Parsec Distance Explained

Astronomers measure the vastness of space using specialized units. The question asks us to relate the parsec, a unit used for large interstellar distances, to the astronomical unit (AU), which is based on the distance between the Earth and the Sun.

Astronomical Unit Definition

An Astronomical Unit (AU) is the average distance separating the Earth from the Sun. It's approximately equal to 150 million kilometers (\(1 \text{ AU} \approx 1.496 \times 10^{11}\) meters).

Parsec to AU Calculation

A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond. It's commonly related to light-years:

• 1 parsec (pc) is approximately 3.26 light-years (ly).
• 1 light-year (ly) is the distance light travels in one year, approximately \(9.461 \times 10^{15}\) meters.

To find the value of 1 parsec in astronomical units, we can use the conversion factor between light-years and AU:

$1 \text{ ly} \approx 63,241 \text{ AU}

Now, we convert parsecs to light-years and then to astronomical units:

$1 \text{ pc} \approx 3.26 \text{ ly}

Substitute the value of light-years in AU:

$1 \text{ pc} \approx 3.26 \times (63,241 \text{ AU})

Calculating the product:

$1 \text{ pc} \approx 206,265 \text{ AU}

This value, when expressed in scientific notation, is approximately \(2.06 \times 10^5\) AU. Rounding this to match the options gives us \(2 \times 10^5\) AU.

Comparing AU and Parsec Values

The calculation confirms that a parsec is a much larger unit than an astronomical unit. While 1 AU represents the Earth-Sun distance, 1 parsec represents approximately 206,265 times that distance, highlighting its use for measuring distances to stars and galaxies.