# Of the 9096 visible stars — 90% are how close?

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.

Here is an update on (my) answer that your refer to. I have changed the visual threshold to V<6.5 mag (which is what Sky and Telescope have done) and I have used the revised Hipparcos reduction from van Leeuwen (2007) to obtain a (almost) complete catalogue of stars with their trigonometric parallaxes. 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, as you wish). 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 are (you can't resolve them, but in many cases Hipparcos could)

• 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. – Tito Piezas III Feb 8 '15 at 14:05
• 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? – pentane Feb 13 '15 at 0:14
• @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. – Rob Jeffries Feb 13 '15 at 0:17

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.

• 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.) :-) – C. Towne Springer Feb 8 '15 at 8:07

## protected by Qmechanic♦Feb 24 '17 at 21:28

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).