Question

How was the parsec derived?

Answer 1

Parsec means 'Parallax of one arcsecond', or the distance to a star/object with a parallax of one arcsecon.

Using the diagram below, we can work out a parsec

The distance `SD` is approximately one parsec.

`tan(/_EDS)=(ES)/(SD)`

`SD=(ES)/(tan(/_EDS))=(1AU)/tan(1text("))`

For small angles of `theta` `tantheta~~theta`

`1text('')=1/3600"th of a degree"`

`SD=(1AU)/(1/3600*pi/180)` (since we need radians)

`SD=648000/piAU~~206264.8062AU`

`206264.8062AU~~3.085677581*10^16m~~3.261563777"ly"`