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The Hubble space telescope performs incredibly detailed and stunning imaging of celestial bodies that are many, many light years away, and yet when it attempts to image objects within our own Solar System, such as of Pluto and Charon, the results appear out of focus and smeared. Why is this so?

I can only guess that the objects within the Solar System have a higher relative intrinsic motion than objects light years away, and thus Hubble can't track them so precisely? Or maybe Hubble's optics are "fixed" at an "infinity point" beyond "nearby" objects? Or...?

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This has to do with the angular resolution of the Hubble telescope and the ratio between the distance of an object in space and its size in space. The galaxies that the Hubble telescope can see are bigger in mass than they are far in light years away compared to pluto from earth.

Take the galaxy NGC 5584 for example:

It spans 50,000 light-years and it's 72 million light-years away which gives us a ratio of 0.00069

Then for pluto:

Pluto spans 2400 km in size and 4675 million km away which gives the ratio of 0.00000051

Take for example a clear view at a mountain with trees on it. You would see the mountain fairly clearly: you can see it has trees on it, perhaps snow, and other aspects. But if you look at any given tree on that mountain you can't make anything other than it's observable color and that it's most likely a tree. The relationship of distance in size is what gives you a good view of the mountain but not a tree on the mountain; the trees size to distance ratio is much smaller than the mountain's size per distance ratio.

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Yes, so very interesting! But even when Hubble images Jupiter, it comes out unclear. Let's see, for Jupiter: 142984 km in diameter and 600 million km away, ratio = 0.00024. Hmm, that's still about 1/3 less than for NGC 5584. It looks like it really does boil down to angular resolution, no motion component at all. –  user3532993 Apr 16 at 17:04
    
TLDR: Pluto might be much closer than the galaxy, but it is much, MUCH smaller. –  Florin Andrei Apr 17 at 17:17

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