How was it determined that a parsec is 3.26 light years?

1 Answer
Dec 17, 2015

A parsec is defined to be the distance to an object that shows a parallax angle of 1 arc-second. That distance happens to be 3.26 light years.

Explanation:

Parallax is an effective way to measure distance to nearby stars because it relies on geometry. When astronomers use parallax, they are measuring how a star appears to move against its background. The unit parsec refers to the distance that an object would have to be from the Earth to have a parallax angle of 1 arc-second.

enter image source here

In the figure above, the angle, α is the angle that is measured by the Earth on opposite sides of the sun. The parallax angle, p is half of this angle.

p=12α

If we define p to be 1 arc-second, then our object will be 1 parsec away. Since light from the sun takes 8 minutes and 20 seconds to reach the Earth, we know that;

1 AU=8.33 light minutes

We can use this information to convert our parsec into light years with the tangent formula.

tan(p)=8.33 light minutesd

Or;

d=8.33 light minutestan(p)

If we convert p to radians, than we can use the small angle approximation, tan(θ)θ.

1 arc-second=4.85×106 radians

Plugging this in for p and using the small angle approximation;

d=8.33 light minutes4.85×106

=1.72×106 light-minutes

=3.26 light years