<h2>You asked for a dumb, tedious way of doing it. So here it is, in all its glory</h2>
<p>One parsec is defined as <span class="math-container">$$\dfrac{1}{\tan(1'')} \text{ AU}=\dfrac{648000}{\pi} \text{ AU}$$</span></p>
<p>As <span class="math-container">$1 \text{ AU} = 149597870700 \text{ m}$</span>, one parsec is equal to <span class="math-container">$$\dfrac{648000}{\pi} \cdot 149\,597\,870\,700 = \dfrac{96\,939\,420\,213\,600\,000}{\pi} \text{ m}$$</span></p>
<p>One light year can be calculated by multiplying <span class="math-container">$c$</span> by the number of seconds in a year: <span class="math-container">$$299792458 \cdot 86400 \cdot 365.25 = 9\,460\,730\,472\,580\,800 \text{ m}$$</span></p>
<p>Dividing the former by the latter, we get <span class="math-container">$\dfrac{1 \text{ pc}}{1 \text{ ly}} = 3.261564$</span></p>

CC BY-SA 4.0
2021-05-29T02:14:16.493Z
2021-05-29T02:14:16.493Z
WarpPrime
<p>From Google I get: A parsec, or “parallax second,” is defined as 3.26 light-years. So using the definition of parsec you can easily determine the distance in light years.</p>

CC BY-SA 4.0
2021-03-30T07:26:03.187Z
Yeah I know, someone smart once said that if you can do something in only one way, you dont understand it well enough (or something along these lines). So here I am converting parsecs to angles :))
xenfoulis
CC BY-SA 4.0
2021-04-29T08:42:28.850Z
Although it's true that 1 pc = 3.26 lyr, this is not the definition of a parsec. The definition is  the distance at which an object, 1 AU across, spans an angle of 1".
pela
CC BY-SA 4.0
2021-03-29T20:55:18.160Z
2021-03-29T20:55:18.160Z
Natsfan
<p>I have to convert 132 parsecs to light years and I'm struggling to get the expected result. Here is my method:</p>
<p><span class="math-container">$132 \text{ pc} = 132'' = 2,2' = 0,03(6)°$</span></p>
<p>I have an equation for stellar parallax which looks like this: <span class="math-container">$d = \Big( \dfrac{1 \text{ AU}}{\tan(0,03(6)°)}\Big)$</span></p>
<p>This should give me the distance to the object in Astronomical Units right? Well It doesn't and I have absolutely no idea why, I'd be very glad if someone could help me out</p>

CC BY-SA 4.0
2021-03-29T17:45:15.443Z
A distance of 1 pc has a parallax angle of 1" so angle made by something 132 pc away is 132 times smaller: 1/132=0.00757"
astrosnapper
CC BY-SA 4.0
2021-03-29T17:55:24.223Z
Yepp this seems to be the issue... thank you very much
xenfoulis
CC BY-SA 4.0
2021-03-29T22:10:43.320Z
A parsec is a distance, and so is a lightyear. There’s no need to involve trigonometry.
pela
CC BY-SA 4.0
2021-03-30T07:26:47.720Z
Ikr? I just love making life hell for myself
xenfoulis
CC BY-SA 4.0
2021-03-30T09:16:29.647Z
@stanisławsłowiński it's always okay to post an answer to your own question. But as comments point out, the distance is 132 times farther by definition, but that doesn't mean that the parallax would be exactly 132 times smaller. It will be close, but that would not be the right way to do it.
uhoh
<distances><mathematics><parsec>
Converting parsecs to light years in the dumbest way possible
xenfoulis
# Converting parsecs to light years in the dumbest way possible

(Asked by: username_0 on 2021-03-29)

I have to convert 132 parsecs to light years and I'm struggling to get the expected result. Here is my method:

$132 \text{ pc} = 132'' = 2,2' = 0,03(6)°$

I have an equation for stellar parallax which looks like this: $d = \Big( \dfrac{1 \text{ AU}}{\tan(0,03(6)°)}\Big)$

This should give me the distance to the object in Astronomical Units right? Well It doesn't and I have absolutely no idea why, I'd be very glad if someone could help me out

**Tags:** distances, mathematics, parsec

> **Comments:**
> **username_1**: A distance of 1 pc has a parallax angle of 1" so angle made by something 132 pc away is 132 times smaller: 1/132=0.00757"  
> **username_0**: Yepp this seems to be the issue... thank you very much  
> **username_2**: A parsec is a distance, and so is a lightyear. There’s no need to involve trigonometry.  
> **username_0**: Ikr? I just love making life hell for myself  
> **username_3**: @stanisławsłowiński it's always okay to post an answer to your own question. But as comments point out, the distance is 132 times farther by definition, but that doesn't mean that the parallax would be exactly 132 times smaller. It will be close, but that would not be the right way to do it.  

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## 2 answers

### Answer by username_4 on 2021-05-29. Score: 2

## You asked for a dumb, tedious way of doing it. So here it is, in all its glory

One parsec is defined as $$\dfrac{1}{\tan(1'')} \text{ AU}=\dfrac{648000}{\pi} \text{ AU}$$

As $1 \text{ AU} = 149597870700 \text{ m}$, one parsec is equal to $$\dfrac{648000}{\pi} \cdot 149\,597\,870\,700 = \dfrac{96\,939\,420\,213\,600\,000}{\pi} \text{ m}$$

One light year can be calculated by multiplying $c$ by the number of seconds in a year: $$299792458 \cdot 86400 \cdot 365.25 = 9\,460\,730\,472\,580\,800 \text{ m}$$

Dividing the former by the latter, we get $\dfrac{1 \text{ pc}}{1 \text{ ly}} = 3.261564$


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### Answer by username_5 on 2021-03-29. Score: 0

From Google I get: A parsec, or “parallax second,” is defined as 3.26 light-years. So using the definition of parsec you can easily determine the distance in light years.

> **Comments:**
> **username_0**: Yeah I know, someone smart once said that if you can do something in only one way, you dont understand it well enough (or something along these lines). So here I am converting parsecs to angles :))  
> **username_2**: Although it's true that 1 pc = 3.26 lyr, this is not the definition of a parsec. The definition is  the distance at which an object, 1 AU across, spans an angle of 1".  

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