# What are the advantages of using the Parsec over the lightyear?

May 7, 2016

If two equidistant light sources 1 AU apart reveal angular spacing of 1"= 1/3600^o, the common distance is 1 parsec. If this angle is 100", quite easily, the distance is 100 parsecs. .

#### Explanation:

Light year is light-speed-oriented unit of distance. Parsec is a distance unit that has other advantages.

Parsec measure is quite useful to study dimensions of galaxies clusters that are thousands/millions of light years away.

Average Earth-Sun distance = 1 AU = 149597871 km

The formula used for evaluating parsec is

the length of circular arc subtending $\theta$ at the center of a circle of radius R,

L = R$\theta$. Here, L is in R units.

1 parsec is defined as 1/ (angular spacing 1" in radian) AU.

Thus, 1 parsec $= \left(\frac{1}{3600}\right) \left(\frac{\pi}{180}\right)$ AU
= 206264.8 AU

Note that the linear spacing in-between very far equidistant objects is approximately the circular arc length, when the angular spacing is quite small.