How is PARsec calculated?

Answer 1

1

Define the parsec. Let ABC be a right triangle with the vertices A, B, and C such that A is the sun, B is the earth and C is a point in space. The angle B is the right angle and angle C has a measure of 1 second. The length of side BC is equal to 1 parsec.

• 2

Determine the measurements of the triangle. There are 60 seconds in a minute and 60 minutes in a degree. Therefore, there are 60 x 60 = 3600 seconds in a degree. Thus, angle C measures 1/3600 degree. The length of side AB is the distance from the earth to the sun, which is 1 astronomical unit (AU) by definition.

• 3

Find the length of side BC, which is the distance from the earth to the point in space described in step 1. From trigonometry, we have BC/AB = cot(C) where cot is the cotangent function. Since AB = 1 AU, we can say that BC = cot(C) where length BC will be measured in AU. Therefore, we have BC = cot(C) = cot(1/3600) = 206,265 AU. Thus, BC = 206,265 AU, so a parsec is therefore equal to 206,265 AU.

• 4

Calculate the distance BC into miles to get the number of miles in a parsec. BC = 206,265 AU and there are about 93,000,000 miles in an AU, so a parsec is 206,265 x 93,000,000 = 1.92 x 10^13 miles.

• 5

Convert 1.92 x 10^13 miles to light years. Light travels 186,282 miles/second, so a parsec is (1.92 x 10^13) / (186,282) = 1.03 x 10^8 seconds. There are about 60 x 60 x 24 x 365 = 31,536,000 seconds in a year so a parsec is about (1.03 x 10^8) / (31,536,000) = 3.26 light years.