How far is a parsec?

2 Answers
Veddesh #phi#
Feb 13, 2016

#3.26.Light# #years#

José F.
Feb 13, 2016

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#

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