Parsecs, trigonometric parallax and light years

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Discussion Overview

The discussion revolves around the concepts of parsecs, trigonometric parallax, and light years, particularly focusing on how to calculate distances in these units based on given parallax angles. The scope includes theoretical understanding and mathematical reasoning related to astronomy.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about calculating distances in parsecs and light years from a given parallax angle of 0.2 arc seconds.
  • Another participant provides a formula for calculating parsecs as the reciprocal of the parallax in arc-seconds and light years as 3.262 divided by the parallax.
  • A detailed explanation is given regarding the definition of a parsec and the relationship between parallax angles and the Earth's motion, emphasizing the need to halve the parallax angle when considering the Earth's orbit.
  • Further examples illustrate how to derive distances based on different parallax angles, highlighting the importance of understanding the factors involved in these calculations.
  • One participant seeks clarification on the concept of parallax error and the meaning of AU (astronomical unit).
  • Another participant clarifies that AU stands for astronomical unit, which is approximately the distance from the Earth to the Sun.

Areas of Agreement / Disagreement

Participants generally agree on the basic definitions and calculations related to parsecs and parallax, but there remains uncertainty regarding the concept of parallax error and the implications of the calculations presented.

Contextual Notes

Some participants mention factors of two in the calculations, indicating potential confusion or complexity in understanding the relationship between parallax angles and distances. The discussion does not resolve these complexities or clarify all assumptions.

Who May Find This Useful

This discussion may be useful for students preparing for exams in astronomy or related fields, as well as anyone interested in understanding the concepts of distance measurement in space using parallax.

Auron87
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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.
 
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In parsecs, it would be just be

[tex]\frac{1}{p}[/tex]

where p[/size] is the parallax in arc-seconds.

Lightyears would be

[tex]\frac{3.262}{p}[/tex]
 
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 let's be as slow and clear as possible

a parsec is 206265 AU
(and it is also 3.26 light years but that doesn't 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 isn't 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.
 
An AU means astronomical unit - roughly the distance from the Earth to the sun [93 million miles]. The rest is trigonometry.
 

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