Textbook Problem

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The nearest star, Alpha Centauri, is 4.3 light- years from Earth. A light-year is the distance that light travels in one year. How far away is Alpha Centauri in kilometers?

Interpretation Introduction

Interpretation:

The distance between Alpha Centauri and the Earth is to be determined in kilometers.

Concept Introduction:

A star is a heavenly body or astronomical object visible in the sky at night.

Speed is the distance travelled per unit of time.

The relation between speed, time and distance is as follows:

$\text{Distance}=\text{Speed}\times \text{Time}$

Here, distance is in meter, speed is in $\text{meter/second}$ and time is in second.

Explanation of Solution

Given information: The distance between Alpha Centauri and the Earth in light years is $4.3\text{light}\text{years}$ and one light year is equal to the distance travelled by light in one year.

Firstly, the relationship between kilometer and meter is as follows:

$\begin{array}{c}1\text{km}=1\times {10}^3\text{m}\\ 3.0\times {10}^8\text{m}=\frac{3.0\times {10}^8\cancel{\text{m}}\times \text{1}\text{km}}{1\text{s}\times \text{1}\times {\text{10}}^3\cancel{\text{m}}}\\ =3.0\times {10}^5\text{km/s}\end{array}$

The relationship between year and hours is as follows:

$\begin{array}{c}1\text{year}\text{=}\text{365}\text{day}\\ \text{1}\text{day}\text{=}\text{24}\text{hr}\\ \text{365}\text{day}\text{=}\frac{\text{365}\cancel{\text{day}}\times \text{24}\text{hr}}{1\cancel{\text{day}}}\\ =8,760\text{hr}\end{array}$

The relationship between hour and second is as follows:

$\begin{array}{c}1\text{hr}\text{=}60\text{min}\\ \text{1}\text{min}\text{=}\text{60}\text{s}\\ 8,\text{760}\text{hr}\text{=}\frac{8,\text{760}\cancel{\text{hr}}}{}\end{array}$