles, represents the massive distance that light covers in a single year, illustrating the incredible scale of space and the importance of the light year as a unit of measurement in astronomy.

Time Conversion

Time conversion is about changing time units from one scale to another, to match the needs of specific calculations. Here, we need to convert 1 year into seconds because the velocity of light is provided in miles per second.
To perform this conversion:

• Start by converting minutes to seconds (60 seconds in a minute).
• Then convert hours into seconds (60 minutes in an hour).
• Next, convert days to seconds (24 hours in a day).
• Finally, convert years to seconds (365 days in a year).

This step-by-step conversion gives us a total of 31,536,000 seconds in one year.
By organizing these conversions systematically, it becomes easier to handle the large numbers and ensure accuracy in calculations. Correct time conversion is key in this exercise because it directly influences how we calculate the total distance light can travel in a year, ultimately converting these light years into practical understanding of cosmic distances.