Question

A parsec is an astronomical unit of distance where 1 parsec \(=\) 3.26 light years \((1 \text { light year equals the distance traveled by }\) light in one year). If the speed of light is \(186,000 \mathrm{mi} / \mathrm{s}\) , calcu- late the distance in meters of an object that travels 9.6 parsecs.

Short answer

The distance of an object that travels 9.6 parsecs can be calculated by converting parsecs to light years, light years to miles, and finally miles to meters: \(9.6 \times 3.26 \times 186,000 \times 31,536,000 \times 1,609.34 = Z \text{ meters}\). Multiply these numbers using a calculator to obtain the final distance of Z meters.

Step-by-step solution

Convert parsecs to light years

We are given that 1 parsec = 3.26 light years. So to convert 9.6 parsecs to light years, we can multiply by the conversion factor: \(9.6 \text{ parsecs} \times 3.26 \frac{\text{light years}}{\text{parsec}} = X \text{ light years}\)

Convert light years to miles

Since 1 light year is the distance traveled by light in one year, we can find out the distance of the object in miles by multiplying the light years with the speed of light and the number of seconds in a year: \(X \text{ light years} \times 186,000 \frac{\text{miles}}{\text{second}} \times 31,536,000 \frac{\text{seconds}}{\text{year}} = Y \text{ miles}\)

Convert miles to meters

Finally, we need to convert the distance in miles to meters. We know that 1 mile = 1,609.34 meters. So we can multiply the distance obtained in Step 2 by this conversion factor: \(Y \text{ miles} \times 1,609.34 \frac{\text{meters}}{\text{mile}} = Z \text{ meters}\)

Calculate the final distance

Now, we can find the distance of the object in meters by combining all conversions and solving for Z: \(9.6 \times 3.26 \times 186,000 \times 31,536,000 \times 1,609.34 = Z \text{ meters}\) Now just use a calculator to multiply these numbers to obtain the final distance of Z meters.

Key concepts

Parsecs

Parsecs are a vital unit of measurement in astronomy and help scientists to navigate the vast interstellar spaces. They are especially useful when discussing distances to stars and galaxies. A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond. This is equivalent to approximately 3.26 light years.
For astronomical purposes, parsecs provide a more manageable number than other measures like kilometers or miles, when calculating astronomical distances. Essentially, when astronomers say a star is "1 parsec away," it means it is at a point where the Earth's orbit around the sun would appear 1 arcsecond in diameter.

Light Years

Light years are another widely used distance measurement in astronomy. They represent the distance that light can travel in a vacuum over the span of one year. Since light travels at about 186,000 miles per second, or approximately 300,000 kilometers per second, this covers an enormous distance. In concrete terms, one light year translates to approximately 5.88 trillion miles or about 9.46 trillion kilometers.
This measurement is exceptionally useful for indicating the scale of space. When considering the distance to other stars or galaxies, using light years makes more sense than quoting the figure in miles or kilometers, which would result in excessively large numbers.

Unit Conversion

Unit conversion is an important skill, especially when dealing with astronomical measurements, where various units might be used interchangeably. Knowing how to transition smoothly between units like parsecs and light years or converting miles to meters is crucial.

• To convert parsecs to light years, multiply by 3.26 (since 1 parsec = 3.26 light years).
• To convert light years to miles, you would use the speed of light and the number of seconds in one year.
• Finally, to get from miles to meters, recognize that 1 mile is approximately 1,609.34 meters.

Understanding and applying these conversions ensures precise calculations which are critical for astronomical observations and research.

Speed of Light

The speed of light is a fundamental constant in physics and a cornerstone of our understanding of space and time. It is typically denoted by the letter 'c' and has a value of approximately 186,000 miles per second or 300,000 kilometers per second. This remarkable speed allows light to traverse vast cosmic distances almost instantaneously on a human scale.
In one year, light can travel about 5.88 trillion miles, a distance recognized as one light year. The speed of light serves not just as a measure for distances (like in the calculation of light years) but also plays a critical role in the theory of relativity and various other scientific principles. When calculating distances in space, using the speed of light as a constant ensures that the numbers remain consistent and reliable.