# Parsecs, trigonometric parallax and light years!

## Main Question or Discussion Point

Hey I'm really confused about these things above (well except for light years). How would you get a distance in parsecs and in light years if there was an annual parallax of say 0.2 arc seconds. I'm just revising for exams but am really confused now! Thanks.

## Answers and Replies

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Janus
Staff Emeritus
Gold Member
In parsecs, it would be just be

$$\frac{1}{p}$$

where p is the parallax in arc-seconds.

Lightyears would be

$$\frac{3.262}{p}$$

marcus
Gold Member
Dearly Missed
Auron87 said:
Hey I'm really confused about these things above (well except for light years). How would you get a distance in parsecs and in light years if there was an annual parallax of say 0.2 arc seconds. I'm just revising for exams but am really confused now! Thanks.
[edit: I see while i was typing my long answer, Janus gave a nice concise one.
so my response is really redundant but I will leave it in case the extra words turn out to help]
========

if you are REALLY confused, then you are probably confused about a factor of two

so lets be as slow and clear as possible

a parsec is 206265 AU
(and it is also 3.26 light years but that doesnt matter now, you can always convert to light years)

why is a parsec equal to 206265 AU?

Because if you move sideways by 1 AU the star position appears to shift
by one arc second which is equal to 1/206265 part of a radian

the official meaning of the parallax angle is HALF the biggest angle the star moves in a 6 month period

because in a 6 month period the earth is moving sideways by TWO AU

they always screw you by factors of 2

So suppose in 6 months the star shifts 0.2 arcseconds to the left and in the next 6 months is shifts back 0.2 arcseconds to the right, returning to its orig. position.

then the official paralax angle corresponding to a 1 AU sideways motion of the earth is half that. Namely 0.1 arcsecond.

You always take the reciprocal of the official parallax angle. And the reciprocal of 0.1 is 10
So the distance to the star is 10 parsecs

===========

Another example. Suppose in the course of a year the maximum angle the sucker moves is 2 arcseconds. She moves 2 arcseconds to the left and then she moves the same amount back so she ends up in the same place.

Well that was associated with an earth motion of 2 AU, the DIAMETER of the earth orbit. So you have to divide that 2 arcseconds in half, to get 1 arcsecond----that is what is associated with the earth moving sideways by ONE AU

So in this example, the official parallax angle is 1 arcsecond.

that means the distance to the star is 1 parsec----or 3.26 lightyear if you have to tell it in lightyear terms.

of course there isnt any star one parsec away, but this is just a hypothetical for illustration.
==========
Remember the basic fact that the AU is the conventional radius of the earth orbit.

Remember that one arcsecond is 1/3600 of a degree and therefore it is
1/206265 of a radian
And that angle can be pictured as a rise of 1 AU over a run of 206265 AU,
that is, as a very long sliver

And that is why an official parallax angle (while earth is shifting 1 AU sideways) of 1 arcsecond must correspond to a distance of 206265 AU

to which distance some brilliant scholar gave the name parsec.

======

Last edited:
Dear all,

After reading the explanations on parsecs, I managed to understand the main idea of what it is. However, what I can't grasp is why there is a parallax error. Also, I don't know what AU stands for. Sorry.

Chronos