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Let's say you look at two relatively dim stars in the night sky. They are close to each other, but they are far apart enough that you can distinguish one from the other. But what if one of them is much brighter than the other, or both of them are very bright, and they look like one star due to it (though you should normally distinguish them as separate objects)? I read about angular resolution, but I never saw any relation of it to magnitude.

In my fictional world, I have two planets with big moons that are separated enough from each other to be visible as separate objects (angular diameter is larger than the angular resolution of the human eye). But both planets have pretty high apparent magnitudes, so I am not sure if they outshine their moons or not. Ganymede should be distinguished as a separate object from Jupiter, but Jupiter is so bright you need a telescope or binoculars to see them as separate objects.

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    $\begingroup$ Some very few people with exceptionally good visual acuity can see some of the Galilean satellites of Jupiter without instruments, at least Ganymede and sometimes also Callisto. Here is an astronomer's report from 1898. If your planet is sufficiently far so that it appears almost star-like, the difference in apparent magnitude between the planet and a satellite will likely be too great to allow casual naked eye observation of the satellite. $\endgroup$
    – AlexP
    Commented Aug 26, 2023 at 6:23
  • $\begingroup$ First planet have maximum apparent magnitude -8,62, first moon have apparent magnitude -3,1, they are both separeted by 0,463° angular diameter. Second planet have maximum apparent magnitude -6,08, second moon have apparent magnitude -2,95, they are both separeted by 1,332° angular diameter. But I am more interested in some calculations or charts which can help to tell if moon can be distinguished from planet or not. $\endgroup$
    – Bedlasky
    Commented Aug 26, 2023 at 15:39
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    $\begingroup$ Oh, they are separated by 27′ and 1° 20′ respectively? That's huge. (To understand how huge that angular distance is, consider that the full moon is about 30′. And it is large, isn't it?) The celestial bodies can absolutely be seen with the naked eye by an average observer, even from a light-polluted city. The celestial bodies with apparent magnitudes of −9 and −6 will be visible in daylight, and even those with apparent magnitudes of −3 may be visible in daylight if not close to the sun. $\endgroup$
    – AlexP
    Commented Aug 26, 2023 at 16:59
  • $\begingroup$ Yes. I calculated values from δ = 2*arcsin(r/D), (δ = angular diameter, r = distance between objects, D = distance from observer). Home planet semi-major axis is 0,574 AU, first planet have SMA 0,399 AU, second planet 0,812 AU. First moon's SMA around planet is 105 900 km, second moon's SMA around planet is 414 320 km. $\endgroup$
    – Bedlasky
    Commented Aug 26, 2023 at 17:48

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Even if two objects are far enough apart to be resolved by the human eye, brightness matters. A very bright object can drown out a nearby dim one due to glare and contrast loss, making them look like a single point. That’s why Jupiter’s moons, like Ganymede, are technically resolvable but still hard to see without binoculars because they’re close and much dimmer. In your world, if the planets are bright enough, they could easily outshine nearby moons, even if the geometry says they should be visible.

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