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A novel of the 'Foundation' series mentioned that the universe being 3-D the shape of a constellation is recognizable only in the near vicinity of a given planet. In other words move out from the planet's surface some distance, and the shape of the constellation changes dramatically. It feels true, but is this observation true?

How far from the planet may one travel, and still recognize the constellation/s that are typically visible on that planet's surface ?

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The observation is true. Stars that look like they are right next to each other can be separated by massive distances. –  Jonathan. Jan 7 '13 at 19:01
    
Perhaps the question should be "How far from the solar system" not from Earth. –  Michael Luciuk Jan 7 '13 at 19:39
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@MichaelLuciuk: on the necessary scales, it's somewhat moot--"how far is Jupiter from Ohio?" is basically the same question as "how far is Jupiter from Earth?" –  Jerry Schirmer Jan 7 '13 at 21:03
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There's some excellent software called Celestia which lets you visualize constellations "from the outside" (among other things). You can easily tell, as you "move" farther away from the Earth, how the shape of the constellations changes. It's truly mind-expanding. They start to change "noticeably" if you go several light years from the solar system.

Nearly all of the stars in all the constellations are within a radius of 1000 light years.

Edit: here's a screen shot. (the constellations, as viewed from about 4Kly away) enter image description here

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It depends on the constellation or the galaxy considered:

  1. The closest visible star is Proxima Centauri at around 4 l.y.

    Proxima Centauri source

  2. The furthest visible star is possibly Rho Cassiopeiae at around 8,100 l.y.

    Rho Cassiopeiae source

  3. The closest visible galaxy is the Andromeda Galaxy (M33), at 2,540,000 l.y.

    Andromeda Galaxy source

  4. The furthest visible galaxy is maybe Bode's Galaxy (M81), at 12,000,000 l.y.

    Bode's Galaxy source

In other words:

  • at around 1 l.y. the Centauri constellation will be significantly distorted,
  • at 1,000 l.y. everything should be quite distorted apart from galaxies
  • at more than 16,200 l.y. no stars that are visible from here to the naked eye should be visible at all
  • galaxies will appear fixed until you are at a distance of around 1 million l.y.
  • at 1 million l.y. significant changes will be noticeable in the position of the Andromeda Galaxy
  • at a distance of more than 24,000,000 l.y. no stars or galaxies visible from here should be visible at all
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And in Asimov's Foundation trilogy, iirc, the change in location was from the galactic empire's capital planet Trantor in the center of the Milky Way to other planets spread across the galaxy, so on the order of a few times 10,000 ly. Also, if you were on a planet near the center of the galaxy, the stars could be much closer packed, so your constellations would be even more sensitive to small changes. –  Chris White Jan 8 '13 at 14:22
    
Proxima Centauri isn't visible to the naked eye; its apparent magnitude is 11.05. It's only barely visible from Alpha Centauri (magnitude about 4.8 if I've done the math correctly). (Higher magnitude numbers are dimmer; the limit of naked-eye visibility is around 6, or 6.5 if you have really good eyes.) –  Keith Thompson Jan 14 '13 at 16:26
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Stars that make up constellations are at varying distances from us, but they typically are hundreds or thousands of light years distant. Therefore, one has to be some light years away from our current position for a constellation to be unrecognizable.
Note also that stars have varying tangential velocities, so even on Earth, constellations will possibly appear changed in millions of years.

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