Question

How far is a parsec?

Answer 1

`3.26.Light` `years`

Answer 2

It is the distance that a star presents a second of parallax.

Explanation:

Parallax in the aparent movement that a close star seems to make in relation to the background stars, due to the movement of the Earth around the Sun.

Imagine a triangle in which the base is the Earth-Sun distance and the opposite angle is one arc second.

There for `(UA)/(parsec)=tan(1second)`

We must turn 1 second into radians:

`(1 s)/(3600 s/(degrees))*(pi (radians)/(180 degrees))=4.84xx10^-6`

For so close angle `tan(alpha)~~alpha`

`(149.5xx10^6 km)/(parsec)=4.84xx10^-6`

`parsec=((149.5xx10^6)/(4.84xx10^-6))=30.9xx10^12 km`

How many light years is this?

One light year is `365*24*3600*299.8xx10^3=9.45xx10^12 km`

So one parsec is `(30.9xx10^12km)/(9.45xx10^12 km)=3.26 ly`