Brightnesses and Distances of stars

Brightness falls away with the square of the distance. So if all stars emit the same amount of light, then if one star is 4 times as far away, it will appear 1/4^2 or 1/16th as bright.

Herschel (1737-1832) used Sirius as his reference star and calculated distances in siriometers.

Freidrich Bessel made the first accurate stellar parallax measurement in1838 to determine the distance to Cygni 61.

Parallax is the apparent shift in position of an object due to a change in an observer's vantage point.

In the case of stellar parallax, nearby stars shift their position relative to far away stars over a 6 month periond.

After spending 28 years perfecting the technique, Bessel determined Cygni 61 shifted its postion by 0.6272 arc seconds (0.0001742 degrees). This is what you would see if you switched eyes observing your finger with a 30Km arm. This corresponds to 10^14km. Actual distance 1.08 * 10^14km which is 11.4 light years, 720,000 times the distance to the sun.

At the time this achievement was quoted as being 'the greatest and most glorious triumph which practical astronomy had ever witnessed'.

 
Note: 60 arc seconds equals 1 arc minute and you guessed it, 60 arc minutes equals 1 arc degree.

The equation for astro distances measured in parsecs, pc is:

d  = 1 / p, d parsec, p seconds of arc.

"A star with a parallax p of 1 arc second lies at a distance of 1 parsec."

The nearest star is proxima centauri, which exhibits a parallax of 0.762 arcsec, and therefore is 1/0.762 = 1.31 pc (parsecs) away, followed by Barnard's star.

Astrophysical Distances
An astronomical unit is the average distance between the Earth and the Sun (AU).

1 AU = 1.5 10^8 Km, 1 AU = 1.495978 x 10^11 m
One light year is the distance light travels in one Year (ly). 1 ly = 9.46053 x 10^15 m = 0.31 pc
One parsec = 3.085678 x 10^16 m = 3.086x10^13 km  = 3.261633 ly