<p>Because a separation of 1 au subtends an angle of 1 arcsecond at 1 parsec. That is the definition of a parsec. As you move further away, the angle gets smaller by a factor of the increase in distance. </p>

<p>Just draw a right-angled triangle where the base length is the distance and the height is the star-planet separation. Now increase the base length and ask yourself what happens to the angle subtended at the Earth? NB All angles are small so <span class="math-container">$\theta \simeq \tan \theta$</span>.</p>

CC BY-SA 4.0
2018-09-29T12:11:44.307Z
That was really helpful :)
Antony Alexander
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2018-09-29T08:25:16.197Z
2018-09-29T08:25:16.197Z
ProfRob
<p>I've been reading the book Welcome to The Universe by Niel De Grasse Tyson. In the tenth chapter he has mentioned "Forty light-years is 12 parsecs. A planet at 1 AU from its star, 40 light-years away, will be 1/12 of a second of arc away from the star in the sky."</p>

<p>Can anyone explain how he got the figure 1/12 arc seconds?</p>

<parsec>
How far in arc seconds is a planet from its star? The star is 12 parsecs away from earth. The planet is 1 AU from its star
Antony Alexander
# How far in arc seconds is a planet from its star? The star is 12 parsecs away from earth. The planet is 1 AU from its star

(Asked by: username_0 on 2018-09-29)

I've been reading the book Welcome to The Universe by Niel De Grasse Tyson. In the tenth chapter he has mentioned "Forty light-years is 12 parsecs. A planet at 1 AU from its star, 40 light-years away, will be 1/12 of a second of arc away from the star in the sky."

Can anyone explain how he got the figure 1/12 arc seconds?

**Tags:** parsec

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## 1 answers

### Answer by username_1 on 2018-09-29. Score: 6

Because a separation of 1 au subtends an angle of 1 arcsecond at 1 parsec. That is the definition of a parsec. As you move further away, the angle gets smaller by a factor of the increase in distance.

Just draw a right-angled triangle where the base length is the distance and the height is the star-planet separation. Now increase the base length and ask yourself what happens to the angle subtended at the Earth? NB All angles are small so $\theta \simeq \tan \theta$.

> **Comments:**
> **username_0**: That was really helpful :)  

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