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I was on a beach on a tropical island one night and, of course, the night sky was magnificent. It got me thinking:

I want to point to a star and say with $90$% certainty that it is probably $x$ light-years away. What should be $x$?

In other words, in this Sky and Telescope list of 9096 stars, $90$% are within how many light-years?

P.S. I had hoped that the answer would be in the post Demographics of stars visible to the naked eye, but it was not.

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2 Answers 2

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Here is an update on (my) answer that you refer to. I have changed the visual threshold to V<6.5 mag (which is what the Sky and Telescope article has done) and I have used the revised Hipparcos reduction from van Leeuwen (2007) (catalogue available here) to obtain a (almost) complete catalogue of stars with their trigonometric parallaxes. A few of the brightest stars are missing or have very poor parallaxes because of saturation. It contains 7892 stars. I am not going to investigate the discrepancy with the Sky and Telecope article which uses the Hoffleit & Jaschek bright star catalogue as their reference.

The distribution of distances is illustrated in the two plots below (labelled in light years). The first shows the number of stars as a function of distance. The second shows the cumulative fraction of stars closer than some distance. From this, you can read off, or I can tell you, that 90% of bright stars in the Hipparcos catalogue are closer than 1175 light years.

NB: I don't think 4 significant figures are warranted. There are some tens of bright stars that are so distant that their parallaxes are too small and are garbage (negative in some cases). I'm also not clear about what the status of binary stars is (you can't resolve them, but in many cases Hipparcos could).

Number of bright stars vs distance

Number of bright stars versus distance

Cumulative frequency of star distance

Normalised cumulative frequency of star distance

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    $\begingroup$ Just what I've been looking for! At least now when I'll look at the night sky, I'll be 75% sure any given star is within 500 light-years, and almost 90% sure it is within 1100 light-years. It gives one a certain quantitative grasp on star-gazing. $\endgroup$
    – Tito Piezas III
    Commented Feb 8, 2015 at 14:05
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    $\begingroup$ Really nice answer Rob! I'd like to be able to generate these plots myself. Did you use cdsarc.u-strasbg.fr/viz-bin/Cat?I/239 ? Do you need specific software to open the files or how did you process the data? $\endgroup$
    – pentane
    Commented Feb 13, 2015 at 0:14
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    $\begingroup$ @pentane Thanks. I used the revised Hipparcos catalogue by van Leeuwen (2007) cdsarc.u-strasbg.fr/viz-bin/Cat?I/311 To generate the plots I read the ascii main table straight into the "topcat" software star.bris.ac.uk/~mbt/topcat Topcat is awesome. $\endgroup$
    – ProfRob
    Commented Feb 13, 2015 at 0:17
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The post you reference gives the distribution of distances as a histogram. It is based on 6000 visible stars, but it is still basically the answer you want. The peak is at $10^2 = 100$ parsecs. 90% of the stars look to be between $10^{1.5} \approx 30$ and $10^{2.5} \approx 300$ parsecs.

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    $\begingroup$ How many light years would it be? About 300 Quatlkoos. Astronomers! Drive ya nuts, don't they? (Multiply parsecs by 3.26 to get the units in the question.) :-) $\endgroup$
    – C. Towne Springer
    Commented Feb 8, 2015 at 8:07

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