RE: ships exploding and Hollywood: I ran some numbers once for the energy in a contained hydrogen plasma (volume and density I think taken from current experimental fusion reactors) and came up with an energy release about equivalent to burning one barrel of oil. That's absolutely going to ruin the decor, but if it's an instant ship-killer you need to seriously reconsider your use of cotton candy as a structural material...

Nitpicking after upvoting: 4.6 millidegrees is more commonly known as 16.5 arc-seconds. And that picture of the pyramids of Giza was most surely taken with a very expensive photocamera; with the naked eye even the largest pyramid is not resolvable from 1680 km altitude, even if we disregard atmospheric bluring.

@AlexP Those are both good nitpicks. I used degrees to keep things simple for the non-mathematicians to emphasize how small an area we're talking about... and I'm not an astronomer, anyway. Your second point is very, very well taken (but I figured I'd beaten the OP up enough).

Disagree--while you are right that the weapons are generally invisible that doesn't mean weapon hits are invisible. Against a night sky it doesn't matter that they're below one "pixel" that the eye can see--observers won't see the ships but they will see the light show.

This answers the question of whether my 400 meter space station at the L-5 point in the moon's orbit will be visible to the naked eye from the surface of the Earth.

Actually, the main thing that might be visible would be destroyed ships burning up in the atmosphere. I agree that explosions are unlikely, so "destroyed" would mean it has a bunch of larges holes in it and can't maintain altitude anymore.

@EvilSnack Unfortunately, and with the greatest regret... no. 😉

@Tom Oh, yeah. Like I said in my answer, "people would notice that."

@LorenPechtel What light show? That science-based tag kinda does this question a disservice. Every joule of energy wasted on the light show is a joule that could have been used to further tear the ship apart. So you're either talking about very wasteful weaponry (something of a paradox with the tech needed to have the battle in the first place) or you're still married to the Hollywood idea of a space battle. Based on that tag, energy weapons wouldn't even be used - too many problems, not enough kick. Nuclear weapons might be used (might see that), but (continued)

...the attacker will also experience the radioactive fallout. That's a big negative. Thanks to that science-based tag, the most likely weaponry will be kinetic weapons that don't cause massive explosions but disable ships - which can then be left to rot and die a very long and painful death. No... unless you can come up with some defensible science-based explanations for why that light show would even exist, I just don't see it happening. (pun... hah....)

IR laser is invisible, yet you can easily see bright flash when that laser hits aluminum block - even when that laser is just few millijoules of energy and lasts few nanoseconds. Sure, distances in space are enormous compared to meters in lab, but energy difference is going to be huge too. You wouldn't resolve anything, but I believe you could be able to see bright spots if you are looking up there.

@ZizyArcher In a science-based world, no one would use a laser. Too much energy must be built up and stored in a system that's whomping dangerous to use. It's like charging up a big capacitor and then hoping nobody hits it before you can use it. If hit first, it blows you up. This (and many other reasons, like how hard it would be to focus the laser on moving targets) are the reasons you don't see lasers in hyper-real SciFi shows like The Expanse. (And all lasers would be invisible. You need something like an atmosphere to see a laser of any frequency.)

One very important thing you're missing is missing . It's highly unlikely you'd see anything about the ships exchanging fire... until they start missing. And then those mass driver projectiles might impact your atmosphere and hit your cities . That's going to be noticeable :D Hopefully, any nuclear missiles they use are set not to detonate upon hitting a planet.

@Luaan That's a good point, but let's be realistic. Even in a 3-D battle the number of misses impacting the atmosphere would be nothing more than, what, 10%? Maybe 20%? I mentioned in an earlier comment why nuclear weapons would be unlikely in such a battle (fallout is not the attacker's friend in a science-based universe) and unless the kinetic weapons were ginormous (not impossible!) they're unlikely to be visible burning up. But you are ultimately correct... that is one path where the consequences of the battle (if not the battle itself) could be seen.

@JBH Laser itself is obviously invisible in space, nothing to scatter from. Laser hit on the target is not invisible. Laser unsuitable - why exactly? Yeah, if they hit it directly at a wrong moment you are screwed. But exit aperture is centimeters to maybe meters for those capital ships and is the only weak spot - the rest is deep in the ship. And aperture is simply closed until shot is ready. If they hit your missile tubes or whatever else directly at a wrong moment you are similarly screwed, and missiles are most likely trivial to be shot down as they are slow.

It's funny that even in softer sci-fi like Star Wars, they're not using lasers . Even though they have absurdly powerful power generation compared to what's even theoretically possible in our own universe, they actually use (unspecified) particle beams. We can even see in episode 3 that they do in fact use some kind of massive projectile, just somehow "imbued" with energy. Heck, even in Star Trek, the phasers clearly aren't lasers. It just seems that a lot of sci-fi likes to use the name laser, while describing something that isn't a laser (presumably the meaning of the word changed).

@ZizyArcher The main problem is that for hard science-based, you don't have magical shields, thermally superconductive hull plating or whatever. That means that centralised power supply for your lasers probably isn't a good idea - there will always be weapons that go straight through any defences you might have. It's not just the lens being a weak point. It's hard to imagine a realistic laser that could be more dangerous to a spaceship than a kinetic round - kinetic rounds are really good at concentrating the impact. Lasers need to be focused and kept on target.

@Luaan You don't do continuous beam when you want to ablate material, you blast it with series of short pulses. A single strong pulse when you just want to make a rough hole. Obviously, you need a power source - but you also need a power source for ship propulsion, for projectile ejection and for whatever else. So if you have a weapon that goes through anything obviously you will use that - aim for the main engines and you win in a single good hit. I am not arguing that lasers are the only way to go. But I believe they are an option, together with various kinetic, plasma etc projectiles.

Anyway, no matter whether you have lasers or plasma whatever, when that thingy hits a ship, the section of the ship with the freshly made hole will be VERY bright.

I'm going to disagree heavily with the visibility here. The ISS has an altitude of 408km, 1% of the value here. It has a peak apparent magnitude of -5.9. So If the ISS was place in the middle of this battle, it's apparent magnitude should be 1/10000 of it's peak. Increasing the value of the apprent magnitude by 5 corresponds to a 100x reduction in brightness. This conveniently means that the Brightness of the ISS here would be equal to -5.9+10=4.1, or equivalent to a reasonably faint star. perfectly Visible at night in rural areas. And the cap ships here are much larger then the ISS.

Railguns have to same issues with requiring large quantities of energy and thye can be dodged at long range.

Missiles take to get up to speed, can be destroyed by point defenses (e.g. lasers) and create visible exhaust flames.

@Vilx-, Nice analogy, but the wave-like disturbance similar to a glider is actually called a photon. I've used Conway's to explain the sometimes-a-wave-sometimes-a particle nature of photons. You could use handwavium to culminate photons into a tighter beam and keep them that way until they hit their target.

What you really want is something that will near-perfectly transmit energy from the source to the target. That's really what all space weapons will do. Lasers, bullets, and rail guns are just variations in the size and energy of the projectile. If you're specifically trying to make the impact point visible from the ground, then you need the weapon to vaporize armor into a large glowing cloud, but then not hit the vaporized armor so it can continue hitting the non-vaporized armor.

The question of "would it be visible from the ground," you can apply Hollywood car-crash rules to failing spacecraft. Any car that goes off the road WILL explode. In the case of a ship, the fusion reactor overloads due to incremental fibulation of the transmogrifier.