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Sometimes when they fly in space there are stars around but sometimes there are no stars at all. Why is that?

For example, when they are flying alongside Saturn, we see the rings of Saturn, but not a single star in space.

I can understand if there are no stars in a black hole or in a worm hole, but not in normal space.

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When a large bright object is in your field of view, smaller dimmer objects are effectively hidden. This is because your eyes adapt to the bright light. Cameras will also adapt to the bright light and so will not pick up the dimmer objects.

This optical effect has been replicated in the film. It is therefore more accurate than any number of space films in which stars are seen clearly in the background near a planet.

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    That's interesting and I'm willing to believe you. But can you provide any source that this was a deliberately replicated effect in the movie? – Napoleon Wilson Apr 7 '15 at 11:46
  • Not immediately. I'm sure I saw it in some interview at the time the film was released. I'll see if I can find it. – Chenmunka Apr 7 '15 at 11:49
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    @NapoleonWilson This might be related, and NASA's site is probably a believable source for the subject. ;-) – Vedran Šego Apr 7 '15 at 22:38
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    @VedranŠego Indeed, together with the fact that various sources say how much Nolan was influenced by existing NASA footage. – Napoleon Wilson Apr 9 '15 at 0:32
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    @NapoleonWilson Their executive producer was Nobel prize winning theoretical physicist Kip Thorne who published three papers as a result of working on the black hole visuals. They're going to get the stars right. – Schwern Jul 25 at 23:16
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In addition and related to Chenmunka's answer: stars bright enough to see with the naked eye (or camera) simply do not exist in particular viewing directions. Our very own Milky Way is a dish-shaped galaxy, which is clearly noticeable for example in a desert or other off place: infinite stars can be seen in two opposite directions and none in the perpendicular directions. Why would that necesserilly not be somewhere else in the universe?

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Gaseous planets like Jupiter and Saturn reflect lots of sunlight falling on them. The Contrast between the reflected light and light coming from stars is minute. A property called Contrast Sensitivity comes into play here. As the eyes of most people aren't that sensitive to contrast changes. This effect is reproduced in greenscreen scenes via contrast stretching.

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