1
$\begingroup$

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?

$\endgroup$
6
$\begingroup$

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 $\theta \simeq \tan \theta$.

$\endgroup$
1
  • $\begingroup$ That was really helpful :) $\endgroup$ Sep 29 '18 at 12:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.