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Is it true that given two celestial objects of the same size and at the same distance, the fainter one will appear smaller? Is there a calculation that can be made about how smaller? Is it the same for naked eye observation or telescope observation?

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  • $\begingroup$ No, this is not, in general true. Most celestial objects do not appear to have any size at all and only appear as points of light. Perhaps you are talking about an optical illusion or misconception that brighter stars are closer. $\endgroup$
    – James K
    Dec 11, 2023 at 19:21
  • $\begingroup$ But if two object have the same size and the same distance, then they will have the same angular size, $\endgroup$
    – James K
    Dec 11, 2023 at 19:23
  • $\begingroup$ @JamesK I might be thinking something wrong, but consider a celestial object (star/planet). The edges are not well defined but rather smoothed due to resolution. The intensity cutoff (which depends on the sensor, your eyes, a camera, etc) will determine how big the actual object appears to be. It's like having a gaussian with threshold in the altitude: the percieved width seems to change, right? $\endgroup$
    – Kim
    Dec 11, 2023 at 19:37
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    $\begingroup$ Perhaps that is an effect with object that actually have indistinct edges, like galaxies. But not with planets and the like, Their edges are very clear and sharp. $\endgroup$
    – James K
    Dec 11, 2023 at 19:46
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    $\begingroup$ It sounds like you might be talking about the "point spread function", which is an optical effect that causes brighter pinpoints of light to appear larger. en.wikipedia.org/wiki/Point_spread_function $\endgroup$ Dec 11, 2023 at 21:06

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In general this is not true. Most celestial objects appear as points of light to the naked eye, and don't have any apparent size. (Though your brain might conflate "bright" with "near" or "large" - giving rise to ufo reports about Venus)

Objects like the moon have a clear edge and making the moon brighter wouldn't make it larger. There are a number of optical illusions relating to the moon's size, but generally the optical illusion is that it seems larger when it is close to the horizon, and so actually dimmer (due to absorbsion of light by the atmosphere).

But some objects have no clear edge. Objects like galaxies just get fainter and fainter as you get further from the centre. A telescope that can see fainter light would see a larger body than one that can only see the central, brightest part of the galaxy. Comets, likewise, can appear larger if they are brighter, simply because we can see the generally fainter outer parts of the comet if it is brighter.

And the optical limitations of lenses and mirrors will turn a point source of light into a (very) little fuzzy disc. This is called the "point spread function". As stars appear as little fuzzy discs, without sharp edges, brighter stars will appear as bigger in photographs taken of the night sky.

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