How was it determined that a parsec is 3.26 light years?
A parsec is defined to be the distance to an object that shows a parallax angle of
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.
In the figure above, the angle,
If we define
We can use this information to convert our parsec into light years with the tangent formula.
If we convert
Plugging this in for