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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?

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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 $\theta \simeq \tan \theta$.

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  • $\begingroup$ That was really helpful :) $\endgroup$ Sep 29, 2018 at 12:11

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