Question

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

Short answer

The object travels a distance of approximately \(2.92 \times 10^{18}\) meters.

Step-by-step solution

Convert parsecs to light years

To convert the distance from parsecs to light years, we multiply the given distance (9.6 parsecs) by the conversion factor (1 parsec = 3.26 light years):\[D_{ly} = 9.6 \ \text{parsecs} * 3.26 \ \text{light years/parsec}\] Step 2: Calculate the distance in light years

Calculate the distance in light years

Now, we will carry out the multiplication to find the distance in light years:\[D_{ly} = (9.6 * 3.26) \ \text{light years} = 31.296 \ \text{light years}\] Step 3: Convert light years to miles

Convert light years to miles

Considering that the speed of light is 186000 mi/s, we convert 1 light year to miles using the relation: \[1 \ \text{light year} = 186,000 \ \text{mi/s} * 31,557,600 \ \text{s/year}\] We can calculate the distance of 31.296 light years in miles.\[D_{mi} = 31.296 \ \text{light years} * 186,000 \ \text{mi/s} * 31,557,600 \ \text{s/year}\] Step 4: Calculate the distance in miles

Calculate the distance in miles

Now, we will carry out the multiplication to find the distance in miles:\[D_{mi} = 31.296 * 186,000 * 31,557,600 \ \text{miles} = 1.817934 \times 10^{15} \ \text{miles}\] Step 5: Convert miles to meters

Convert miles to meters

To convert miles to meters, we use the conversion factor (1 mile = 1,609.344 meters):\[D_{m} = 1.817934 \times 10^{15} \ \text{miles} * 1,609.344 \ \text{meters/mile}\] Step 6: Calculate the distance in meters

Calculate the distance in meters

Finally, we will carry out the multiplication to find the distance in meters:\[D_{m} = ( 1.817934\times 10^{15} * 1,609.344 )\ \text{meters} = 2.9240799 \times 10^{18} \ \text{meters}\] The object travels a distance of approximately \(2.92 \times 10^{18}\) meters.

Key concepts

Parsec to Light Years Conversion

Understanding the vastness of outer space requires a measurement system that can capture the immense distances involved. That's where astronomical units like the parsec come in handy. To put it simply, a parsec is a unit of distance used in astronomy to describe the space between celestial bodies. It is equivalent to approximately 3.26 light years.

Light years, on the other hand, measure the distance light can travel in one year. Given that light speeds through space at about 186,000 miles per second, you can imagine how far it can go in an entire year!

Calculating Parsecs to Light Years

To convert parsecs to light years, we use the established equivalence of 1 parsec being approximately 3.26 light years. For instance, if a star is 9.6 parsecs away, we just multiply 9.6 by 3.26 to determine the distance in light years. This straightforward multiplication gives us a clearer picture of distance in terms of how far light travels in a year, making it easier to comprehend space-related distances.

Speed of Light in Miles Per Second

The speed of light is not just a cosmic speed limit but also a fundamental constant in physics, playing a vital role in our understanding of the universe. It races through the vacuum of space at a staggering 186,000 miles per second (or approximately 299,792 kilometers per second). Because of this incredible speed, light can circle the Earth more than seven times in just one second!

Appreciating the Speed of Light

This constant isn't just for measuring; it's essential in formulas and theories across multiple scientific disciplines, including Einstein's famous equation, E=mc^2. The speed of light enables us to calculate vast distances, like those between stars and galaxies, making it a cornerstone of astronomical unit conversion. Even when planning space missions, scientists must account for light speed to communicate with distant spacecraft. By knowing the speed of light, converting light years to more familiar units, like miles or kilometers, becomes an achievable task.

Light Year Distance Calculation

Calculating distances in light years is a fundamental part of astronomy, providing a window into the scale of the cosmos. Since a light year is the distance that light travels in a year, it's a huge stretch—about 5.88 trillion miles! With such large numbers, understanding light year calculations can be daunting, but it’s essential for grasping the scale of the universe.

From Light Years to Miles

To find the distance of an astronomical object in light years, we start by taking the object's distance in parsecs and converting it to light years. Once we have the distance in light years, we use the speed of light—186,000 miles per second—to calculate the distance in miles. Multiplying the number of light years by the speed of light and then by the number of seconds in a year gives us a mileage that, while incredibly large, is easier to compare to distances we're familiar with on Earth.