Question

Astronomy One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year \((365\) days \() .\) If the speed of light is 186,000 miles per second, how many miles are in a light-year? Express your answer in scientific notation.

Short answer

A light-year is approximately \(5.87 \times 10^{12}\) miles.

Step-by-step solution

- Understanding Time in a Year

We need to calculate the number of seconds in one year. A year has 365 days, with each day having 24 hours, each hour having 60 minutes, and each minute having 60 seconds.

- Calculate Seconds in a Year

Calculate the total number of seconds in a year. \(365 \text{ days/year} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 31,536,000 \text{ seconds/year}\)

- Multiply Speed by Time

Multiply the speed of light by the number of seconds in a year to find the total distance traveled. \(186,000 \text{ miles/second} \times 31,536,000 \text{ seconds/year} = 5,865,696,000,000 \text{ miles/year}\)

- Express the Result in Scientific Notation

Convert the numerical answer into scientific notation. \(5,865,696,000,000 \text{ miles/year} = 5.865696 \times 10^{12} \text{ miles/year}\)

Key concepts

scientific notation

Scientific notation is a way to express very large or very small numbers in a compact form. It makes computations easier and helps avoid errors. In scientific notation, a number is written as the product of two factors: a decimal and a power of ten. For example, the number 5,865,696,000,000 becomes 5.865696 × 10¹². Here, 5.865696 is the decimal part, and 10¹² indicates that you multiply the decimal part by 10 a dozen times.

To convert a large number into scientific notation, count the number of places you move the decimal point to get a number between 1 and 10. This count becomes your exponent.

For instance, in light-year calculations, after finding the total miles, convert it to scientific notation to make it easier to work with and understand.

speed of light

The speed of light is a key constant in physics and astronomy. It is the rate at which light travels through space, roughly 186,000 miles per second (299,792 kilometers per second). This speed is incredibly fast, allowing light to travel immense distances in a short time.

When we talk about light-years, we’re essentially discussing how far light can travel in one year. Given that light travels 186,000 miles every second, it's easy to see how distances can add up quickly.

Calculating the distance covered by light over longer timescales involves multiplying this speed by the number of seconds in the given period. This forms the basis for understanding astronomical distances.

distance conversion

Distance conversion is about converting one unit of distance to another. In this exercise, converting time to distance involves using the speed of light. Since we know the speed of light and the time period (one year), we can determine the total distance light travels in that time.

Let's break it down:

• First, determine the number of seconds in one year.
• Next, multiply that by the speed of light to get the distance in miles.

This is crucial in astronomy because distances are vast, and simple unit conversions help us understand these immense scales. The combined method of multiplying time by speed gives us a straightforward way to convert years into light-years.

time calculation

Time calculation is essential when working with distances that rely on a fixed speed over a time period. To find the distance light travels in a year, we first need the total seconds in that year. This involves:

• Calculating the number of days in a year (usually 365 days).
• Multiplying that by the number of hours in a day (24).
• Then multiplying the result by the number of minutes in an hour (60), and finally, the number of seconds in a minute (60).

This gives us the total seconds in a year. Knowing the speed of light in miles per second, we then multiply this total by 186,000 miles per second. This multiplication gives us the distance light travels in one year in miles, which is what a light-year measures. An accurate time calculation ensures we get the correct figure for astronomical distances.