A parsec is defined as the distance at which one astronomical unit subtends one arcsecond; approximately how many light-years is a parsec?

A parsec is defined as the distance at which one astronomical unit subtends one arcsecond; approximately how many light-years is a parsec?

• A. About 1 light-year
• B. About 10 light-years
• C. About 0.3 light-years
• D. About 3.26 light-years

Answer: (D)

A parsec is a distance defined by geometry: it’s the distance at which an object with an astronomical unit as its baseline subtends an angle of one arcsecond. An arcsecond is 1/3600 of a degree, and this tiny angle translates into a large distance because of the way similar triangles work in celestial geometry. In practical terms, 1 parsec equals about 206,265 astronomical units. A light-year, the distance light travels in a year, is about 63,241 AU. Dividing 206,265 by 63,241 gives roughly 3.26, so 1 parsec is about 3.26 light-years. That’s why the correct answer is about 3.26 light-years. The other numbers don’t match this established conversion (for example, 1 ly is too small, 0.3 ly is much too small, and 10 ly is too large).

A parsec is a distance defined by geometry: it’s the distance at which an object with an astronomical unit as its baseline subtends an angle of one arcsecond. An arcsecond is 1/3600 of a degree, and this tiny angle translates into a large distance because of the way similar triangles work in celestial geometry. In practical terms, 1 parsec equals about 206,265 astronomical units. A light-year, the distance light travels in a year, is about 63,241 AU. Dividing 206,265 by 63,241 gives roughly 3.26, so 1 parsec is about 3.26 light-years. That’s why the correct answer is about 3.26 light-years. The other numbers don’t match this established conversion (for example, 1 ly is too small, 0.3 ly is much too small, and 10 ly is too large).