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To make it easier, assume both planets have same mass, radius, and atmosphere as Earth, they orbit each other at a very close distance of 30,000km and they are tidally-locked, in that case the other planet will look very big.

They are orbiting a Sun-like star, in the habitable zone.

So if I was in one of them, and looked directly at the other with my naked eyes, would it damage my eye?

Case two: if the other planet that we are looking at have a Venus-like (or even gas giant-like but focus at Venus) atmosphere.

How safe it would be to look at the other planet in double-planet system with naked eye in each case?

(edited: I wrote 30km by wrong, I meant 30000km ofc)

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    $\begingroup$ It's safe to look at the Moon, and even if were closer, it's surface brightness wouldn't be higher. $\endgroup$
    – Alexander
    Feb 25, 2023 at 17:58
  • $\begingroup$ Yeah, but moons atmosphere is thin, while Earth's will send light into your eyes and Venus is even thicker $\endgroup$
    – Khalid
    Feb 25, 2023 at 18:09
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    $\begingroup$ yes, that a valid point - but only to an extent. Venus' albedo is significantly higher that Moon's (0.69 vs 0.14), which means that Venus' surface would be 4-5 times brighter than Moon's. But worry not - this brightness will still be much less than Sun's. Here's another comparison - astronauts have no problem looking at the Earth from space (from any distance). Though looking at the Sun is indeed dangerous. $\endgroup$
    – Alexander
    Feb 25, 2023 at 19:00
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    $\begingroup$ Your double planet's brightness in daylight is presumably the same general magnitude as your own planet's brightness in daylight, and that doesn't bother your eyes, does it? $\endgroup$
    – Cadence
    Feb 25, 2023 at 22:29
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    $\begingroup$ Your orbital distance should be about 10x that. 30,000 km is very close. The moon is 380,000 km away from the earth. If the moon were 1/2 the distance, the tides would be 8 times higher. 1/10th the distance would cause tides roughly 1000x higher. They're more likely to be tidally torn apart than tidally locked. $\endgroup$
    – Wyck
    Feb 27, 2023 at 16:53

3 Answers 3

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Eye damage from looking at the sun is mostly a result of ultra-violet light. The amount of reflected U/V would be miniscule compared to looking at the sun. U/V is reflected even more poorly than most light for most surfaces.

But, even assuming 100% of solar U/V was reflected, the amount would still be much less than direct solar light. Light reflecting off the orbital partner expands in a spherical shell - thus the area of the reflected light must is spread out over a much larger area than the cross-sectional area of the other orbital body doing the reflecting.

Because of many additional complications, an exact calculation would be much more complicated, but as a first approximation compare the cross-section area of one of the planets (Rp=6317 km - pi x Rp^2) or about 1.25E8 sq km, with the area of the hemi-spherical shell (Rs=30000 km - 2 x pi x Rs^2) or about 6.65E9 sq km and only about 2.2% of the reflected light lands on the other planet.

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    $\begingroup$ To expand, staring at the sun under normal conditions triggers two defense mechanisms (pain and pupil contraction) that will help limit the amount of UV radiation that reaches your retina. During an eclipse, only the corona is "visible", which emits little of the visible wavelengths of light that trigger either defense mechanism, increasing your retina's UV exposure. $\endgroup$
    – chepner
    Feb 26, 2023 at 16:11
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There would be nothing unsafe about looking at such a planet, in either case. It would be quite bright, but only as much so as your surroundings on your own planet on a very sunny day.

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  • $\begingroup$ i meant 30000km, that was by wrong $\endgroup$
    – Khalid
    Feb 25, 2023 at 17:40
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    $\begingroup$ As evidenced by the fact that astronauts orbiting Earth, even in low Earth orbit, are not blinded by looking at it. $\endgroup$ Feb 26, 2023 at 1:30
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    $\begingroup$ @KerrAvon2055 I thought their "helmet glass" and "windows" that they are see throw might be made of something that will protect their eyes $\endgroup$
    – Khalid
    Feb 26, 2023 at 11:23
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    $\begingroup$ @Khalid, the Earth's atmosphere blocks almost all ultraviolet light from the Sun. In space, you don't have that protection, so spacesuits (and spacecraft windows) need enhanced UV-protective coatings. $\endgroup$
    – Mark
    Feb 27, 2023 at 2:56
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The brightness of the other planet would be exactly the same as what an observer would see while standing on it looking down at the ground. Or, if you are worried about the atmosphere scattering light, exactly the same as someone flying a plane high in the atmosphere near space, looking down at the ground.

Why? Because the brightness of extended objects is unaffected by how far away from them you are. Extended objects are objects bigger than a single point -- your hand, the ground, the moon, the sun. Basically everything other than far-away stars.

There are 2 things which cancel out:

  1. As you get farther away from an object, the amount of light from a single point on that object is diminished by 1/r^2.
  2. As you get farther away from an object, the amount of "stuff" that one "pixel" of your eye sees (e.g., the amount of area seen by one photoreceptor) is a cone projected out into space, so the area at distance r grows like r^2.

These exactly cancel out -- as you get farther away the individual points send out less light but you see more points for each eye photoreceptor, in the exact same proportion, so there is no change.

You can of course observe this in your daily life -- your wall does not get brighter or dimmer as you get closer or farther. Interestingly, this means that the brightness of the sun doesn't increase either as you get closer -- standing in space right next to the sun it is exactly as bright as seen from Earth (or, from just outside the atmosphere of Earth anyways). Of course it will fill the entire field of view so the total energy received by your eye will be much higher, but the per-pixel perceived brightness is the same.

One final notes -- at some point your other planet will be small enough that it is no longer an extended object, and becomes a point-like source like a star. But this will only ever decrease the brightness, since you are now getting the 1/r^2 falloff without the increased area of the object per-pixel.

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    $\begingroup$ The easiest way to see this is to take a picture of the Moon. If you want to keep the surface details from getting washed out, you need the same exposure settings as you'd use for a dark object (such as an asphalt road) in direct sunlight. $\endgroup$
    – Mark
    Feb 27, 2023 at 2:58
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    $\begingroup$ @Mark (just to finish your thought: that's because the Moon's surface is quite dark in colour, about the same as as asphalt. If the Moon were white instead then you'd use the same exposure settings as for a sheet of white paper in direct sunlight.) $\endgroup$
    – N. Virgo
    Feb 27, 2023 at 7:15

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